year 6 maths worksheets
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1
Year 6 Worksheets
200 Maths Worksheets
Ages 10 -11 years
Includes: Place, value and ordering
Addition
Subtraction
Multiplication and Division
Factors and Multiples
Fractions and Decimals
Ratio and Probability
Shape, Angles
Measuring, Time
Money
Handling Data
Number Problems
Answers Included
© C. Diamond – Not for resale
2
Contents
Page
1. Place, value and ordering 3
2. Addition 16
3. Subtraction 31
4. Multiplication 40
5 Factors and Multiples 66
6. Division 74
7. Multiplication and Division 90
8. Fractions and Decimals 95
9. Ratio and Probability 124
10. Handling Data 131
11. Shape 145
12. Time 167
13. Measuring 172
14. Money 179
15. Number Problems 185
Answers 202
End 252
3
Place, value and ordering 1
What is the place value of the blue digits?
Draw a place value chart if it helps!
Example:
45713
The 5 is 5000
1. 62871 2. 9240
3. 617450 4. 42601
5. 237380 6. 960193
7. 344169 8. 75328
Write these numbers out in words.
9. 57826
10. 46310
11. 3290
12. 25891
Write these numbers in figures.
13. Seventeen thousand, one hundred and twenty
14. Fifty nine thousand, two hundred and six
Tth Th H T U
4 5 7 1 3
800
Fifty seven thousand, eight hundred and twenty six
4
Place, value and ordering 2
Read these decimal fractions. What does the blue digit
represent?
1. 6·48
2. 3·78
3. 2·91
4. 5·14
5. 3.342
Write these numbers in order, smallest to largest.
6. 9·45 9·55 5·95 7·73 5·09
7. 1·68 1·86 1·62 1·87 1·61
8. 2·35 20·15 2·53 0·53 2·05
9. 1·17 1·117 1·07 1·007 1·71
Eight hundredths
5
1·21
Place, value and ordering 3
Write the missing hundredth on the number lines.
1.
2.
3.
Write the missing thousandths on the number lines.
4.
5.
6.
1·364 1·35 1·351
4·044 4·03
1·34 1·2 1·22
5·69 5·55
4·0
2·890
6
Place, value and ordering 4
For each set of numbers, underline the smallest number
and a cross through the largest number.
1. 4·13 3·672 4·013 3·009 4·123
2. 15·75 16·01 15·07 16·13 16·103
3. 23·12 23·21 23·02 23·01 23·13
4. 124·60 123·9 124·06 123·09 124·006
5. 0·01 0·02 0·002 0·1 0·03
What is the value of 4 in each of these numbers?
6. 17435 7. 14879
8. 40121 9. 377·4
Here are four digit cards.
10. What is the smallest number you can make using all
four cards?
11. What is the largest number you can make using all
four cards?
12. Underline the largest number.
9 2 0 3
Ninety five thousand, eight hundred and two Ninety five thousand, six hundred and sixty- two
7
Place, value and ordering 5
1. Put these prices in order starting with the smallest.
£12425 £14908 £13967 £12245 £12634 £14900
2. Put these prices in order starting with the highest.
£12·15 £11·05 £12·75 £12·50 £11·06 £12·02
3. Put these masses in order starting with the heaviest.
9·06 kg 8·07kg 9·6kg 7·08kg 0·75kg 0·76kg
4. Find and mark the position of the following
numbers on the number line.
2·8 3·25 3·1 2·95
2.7 3.0 25 26 27 28 29 30 31
£ £ £ £ £ £
kg kg kg kg kg kg
£ £ £ £ £ £
2·7 3·0 3·4
8
Place, value and ordering 6
Round these numbers to the nearest multiple of 10.
1. 45897 2. 2364
3. 5601 4. 90456
Round these numbers to the nearest multiple of 100.
5. 15756 6. 1387
7. 39004 8. 40318
Round these numbers to the nearest multiple of 1000.
9. 134894 10. 1399
11. 87417 12. 56328
Round these numbers to the nearest whole number.
13. 24·9 14. 16·4
15. 9·45 16. 11·09
17. 45·26 18. 23·55
19. 15·15 20. 0·56
9
Place, value and ordering 7
Round the numbers to the nearest multiple of 10
1. 67 456
2. 15 894
3. 62 129
4. 34 592
Round the numbers to the nearest multiple of 100
5. 47 635
6. 25 001
7. 12 890
8. 31 504
9. 83 251
Round the numbers to the nearest multiple of 1000
10. 77 462
11. 19 921
12. 99 978
13. 289 131
10
Place, value and ordering 8
Use the thermometer to help you work out these positive
and negative temperatures questions.
This thermometer shows
1. The temperature is 8°C. It drops by 12 degrees.
What is the temperature now?
2. The temperature is -12°C. It rises by 7 degrees.
What is the temperature now?
3. At night, the temperature was -8°C, in the day it
was 2°C. What was the difference between the
temperatures?
4. In Paris the temperature is -2°C and in Moscow it is
-11°C. How much colder is Moscow than Paris?
5. The temperature is -7°C. It rises by 17 degrees.
What is the temperature now?
6. The temperature in Oslo is -16°C. How much will
the temperature need to rise to be -3°C?
___________________________________________________________________________________________________
- 20 -15 -10 -5 0 5 10 15 20
11
Place, value and ordering 9
Order these positive and negative numbers from lowest
to highest.
1.
2.
3.
4.
Work out these calculations.
5. 6-8= 6. -9+4=
7. -7+15= 8. 0-18=
9. -11-8= 10. -13+17=
- 4 - 7 8 - 10 4 -2
0 - 3 -22 - 14 2 -9
- 22 -5 20 -13 15 -12
-8 - 18 -28 -9 3 -19
12
Place, value and ordering 10
Find the difference between these numbers.
Use the number line to help you.
A.
1. -8, 2 2. 4, -6
3. -9, -3 4. 1, -10
5. -7, 4 6. 8, -7
7. -10, 10 8. -3, -6
9. 9, -8 10. 0, -9
Work out these calculations without using a number line.
B.
1. -104 +12 2. -123 - 47
3. -80 - 23 4. 44 -123
5. 83 - 21 6. -147 - 24
7. -124+22 8. -163 - 65
9. -228+112 10. 452 -156
- 9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 - 10
10
13
Place, value and ordering 11
A. Work out these square numbers.
1. 4² = 2. 9² =
3. 7² = 4. 1² =
5. 12² = 6. 2² =
7. 5² = 8. 8² =
9. 10² = 10. 11² =
11. 6² = 12. 13² =
B. Complete each of the following.
1. 4² + 6 = 2. 10² - 9 =
3. 12² + 11 = 4. 7² + 24 =
5. 4² + 2² = 6. 6² - 21 =
7. 11² - 3² = 8. 9² + 19 =
9. 6² + 6² = 10. 4² + 5² =
11. 12² - 5² = 12. 8² + 7² =
13. 9² - 7² = 14. 6² + 4² =
15. 13² - 9² = 16. 7² + 9² =
16
14
Place, value and ordering 12
Work out the rule for each sequence below.
Write the next 3 numbers in each sequence, then write
the rule.
1. 100, 106, 112, , ,
The rule is add 6.
2. 445, 450, 455, , ,
The rule is _________________________________
3. -53, -50, -47, , ,
The rule is _________________________________
4. -24, -12, 0, , ,
The rule is _________________________________
5. 150, 125, 100, , ,
The rule is _________________________________
6. -60, -36, -12, , ,
The rule is _________________________________
7. 36, 45, 54, , ,
The rule is _________________________________
8. 15, -5, -25, , ,
The rule is _________________________________
15
Place, value and ordering 13
Use the numbers from the cards to make general
statements about odd and even numbers.
Try at least three examples for each statement.
1. The sum of 3 odd numbers is
2. The sum of 2 even numbers is
3. The sum of an odd number and an even number is
4. The difference between 2 even numbers is
20 7 3 2 28 17 11
5 8 16 9 15 4 10
odd
3 + 5 + 9 = 17 7 + 17 + 11 = 35 15 + 9 + 7 = 31
16
Place, value and ordering 14
Use the numbers from the cards to make general
statements about odd and even numbers.
Try at least three examples for each statement.
1. The product of 3 odd numbers is
2. The product of 2 even numbers is
3. The product of 2 odd numbers is
4. The product of 1 even number and 1 odd number is
2 9 1 12 22 7 10
4 5 15 3 6 11 8
17
Addition 1
Partition the numbers into hundreds tens and units to help
you add them.
1. 325 + 278 = 300 +200 = 500 2. 167 + 164=
20 + 70 = 90
5+ 8 = 13
= 603
3. 456 + 234 = 4. 645 + 357=
5. 552 + 268 = 6. 785 + 247=
Round the second number to the nearest multiple of 10 or
100 to help work out these calculations.
7. 156 + 69 = 156 + 70 = 226 8. 456 + 89 =
226 - 1 = 225
9. 433 + 102 = 10. 391 + 99 =
18
+ + +
Addition 2
Add these numbers using the vertical method.
1. 3568 2. 8501 3. 7494 4. 3464
+ 455 + 178 + 267 + 389
4023 1 1 1
5. 2784 6. 6891 7. 2879 8. 8936
246 567 352 957
9. 3046 10. 8501 11. 7494 12. 3464
+ 3589 + 2673 + 4761 + 3678
13. 7649 14. 6832 15. 9452 16. 3764
+ 8463 + 6945 + 7902 + 9673
17. 1388 18. 8501 19. 7494 20. 3464
38 3490 96 2389
239 594 2385 784
+ 2784 + 4891 + 3570 + 2754
4449 1 2 2
21. 1449 22. 9502 23. 6491 24. 4462
247 693 3479 593
5937 8462 2845 6936
+ 7461 + 794 + 6743 + 8931
+
19
Addition 3
Write these calculations vertically and then work out the
answer.
1. 56987 + 6390 2. 98236 + 43367
3. 671782 + 87345 4. 378140 + 29893
5. 135899 + 89246 6. 783478 + 34729
7. 989367 + 35924 8. 45612 + 89249
20
Addition 4
Write these calculations vertically and then work out the
answer.
1. 23789 + 3897 + 345 2. 13762 + 2351 + 899
3. 7335 + 25978 + 8935 4. 67789 + 4589 + 136
5. 99672 + 7824 + 189 6. 6849 + 9856 + 92361
7. 3893 + 98026 + 5864 8. 89572 + 9994 + 989
21
Addition 5
Write these calculations vertically and then work out the
answer.
1. 6·98 + 34·78 2. 782·98 + 137·985
3. 67·981 + 257·452 4. 6712·12 + 95·246
5. 5036·89 + 467·907 6. 67·446 + 137·009
7. 904·136 + 984·341 8. 672·981 + 90·398
22
Addition 6
Write these calculations vertically and then work out the
answer.
1. 73·34 + 56·34 + 3·45 2. 93·034 + 12·78 + 8·9
3. 1·945 + 89·231 + 9·45 4. 304·52 + 4·89 + 3·87
5. 98·452 + 2·341 + 9·98 6. 34·002 + 9·009 + 3·61
7. 78·34 + 10·007 + 3·679 8. 902·12 + 0·135 + 9·59
23
Addition 7
Write in the missing numbers.
1. 2.
1 5 9 0 3 5 6 7
+ 1 + 7 4
1 8 4 1 5 3 1 2
3. 4.
5 7 2 8 3 5 6 7
+ 3 + 1 3
6 4 5 1 8 4 8 0
5. 6.
1 6· 3 5 2 5 4· 7
+ · 2 + 7 4·
1 9· 6 1 2 9· 5
7. 8.
2 ·5 7 3 1 9· 2 5
+ ·8 2 + 7 4·
3 ·4 1 5 9 3· 6 1
24
Addition 8
Add the 2 digit numbers together, then use the answer to
work out the other calculations.
1. 57 + 21 = 2. 78 + 65 =
570 + 210 = 780 + 650 =
5700 + 2100 = 7800 + 6500 =
0·57 + 0·21 = 0·78 + 0·65 =
5·70 + 2·10 = 7·80 + 6·50 =
0·057 + 0·021= 0·078+0·065 =
3. 98 + 24 = 4. 56 + 75 =
980 + 240 = 560 + 750 =
9800 + 2400 = 5600 + 7500 =
0·98 + 0·24 = 0·56 + 0·75 =
9·80 + 2·40 = 5·60 + 7·50 =
0·098 + 0·024= 0·056+0·075 =
25
Addition 9
Work out these addition calculations.
1. 5700 + 2500 =
2. 6400 + 3400 =
3. 5900 + 1800 =
4. 6600 + 7200 =
5. 1300 + 2900 =
6. 2900 + 7800 =
7. 5100 + 9900 =
8. 9300 + 7800 =
9. 6700 + 5800 =
10. 5600 + 8900 =
11. 4500 + 8600 =
12. 5800 + 3700 =
13. 9200 + 9600 =
What is the missing number in these calculations?
14. 5600 + = 7900
15. + 6800 = 11700
16. + 1400 = 5600
17. 5900 + = 7500
18. + 1300 = 8900
19. + 4900 = 7800
20. 2200 + = 8700
21. + 9500 = 14200
22. 9600 + = 22700
23. + 3800 = 17800
24. 4800 + = 6900
26
Addition 10
What is the missing number in these calculations?
1. 5·71 + = 5·8
2. + 9·31 = 9·4
3. + 14·22 = 14·3
4. 5·52 + = 5·6
5. + 11·67 = 11·7
6. + 4·33 = 4·4
7. 2·27 + = 2·3
8. + 6·91 = 7
9. 9·12 + = 9·3
10. + 2·03 = 3·1
11. 4·36 + = 4·4
What is the missing number in these calculations?
12. 6·7 + = 7
13. + 5·3 = 6
14. + 14·2 = 15
15. 5·55 + = 6
16. + 13·46 = 14
17. + 4·83 = 5
18. 2·2 + = 3
19. + 6·91 = 7
20. 9·12 + = 10
21. + 2·03 = 3
22. 4·56 + = 5
27
Addition 11
Work out these decimal calculations.
1. 0·3 + 0·26 =
2. 0·5 + 0·42 =
3. 0·15 + 0·62 =
4. 0·22 + 0·16 =
5. 0·73 + 1·44 =
6. 1·19 + 1·25 =
7. 5·51 + 3·93 =
8. 8·19 + 0·09 =
9. 7·37 + 4·67 =
10. 0·951 + 0·921 =
11. 7·142 + 0·497 =
12. 1·081 + 1·065 =
13. 1·032 + 0·079 =
14. 8·187 + 3·973 =
28
Addition 12
1. Circle the two numbers which add up to 500.
2. Circle the two numbers which add up to 350.
3. Circle the two numbers which add up to 800.
4. Circle the three numbers which add up to 850.
5. Circle the three numbers which add up to 600.
201 175 425 199 325 256 254
225 175 150 250 195 100 155
555 350 125 150 450 255 375
225 150 300 450 350 250 425
25 125 150 275 75 425 200
29
Addition 13
Use an empty number line to add up two numbers. Fill
in the missing numbers.
1. 7624 + 3957 = 7624 + 7 + 50 + 900 + 3000 = +7 + 50 +900 +3000
7624 7631 7681 8581
2. 1357 + 297 = 1357 + 7 + 90 + 200 = + + 90 +200
1357 1364
3. 5724 + 562 =
4. 7534 + 1582 =
11581
30
Addition 14
Use an empty number line to add up two numbers.
Fill in the missing numbers.
1. 9241 + 5176 = 9241 + 6 + 70 + 100 + 5000 = +6 +70 +100 +5000
9247 9317 9417 14417
2. 4276 + 247 = 4276 + 7 + 40 + 200 = + + 40 +
4276 4283
3. 3793 + 493 =
4. 5056 + 3873 =
9241
31
Subtraction 1
Use complementary addition to find the difference
between two numbers. Use an empty number line.
Example:
604 – 74 = 6 + 20 + 500 + 4 = 530 +6 +20 +500 +4
74 80 100 600 604
1. 403 – 67 =
2. 309 – 94 =
3. 713 – 83 =
4. 521 – 78 =
32
Subtraction 2
Subtract these numbers using the vertical method.
4 1 8 1
1. 5697 2. 5134 3. 7634 4. 4494
- 749 - 623 - 805 - 865
4948
5. 2845 6. 6793 7. 2942 8. 8634
- 783 - 985 - 836 - 459
9. 3049 10. 8467 11. 1123 12. 4678
- 2457 - 6734 - 1034 - 2489
13. 7356 14. 8469 15. 8174 16. 8312
- 4378 - 7356 - 4286 - 4295
17. 56345 18. 98534 19. 16474 20. 53464
- 7891 - 7351 - 7891 - 34897
21. 89321 22. 12567 23. 23870 24. 90501
- 6712 - 7834 - 12671 - 67232
33
Subtraction 3
Write these calculations vertically and then work out the
answer.
1. 9746 - 6358 2. 8995 - 8439
3. 67986 - 8399 4. 67780 - 29936
5. 155783 - 84196 6. 93489 - 82457
7. 903401 - 98922 8. 65690 - 39897
34
Subtraction 4
Write these calculations vertically and then work out the
answer.
1. 156·980 - 134·981 2. 782·98 - 137·99
3. 679·81 - 259·45 4. 6712·12 - 98·986
5. 1036·895 - 368·908 6. 267·446 - 189·77
7. 901·182 - 784·347 8. 872·981 - 89·396
35
Subtraction 5
Write in the missing numbers.
1. 2.
3 2 9 0 5 3 2 4
- 8 - 3 7
2 7 5 2 1 9 5 4
3. 4.
6 3 2 7 8 6 1 9
- 8 3 - 2 3
3 6 4 4 3 5 9 6
5. 6.
2 2· 1 7 6 2 1· 6
- · 3 - 2 7 5·
1 6· 7 8 45 · 7
7. 8.
6 ·3 7 2 4 9· 1 6
- ·1 4 - 2 4·
1 ·2 3 8 2 4 · 6 8
36
Subtraction 6
Subtract the 2- digit numbers from each other, then use
the answer to work out the other calculations.
1. 87 - 25 = 2. 74 - 35 =
870 - 250 = 740 - 350 =
8700 - 2500 = 7400 - 3500 =
0·87 - 0·25 = 0·74 - 0·35 =
8·70 - 2·50 = 7·40 - 3·50 =
0·087 - 0·025 = 0·074 - 0·035 =
3. 92 - 37 = 4. 76 - 29 =
920 - 370 = 760 - 290 =
9200 - 3700 = 7600 - 2900 =
0·92 - 0·37 = 0·76 - 0·29 =
9·20 - 0·37 = 7·60 - 2·90 =
0·092 - 0·037 = 0·076 - 0·029 =
37
Subtraction 7
Work out these subtraction calculations.
1. 8700 - 2600 =
2. 6300 - 5400 =
3. 5800 - 2700 =
4. 8300 - 5800 =
5. 7300 - 2900 =
6. 2900 - 2200 =
7. 9600 - 3700 =
8. 9500 - 7700 =
9. 6400 - 4900 =
10. 11700 - 8700 =
11. 12400 - 3800 =
12. 22800 - 11700 =
13. 19200 - 15600 =
What is the missing number in these calculations?
14. 9600 - = 3400
15. - 4700 = 2700
16. - 1800 = 7600
17. 2400 - = 1900
18. - 1800 = 3700
19. - 4300 = 6700
20. 8200 - = 4700
21. - 9500 = 9200
22. 7400 - = 6700
23. - 2800 = 3800
24. 9800 - = 3900
38
Subtraction 8
Work out these decimal calculations. Sometimes it helps
to change tenths to hundredths.
1. 1·3 - 0·6 =
2. 0·5 - 0·4 =
3. 0·75 - 0·6 =
4. 0·82 - 0·10 =
5. 0·77 - 0·34 =
6. 1·19 - 0·95 =
7. 5·5 - 0·43 =
8. 2·27 - 0·09 =
9. 6·37 - 4·69 =
10. 0·951 - 0·021 =
11. 7·282 - 0·297 =
12. 1·081 - 1·065 =
13. 1·067- 0·039 =
14. 8·163 - 3·952 =
39
Subtraction 9
1. Circle the two numbers with a difference of 3.
2. Circle the two numbers with a difference of 8.
3. Circle the two numbers with a difference of 12.
4. Circle the two numbers with a difference of 0·5.
5. Circle the two numbers with a difference of 0·75.
-8 - 1·5 3·5 -6 7·5 5·5 1·5
11·5 17·5 -4·5 -2·5 -5·5 3·5 2·5
-8·8 -1·2 2·2 3·2 -5·2 8·5 1·2
1·25 -2·5 -1·5 -2·5 0·25 3·5 -1·0
1·75 - 1·5 1·25 -0·5 0·25 2·5 -0·2
40
Multiplication 1
Multiply these numbers by 10.
1. 56 2. 78
3. 236 4. 600
5. 3912 6. 52891
7. 13 8. 2689
Multiply these numbers by 100.
9. 24 10. 14
11. 789 12. 400
13. 4510 14. 46813
15. 2296 16. 35891
Complete the multiplication calculations.
17. 80 × = 800 18. 37 × 100 =
19. 70 × = 700 20. 99 × 100 =
21. x × 10 = 500 22. 171 × = 1710
23. 124 × 100 = 24. 456 × = 4560
560
2400
41
Multiplication 2
Work out these pairs of calculations.
1. 45 ×10 ×10 = 45 × = =
2. 89 ×10 ×10 = 89 × =
3. 24 ×10 ×10 ×10 = 24 × =
4. 321 ×10 ×10 = 321 × =
5. 90 ×10 ×10 ×10 = 90 × =
6. 305 ×10 ×10 ×10 = 305 × =
Decide whether to multiply by 10, 100 or 1000 to change
the first number to the second.
7. 236 2 360
8. 14 1 400
9. 27 270
10. 253 256 000
11. 98 9 800
12. 72 72 000
4500
×10
42
Multiplication 3
Look at the rule for multiplying by 50.
Rule: To × 50 first × 100 then ÷ 2
Example 14 × 50 (14 × 100) ÷ 2 1400 ÷ 2 = 700
Multiply the numbers below by 50.
1. 11
2. 24 3. 29
4. 50
5. 36
Now look at the rule for multiplying by 25.
Use the rule to multiply these numbers by 25.
Rule: To × 25 first × 100 then ÷ 4
Example 18 × 25 (18 × 100) ÷ 4 1800 ÷ 4 = 450
Multiply the numbers below by 25.
6. 20
7. 16
8. 50
9. 34
10. 48
43
16.
24.
= 384
Multiplication 4
Use the 8 times table and doubling to help multiply by
Example 13 × 16 (13 × 8) × 2 104 × 2 = 208
Multiply the numbers below by 16.
1. 14
2. 22
3. 15
4. 32
5. 42
Use the 6 times table and doubling to help multiply by
Example 16 × 24 (16 × 6 ) × 2 × 2 (96 × 2) × 2
Multiply the numbers below by 24.
6. 6
7. 14
8. 15
9. 50
10. 42
44
Multiplication 5
Sweets come in different sized bags. Calculate how
many sweets you have altogether when you buy more
than one bag.
Try to work out the answers in your head.
1. a. Buy 7 bags
b. Buy 4 bags
c. Buy 9 bags
2. a. Buy 3 bags
b. Buy 5 bags
c. Buy 8 bags
3. a. Buy 4 bags
b. Buy 7 bags
c. Buy 9 bags
26 Strawberry
Chews
per bag
64
Chocolate
Drops
per bag
48
Lemon
Melts
per bag
45
Multiplication 6
Partition each of these calculations to find the answer.
Example
46 × 4 = (40 × 4) + (6 × 4) = 160 + 24 = 184
1. 37 × 3 =
2. 65 × 4 =
3. 43 × 7 =
4. 59 × 8 =
5. 76 × 9 =
6. 87 × 6 =
7. 58 × 7 =
8. 79 × 8 =
46
Multiplication 7
Partition each of these calculations to find the answer.
Example
92 × 8 = (90 × 8) + (2 × 8) = 720 + 16 = 736
1. 65 × 6 =
2. 45 × 9 =
3. 72 × 7 =
4. 49 × 9 =
5. 67 × 8 =
6. 54 × 6 =
7. 98 × 7 =
8. 73 × 8 =
47
Multiplication 8
Find the missing number by multiplying mentally.
1. 64 × = 448
2. 134 × = 536
3. 115 × = 345
4. 144 × = 864
5. 132 × = 924
6. 87 × = 522
7. 29 × = 203
8. 63 × = 504
9. 5 × = 380
10. 4 × = 328
11. 3 × = 285
12. 8 × = 616
13. 9 × = 243
14. 11 × = 308
15. 4 × = 312
7
48
Multiplication 9
Multiply these numbers by 49.
Multiply by 50 first then adjust.
Example
17 × 49 = (17 × 50) – 17 = 850 -17 = 833
1. 6 × 49 =
2. 4 × 49 =
3. 15 × 49 =
4. 8 × 49 =
5. 26 × 49 =
6. 33 × 49 =
7. 49 × 49 =
8. 94 × 49 =
49
Multiplication 10
Multiply these numbers by 51.
Multiply by 50 first then adjust.
Example
14 × 51 = (14 × 50) + 14 = 700 -14 = 686
1. 5 × 51 =
2. 7 × 51 =
3. 9 × 51 =
4. 12 × 51 =
5. 24 × 51 =
6. 36 × 51 =
7. 78 × 51 =
8. 53 × 51 =
50
Multiplication 11
When we multiply large numbers, we can use the grid
method. Fill in the gaps.
Example
628 × 7 = 600 20 8 = 4396
7
1.
465 × 5 = 400 60 5 =
4
2.
748 × 6 = 700 40 8 =
6
3.
734 × 3 = =
4.
876 × 9 = =
5.
978 × 8 = =
4200 140 56
51
Multiplication 12
When we multiply large numbers we can use the grid
method. Fill in the gaps.
Example
5674 × 6 = 5000 600 70 4 = 34044
6
1.
2461 × 4 = 2000 400 60 1 =
4
2.
3255 × 5 = 3000 200 50 5 =
5
3.
6328 × 3 = =
4.
1289 × 7 = =
5.
4196 × 8 = =
30000 3600 420 24
52
Multiplication 13
When we multiply large numbers, we can use the grid
method. Fill in the missing numbers.
Example
2__83 × 5 = 2000 600 80 3 = 13415
5
1.
4__56 × 3 = = 12768
3
2.
37__8 × 6 = = 22368
6
3.
614__ × 7 = = 43022
7
4.
__578 × 9 = = 41202
9
5.
7__52 × 8 = = 60416
8
10000 3000 400 15
53
Multiplication 14
Approximate the answer to each calculation.
Fill in the gaps. Complete each multiplication.
1. 126×5 125 × 5 = 600 2. 756×4
126 756
× 5 × 4
500 (100 × 5) (700 × 4)
100 ( 20 × 5) ( 50 × 4)
30 ( 6 × 5) ( 6 × 4)
(126 × 5) (756 × 4)
3. 453×8 4. 691 × 6
453 691
× 8 × 6
( ) ( )
( ) ( )
( ) ( )
( ) ( )
5. 728×9 6. 847 × 8
728 847
× 9 × 8
( ) ( )
( ) ( )
( ) ( )
( ) ( )
+ +
+ +
+ +
54
Multiplication 15
Approximate the answer to each calculation.
Fill in the gaps. Complete each multiplication.
1. 1526× 5 1500 × 5 = 7500 2. 2715 × 3
1526 2715
× 5 × 3
(1000 × 5) (2000 × 3)
( 500 × 5) ( 700 × 3)
+ ( 20 × 5) + ( 10 × 3)
( 6 × 5) ( 3 × 3)
3. 3642 × 5 4. 7367 × 3
3642 7367
× 5 × 3
( ) ( )
( ) ( )
+ ( ) + ( )
( ) ( )
5. 4318× 7 6. 6967×8
4318 6967
× 7 × 8
( ) ( )
( ) ( )
+ ( ) + ( )
( ) ( )
55
Multiplication 16
Work out an approximate answer for each
multiplication. Then calculate the answer using a
standard method of multiplication.
1. 597×6 600 × 6 =3600 2. 736×6
597 736 × 6 × 6 3582 5 4
3. 268×6 4. 947× 8
268 947 × 6 × 8
5. 783×7 6. 937 × 7
783 937 × 7 × 6
56
Multiplication 17
Work out an approximate answer for each
multiplication. Then calculate the answer using a
standard method of multiplication.
1. 4895×6 5000 × 6=30000 2. 6309 × 4
4895 6309 × 6 × 4 29370 5 5 3
3. 1297×5 4. 3437 × 6
1297 3437
× 5 × 6
5. 4779×7 6. 9786 × 8
4779 9786 × 7 × 8
57
Multiplication 18
Answer these multiplication questions.
Calculate an approximate answer first, and then use the
standard method of recording. Show your working.
1. There are 4726 paper clips
in a box. How many paper clips
are there in 4 boxes?
2. The shop sells 2678 cakes
each day. How many cakes
are sold in 5 days?
3. A bus travels 3679 km
every week. How far does it
travel in 6 weeks?
4. A school cook buys 3478
carrots every week.
How many carrots did she buy
in 9 weeks?
58
Multiplication 19
To multiply decimals numbers. First work out an
approximate answer then partition the number, multiply
each part and add them up.
Example
5·93 × 3 (6 × 3) = 18
5·00 × 3 = 15·00
0·90 × 3 = 2·70
0·03 × 3 = 0·09
17·79
1. 8·26 × 4 ( ) = 2. 4·81 × 5 ( ) =
8·00 × 4 = 4·00 × 5 =
0·20 × 4 = 0·80 × 5 =
0·06 × 4 = 0·06 × 5 =
3. 5·17 × 6 ( ) = 4. 6·35 × 4 ( ) =
5·00 × 6 = 6·00 × 4 =
0·10 × 6 = 0·30 × 4 =
0·07 × 6 = 0·05 × 4 =
5. 6·84 × 7 ( ) = 6. 9·68 × 8 ( ) =
6·00 × 7 = 9.00 × 8 =
0.80 × 7 = 0.60 × 8 =
0.04 × 7 = 0.08 × 8 =
59
Multiplication 20
To multiply decimals numbers. First work out an
approximate answer then partition the number, multiply
each part and add them up.
1. 7·54 × 7 (8×7)= 56 2. 9·78 × 6 ( ) =
7·00 ×7= 9·00 × 6 =
0·50 ×7= 0·70 × 6 =
0·04 ×7= 0·08 × 6 =
3. 6·05 × 8 ( )= 4. 5·73 × 9 ( ) =
5. 12·24 × 3 ( ) = 6. 24·72 × 4 ( ) =
7. 16·82 × 5 ( )= 8. 23·06 × 6 ( ) =
60
Multiplication 21
Write in the missing three-digit numbers.
1. × 2 = 300
2. × 2 = 354
3. × 10 = 2000
4. × 100 = 34000
5. × 0·1 = 50
6. × 1·5 = 300
7. × 0·5 = 200
8. × 0·2 = 120
61
Multiplication 22
When we multiply numbers by a 2 digit number we can
use the grid method. Fill in the gaps.
Example 785 × 16 =
× 700 80 5 =
1. 476 × 15 =
× 400 70 6 =
2. 694 × 24 =
× 600 90 4 =
3. 829 × 37 =
× =
4. 497 × 68 =
× =
7000 800 50
4200 480 30 6
10
7850
4710
12560 1
+
4000 700 60
350 5
10
4760
+
4
20
+
+
+
62
Multiplication 23
When we multiply large numbers by a 2 digit number we
can use the grid method. Fill in the gaps.
Example 5536 × 17 =
× 5000 500 30 6 =
1. 3472 × 25 =
× 3000 400 70 2 =
2. 6193 × 32 =
× 6000 100 90 3 =
3. 3831 × 53 =
× =
4. 8456 × 24 =
× =
5000 300 60
35000
50000
3500 210 42 7
10
55360
38752
94112 1 1 1
+
1400 40
60000
5
20
69440
+
2
30
+
+
+
63
6 2 2
4 4
2 ×
(
1 1
0 0 8 4
8 0
4 1
4 5
)
)
4
4
2
2
2
×
×
× 2 0 0
( 2 0
( 6
4
)
Multiplication 24
Complete each multiplication.
Example 226 × 24 = 5424
1. 345 × 35 =
2. 746 × 43 =
2
4
2
4
4
64
(
2 2
4
0 4 8
5 2
8 4
×
)
)
) 4
2
2
2
× 0
( 6 ×
( ×
6
2
2
0 2
0
4
0
0
2
Multiplication 25
Complete each multiplication.
1. 262 × 42 =
2. 756 × 36 =
3. 534 × 65 =
4
4
2 (
65
Multiplication 26
Write in the missing numbers. You can use a calculator.
1. 2.
4 8 0 6 0
× 1 × 3 5
1 0 0 8 0 1 2 6 0 0
3. 4.
6 4 2 6 1
× 3 × 4 9
2 1 8 2 8 2 7 4 8 9
5. 6.
1 5· 3 1 2 6· 5
× 1· × 5·
2 ·6 0 1 6 9 5· 7 5
7. 8.
2 · 5 6 1 2 · 2 5
× 4 · 0 × 7 5 · 6 0
1 2 ·2 8 8 9 4 6 8· 9 0
66
Factors and Multiples 1
Find all the factors of these numbers.
1. 18
2. 40
3. 64
4. 20
5. 36
6. 48
7. 24
Find three different ways to split these calculations using
factors. Then write the answer to the calculation.
1, 2, 3, 6, 9, 18
12 × 3 × 5, 15 × 6 × 2, 15 × 3 × 4 = 180
8. 12 × 15
9. 16 × 12
10. 24 × 18
11. 33 × 16
12. 27 × 18
13. 25 × 16
14. 24 × 25
67
1 1 1
2 2 1 2
6 1 2 3 6 4
Factors and Multiples 2
A prime number has only 2 factors, itself and 1.
A composite number has more than 2 factors.
1 is neither a prime nor a composite number.
Fill in this table of factors for the numbers up to 20
Number Factors Number of Factors
68
1 3 7 21
1
4
Factors and Multiples 3
Fill in this table of factors for the numbers from 21 to 45.
Number Factors Number of Factors
21
1
69
Factors and Multiples 4
Look at the tables of numbers from 1 to 45 on the
previous two pages.
1. a. Make a list of all the numbers you found with
only two factors.
b. What are these numbers called?
2. a. Make list of all the numbers over 5 you found
with three factors.
b. What are these numbers called?
70
Factors and Multiples 5
Answer these questions about factors, prime numbers
and composite numbers.
1. Are square numbers prime numbers or composite
numbers?
2. Can you find pairs of numbers up to 99 where the
digits are reversed and they are both prime
3. Explain why 845 could not be a prime number?
4. Explain why 266 could not be a prime number?
5. The sum of the digits in the number 21 are prime,
2+1 =3. Find 5 other numbers like this?
13, 31
numbers?
?
71
Factors and Multiples 6
Find 10 multiples of these pairs of numbers. Underline
the common multiples.
1. 2
3
2. 5
4
3. 3
9
4. 5
7
5. 4
10
6. 6
9
2, 4, 6, 8, 10, 12, 14, 16, 18
3,6,9,12,15 18,21,24,27,30
72
Factors and Multiples 7
Find 10 multiples of these sets of 3 numbers. Underline
the lowest common multiple.
1. 6
3
5
2. 3
6
8
3. 5
6
10
4. 4
6
9
5. 9
8
12
6,12,18,24,30,36,42,48,54,60
3,6,9,12,15 18,21,24,27,30
5,10,15,20,25,30,35,40,45,50
73
Factors and Multiples 8
Work out the answer to these multiplication problems.
1. Write the first 6 multiples of 24.
2. Write the lowest common multiple of 3, 10 and 15
3. Find 3 common multiples of 7 and 6.
4. What is the third common multiple of 8 and 12?
5. Tom goes swimming every four days. Paul swims
every Saturday. They meet at the swimming pool
this Saturday, how long before they meet again?
6. Jane is threading beads. She starts with a red bead
and puts another red one every ninth bead. Her
second bead is a silver bead. She uses a silver bead
every fifteenth bead. How many beads will be
threaded before they are together again?
74
Factors and Multiples 9
Work out the answer to these multiplication problems.
1. Write the first 8 multiples of 13.
2. Write the lowest common multiple of 4, 7 and 12.
3. List 10 multiples of 5 between 300 and 600.
4. a. Write the first 10 multiples of 25.
b. What do you notice about the multiples of 25?
5. List the first 20 multiples of ll.
75
Division 1
Divide these numbers by 10.
1. 240 2. 3690
3. 130 4. 340
5. 4500 6. 46700
7. 1230 8. 78200
Divide these numbers by 100.
9. 6600 10. 400
11. 2300 12. 100
13. 6700 14. 92300
15. 2200 16. 54600
Complete the division calculations.
17. 80 ÷ = 8 18. 900 ÷ 100 =
19. 370 ÷ = 37 20. 5600 ÷ 100 =
21. ÷ 10 = 430 22. 130 ÷ = 13
23. 1200 ÷ 100 = 24. 98300 ÷ = = 983
24
66
76
Division 2
Work out these calculations.
1. 400 ÷ 10 ÷ 10 = 400 ÷ =
2. 4500 ÷ 10 ÷ 10 = 4500 ÷ =
3. 9000 ÷ 10 ÷ 10 ÷10 = 9000 ÷ =
4. 80000 ÷ 10 ÷10 = 80000 ÷ =
5. 934 ÷ 10 ÷ 10 = 934 ÷ = =
6. 3215 ÷ 10 ÷10 ÷ 10 = 3215 ÷ =
7. 456 ÷ 10 ÷10 ÷ 10 = 456 ÷ =
Decide whether to divide by 10, 100 or 1000 to change
the first number to the second.
8. 560 56
9. 14400 144
10. 2490 249
11. 17200 172
12. 98000 98
13. 1380 1·38
100 4
÷10
77
Division 3
Find all the factors of these numbers.
1. 32
2. 25
3. 48
4. 54
5. 60
6. 100
7. 108
Find three different ways to split these calculations using
factors. Then write the answer to the calculation.
1, 2, 4, 8, 16, 32
12. 800 ÷ 16
18
(168÷3)÷4, (168÷6) ÷2,(84÷12)+(84÷12)=14
4
11. 120 ÷ 24
18
10. 60 ÷ 15
9. 180 ÷ 15
8. 168 ÷ 12
13. 108 ÷ 27
14. 390 ÷ 15
78
Division 4
Divisibility Tests
A number is divisible by 2 if the last digit is 0,2,4,6 or 8.
A number is divisible by 3 if the sum of its digits is
divisible by 3.
A number is divisible by 4 if the tens and units divide
exactly by 4.
A number is divisible by 5 if the last digit is 0 or 5.
A number is divisible by 9 if the sum of its digits are
divisible by 9.
A number is divisible by 10 if the last digit is 0.
Use the divisibility tests and approximation to decide if
the division calculations below are true or false.
Mark with a √ or x.
1. 468 ÷ 9 = 52 2. 560 ÷ 10 = 56
3. 154 ÷ 2 = 77 4. 326 ÷ 4 = 88
5. 264 ÷ 3 = 88 6. 92 ÷ 4 = 23
7. 232 ÷ 5 = 46 8. 369 ÷ 9 = 41
9. 171 ÷ 2 = 86 10. 405 ÷ 9 = 35
11. 176 ÷ 2 = 88 12. 240 ÷ 5 = 48
13. 465 ÷ 5 = 91 14. 148 ÷ 4 = 37
15. 189 ÷ 3 = 69 16. 324 ÷ 9 = 36
√
79
3
8
1
2
3
8
2
4
Division 5
Approximate the answer first. Choose a standard method
of recording to work out the answer to each calculation.
Record any remainder as a mixed number.
Example
227 ÷ 8 240 ÷ 8 = 30
28 Answer 28
8 227
160 (20 × 8)
67
64 (8 × 8)
3
1. 246 ÷ 4 240 ÷ 4 = 60 2. 566 ÷ 5
61
4 246
240 ( × 4)
6
4 ( 1 × )
2
Answer 61 Answer
3. 294÷ 6 4. 451 ÷ 7
Answer Answer
~
~
~
~
~
~
~
~
~
~
80
2
7
2
7
Division 6
Approximate the answer first. Choose a standard method
of recording to work out the answer to each calculation.
Record any remainder as a mixed number.
1. 149 ÷ 7 140 ÷ 7 = 20 2. 325 ÷ 6
21
7 149
140 (20 × 7)
9
7 ( 1 × 7)
2
Answer 21 Answer
3. 230 ÷ 6 4. 259 ÷ 5
Answer Answer
5. 748 ÷ 9 6. 685 ÷ 7
Answer Answer
~
~
~
~
~
~
~
~
~
~
~
~
81
Division 7
Approximate the answer first. Choose a standard method
of recording to work out the answer to each calculation.
Record any remainder as a decimal number. Remember
to line the decimal points up under each other.
Example
28·3 ÷ 4 28 ÷ 4 = 7
7·075 Answer 7·075
4 28·3
28·0 (7 × 4)
0·30
0·28 (0.07 × 4)
0·02 (0.005 × 4)
1. 46·2 ÷ 7 42 ÷ 7 = 6 2. 11·75 ÷ 5
7 46·2
42·0 (6 × 7)
4·2 ( 0·7 × 7 )
Answer Answer
3. 25·9 ÷ 2 4. 18·9 ÷ 9
Answer Answer
~
~
~
~
~
~
~
~
~
~
82
Division 8
Approximate the answer first. Choose a standard method
of recording to work out the answer to each calculation.
Record any remainder as a decimal number. Remember
to line the decimal points up under each other.
1. 84·6 ÷ 9 81 ÷ 9 =9 2. 32·5 ÷ 5
9 84·6
81·0 (9 × 9)
3·6 (0.4 × 9)
Answer Answer
3. 47·4 ÷ 5 4. 24·72 ÷ 2
Answer Answer
5. 28·2 ÷ 6 6. 60·8 ÷ 8
Answer Answer
~
~
~
~
~
~
~
~
~
~
~
~
83
Division 9
Answer these problems on divisibility tests.
1. A number is divisible by 2 if the last digit divides
exactly by 2.
Underline the numbers that are divisible by 2?
2156 123 470 140 678 467 998 1002 771 43
2. A number is divisible by 4 if the last 2 digits divide
exactly by 4.
Underline the numbers that are divisible by 4?
12 66 94 104 236 126 282 398 448 732 512
3. A number is divisible by 25 if the last 2 digits are 00
25, 50 or 75.
Underline the numbers that are divisible by 25.
1025 1660 3450 36 775 240 900 3335 11175 45
6700 385 67450 24200 6590 1100 750 6648 175
4. A number is divisible by 8 if half of it is divisible by
4 or the last 3 digits are divisible by 8.
Underline the numbers that are divisible by 8.
6800 216 4256 444 816 612 2680 3156 796
84
Division 10
Use your knowledge of the divisibility tests of 2, 4, 8 and
25 to answer these problems.
1. The year 2000 was a leap year. They occur every
four years.
a. Will the year 2024 be a leap year?
b. Will the year 2078 be a leap year?
c. Will the year 2036 be leap year?
2. Cookies come in packets of eight.
If Salford Junior school wants to buy 864 cookies.
Can they buy the exact number of packets of
biscuits?
How do you know?
3. A box of chocolates has 25 chocolates.
Could 3500 chocolates fit exactly into boxes?
How do you know?
4. There are four cups of water in litre.
Could 1786 cups of water be made into whole
litres?
How do you know?
85
Division 11
Answer these problems on divisibility tests.
1. A number is divisible by 5 if the last digit is 0 or 5.
Underline the numbers that are divisible by 5.
6500 219 4250 445 805 610 2681 3156 790
2. A number is divisible by 3 if the sum of its digits is
divisible by 3.
Underline the numbers that are divisible by 3?
68 99 123 672 560 742 919 678 145 252
2106 178 471 142 6765 465 981 1002 771 43
3. A number is divisible by 6 if it is even and also
divisible by 3.
Underline the numbers that are divisible by 6.
69 72 94 1242 236 99 282 398 448 732 512
4. A number is divisible by 9 if the sum of its digits
are divisible by 9.
Underline the numbers that are divisible by 9.
68 900 609 504 112 799 75 810 702 333
86
Division 12
Use the tests of divisibility to write 6 numbers:
1. divisible by 2 between 300 and 400
2. divisible by 5 between 1500 and 2000
3. divisible by 3 between 600 and 700
4. divisible by 6 between 900 and 1200
5. divisible by 4 between 2000 and 2100
6. divisible by 9 between 1500 and 2000
7. divisible by 8 between 1600 and 2000
8. divisible by 10 between 400 and 800
9. divisible by 9 between 1000 and 1400
10. divisible by 8 between 700 and 1000
87
Division 13
1. Circle the two numbers with a remainder of 2
when divided by 6.
2. Circle the two numbers with a remainder of 5 when
divided by 12.
3. Circle the two numbers with a remainder of 3
when divided by 5.
4. Circle the two numbers with a remainder of 1 when
divided by 13.
5. Circle the two numbers with a remainder of 4
when divided by 8.
36 46 58 38 30 74 66
66 27 89 76 52 18 53
25 47 48 59 42 71 93
65 37 79 40 28 15 24
36 30 22 72 42 62 92
88
Division 14
Write in the missing three-digit numbers.
1. ÷ 2 = 75
2. ÷ 3 = 122
3. ÷ 10 = 27
4. ÷ 5 = 25
5. ÷ 100 = 4·25
6. ÷ 50 = 8
7. ÷ 100 = 7·62
8. ÷ 25 = 20
89
Division 15
Approximate the answer first. Choose a standard method
of recording to work out the answer to each calculation.
1. 437 ÷19 2. 648÷ 24
19 437 24 648
Answer Answer
3. 459 ÷17 4. 5 4. 546÷14
Answer Answer
5. 522 ÷29 6. 663÷13
Answer Answer
~
~
~
~
~
~
~
~
~
~
~
~
90
Multiplication and Division 1
Here is the guide to prices the London Express Bus
Services use in Southern England.
Use it to help you to answer these questions.
1. What is the total cost for a family of four to travel to
Worthing?
2. Three people took a bus ride it cost them £34.
Where did they travel to?
3. Four people travelled separately to Dover.
How much would each person save if they travelled
as a family?
4. Six people travel to Worthing.
What is the cheapest price they pay?
5. Nine people travel to Brighton.
What is the cheapest price they pay?
6. Seven people travel together to Brighton.
The driver gave them £8 change.
How much money did they give him?
London Express Bus Service
Worthing Brighton Dover
1 person £10 £12 £14
2 people £8 each £11each £12 each
A group of 4 £6 each £7 each £9 each
91
17
27
Multiplication and Division 2
How many different answers can you get from these
calculations? (Use brackets and calculate the numbers
inside the brackets first!)
Example 6 × 5 + 4 ÷ 2 = (6 × 5) + 4 ÷ 2 = 30+4 ÷ 2 =
= 6 × (5 + 4) ÷ 2 = 9 × 6 ÷ 2 =
= 6 × 5 + (4 ÷ 2) = 2 + 30 = 32
1. 4 + 8 × 7 + 6 =
2. 64 ÷ 8 × 4 × 3 =
3. 100 ÷ 5 × 5 +4 =
4. 56 ÷ 4 × 2 × 7 =
5. 3 + 7 × 5 + 6 =
92
Multiplication and Division 3
Use brackets to make each answer an even number.
Example:
30 ÷ 6 + 5 × 3 = (30 ÷ 6) + (5 × 3) = 5 + 15 = 20
1. 56 – 24 ÷ 8 =
2. 48 + 15 ÷ 3 + 7 =
3. 13 × 4 × 2 - 20 =
4. 56 ÷ 8 + 6 =
5. 47–11 × 12 ÷ 3 =
6. 7 × 7 + 9 × 3 =
Use brackets to make answers totalling 100.
7. 13 + 7 × 14 – 9 =
8. 14 + 6 × 9 + 32 =
9. 26 + 24 × 16÷8 =
10. 28 × 2 – 31 × 4 =
11. 56 ÷ 2 + 8 × 9 =
12. 5 × 12 × 4 – 28 =
93
Multiplication and Division 4
It has been agreed by mathematicians that if a sum has a
bracket as part of it then the part inside the brackes will
be calculated first. Then if there is any division this is
calculated next followed by multiplication, addition and
finally subtraction. This is known as BODMAS.
Brackets Of Division, Multiplication, Addition, Subtraction
Use BODMAS to answer these questions.
1. 15 +19 – 7 = 2. 5 + 8 × 3 =
3. (14 + 7) – 15 = 4. 6 + 6 ÷3 =
5. 11 + 5 × 6 = 6. (24 – 9) + (19 – 8) =
7. 12 + (7 × 7) = 8. 60 – (3 × 9) =
9. 72 – (8 × 5) = 10. (11 × 5) + (7 × 6) =
11. (8 × 8) – (6 × 9) = 12. 9 + 32 ÷ 8 =
13. 45 ÷ (3 × 3) = 14. 130 – 25 × 3 =
15. 150 + (20 × 4) = 16. (36 ÷ 3) + (24 ÷ 4) =
17. 2000 – (12 × 4) = 18. 97 – (36 ÷ 2) =
19. (38 ÷2) + 42 ÷ 2 = 20. 420 – 12 × 11=
94
Multiplication and Division 5
Write in the missing three-digit numbers.
1. ÷ 2 = 450
2. × 2 = 700
3. ÷ 10 = 39
4. × 10 = 1000
5. ÷ 100 = 7·55
6. × 1·5 = 375
7. × 0·5 = 250
8. ÷ 100 = 2·01
95
7
12
3
8
15
100
5
8
15
100
3
10
8
9
Fractions and Decimals 1
Change these improper fractions to mixed numbers.
A 1. 11 = 2. 13 =
8 6
3. 22 = 4. 8 =
9 5
5. 17 = 6. 137 =
8 100
7. 20 = 8. 29 =
19 4
Change each mixed number to an improper
fraction.
B
1. 2 = 2. 2 =
3. 4 = 4. 4 =
5. 2 = 6. 3 =
1
96
1
2 1
6
Fractions and Decimals 2
What is the relationship between these fractions?
Use the diagrams to help you.
1.
2.
3.
4.
1
6
is three times as big as
1
2
1
6
1
3
1
12
1
2
1
2
1
8
97
Fractions and Decimals 3
What is the relationship between these fractions?
Use the diagrams to help you.
1.
2.
3.
4.
1
4
1
2
1
12
1
4
1
10
1
5
1
2 1
4 1
16
98
Fractions and Decimals 4
Part of each shape below had been shaded.
Work out which part has been shaded and circle the
fraction on the number line below.
1.
2.7 3.0 25 26 27 28 29 30 31
2.7 3.0 25 26 27 28 29 30 31
3.
2.7 3.0 25 26 27 28 29 30 31
0 ⅛ ¼ ⅜ ½ ⅝ ¾ ⅞ 1
0 ⅛ ¼ ⅜ ½ ⅝ ¾ ⅞ 1
0 ⅛ ¼ ⅜ ½ ⅝ ¾ ⅞ 1
99
Fractions and Decimals 5
Answer these fraction questions.
1. Which of these fractions are less than 1?
2. Which of these fractions are less than 2?
3. Which of these fractions are more than 1?
1
6
2
5
5
2 12
9
3
4 8
7
9
6
12
5 18
10
9
4 11
7
5
2
3
2
2
7
8
9 9
8
3
10 10
7
100
Fractions and Decimals 6
Divide the numerator and the denominator by two to
simplify the fractions.
1. 2 = 2. 6 =
8 8
3. 14 = 4. 10 =
20 18
5. 12 = 6. 6 =
100 10
Divide the numerator and denominator by three to
simplify the fractions.
7. 3 = 8. 3 =
6 9
9. 9 = 10. 3 =
15 18
11. 6 = 12. 9 =
21 24
1
4
101
Fractions and Decimals 7
Multiply the numerator and the denominator by two to
find an equivalent fraction.
1. 7 = 2. 5 =
9 9
3. 3 = 4. 4 =
4 5
5. 5 = 6. 7 =
6 10
Reduce the fractions to their simplest form.
7. 3 = 8. 6 =
9 16
9. 30 = 10. 45 =
100 100
11. 21 = 12. 14 =
49 36
14
18
102
Fractions and Decimals 8
Order these fractions.
First, convert them to equivalent fractions.
1. 3 6 2 4 10 5
2. 1 5 2
2 6 3
3. 1 1 2 3 6 9
4. 1 1 1
4 2 3
5. 3 7 1 4 8 2
6. 2 7 2
5 10 3
7. 7 2 1 18 9 3
8. 4 3 1
7 4 2
9. 5 6 2 8 24 3
15 12 8 2 6 3
20 20 20 5 10 4 =
103
=
Fractions and Decimals 9
Add these fractions together.
You will need to convert the fractions to the same
denominator before you can add them.
1. + = + =
2. + =
3. + =
4. + =
5. + =
6. + =
7. + =
8. + =
1
4 1
3
3
12
4
12
7
12
1
4 1
5
1
2 1
3
1
9 2
3
5
12 1
4
7
10 1
5
9
20 2
5
5
18 2
3
104
= 1
15
24
Fractions and Decimals 10
Add these fractions together.
You will need to convert the fractions to the same
denominator before you can add them.
1. + = + =
2. + =
3. + =
4. + =
5. + =
6. + =
7. + =
8. + =
5
6
19
24
24
20
24 19
24
2
5
7
10
2
3
3
4
6
7
5
14
7
12
3
4
9
15
2
3
9
10
4
5
17
20
3
10
105
= 3
10
Fractions and Decimals 11
Subtract the second fraction.
You will need to convert the fractions to the same
denominator before you can subtract them.
1. - = - =
2. - =
3. - =
4. - =
5. - =
6. - =
7. - =
8. - =
3
5
3
10
6
10 3
10
1
2 1
4
2
3 1
6
3
4 1
2
9
10 3
5
5
12 1
3
7
10 3
5
3
4 2
3
106
= 1
6
Fractions and Decimals 12
Subtract the second fraction.
You will need to convert the fractions to the same
denominator before you can subtract them.
1. - = - =
2. - =
3. - =
4. - =
5. - =
6. - =
7. - =
8. - =
5
6
2
3
5
6 4
6
4
5 3
10
2
3
1
4
7
8
1
4
11
12 3
4
13
15 2
5
9
10 3
5
19
20
3
4
107
- = 1
1
5
3
4 1
12
1
2
3
7
8
3
4
3
8
7
15
4
5
7
10
19
24
Fractions and Decimals 13
Subtract the second fraction.
You will need to convert the fractions to the same
denominator before you can subtract them.
1. 1 - =
2. 1 - =
3. 1 - = =
4. 2 - =
5. 4 - 2 =
6. 5 - 3 =
7. 1 - =
8. 1 - =
2
3 21
12 8
12
1
10
1
6
3
4
9
20
7
8
108
19
Fractions and Decimals 14
To multiply fractions:
1. Multiply the top numbers (the numerators)
2. Multiply the bottom numbers (the denominators)
3. Simplify the fractions.
Example × = = =
Multiply these fractions.
1. × = 2. × =
3. × = 4. × =
5. × = 6. × =
To divide a fraction by a whole number:
1. Multiply the denominator by the whole number.
2. Simplify the fraction if needed.
Example
Divide these fractions by the whole number.
1. ÷ 2. ÷ 6 =
3. 4. ÷ 3 =
5. 6. ÷ 6 =
4 =
2 =
2
12
=
=
1
6
1
4 2
3
1 × 2
4 × 3
2
12 1
6
1
2
1
3 1
2
1
4
1
4
1
4
2
3
1
2
=
4
5
1
3 5
6
1
5
2
3 ÷
1 × 2
3 × 4
1
5 3 =
2
3
1
4 ÷ 5 =
3
4
1
6 ÷ 3 =
3
5
109
3
4
¼ of 60 =15
(60÷4 = 15)
¾ of 60 = 45
(15×3 = 45)
1
3
of 102 = 34 (102÷3 = 34)
1
3
2
5
4
9
2
3
7
10
0
3
10
0
Fractions and Decimals 15
Find the fractions of these numbers and quantities.
Example
of 60 = 45
1. of £102 =
2. of 126 =
3. of 35 =
4. of 200 =
5. of 81km =
6. of 230 =
110
43
100
7
100
Fractions and Decimals 16
Find the fractions of these numbers and quantities
1. of £48 =
2. of 96 =
3. of 200cm =
4. of 3000g =
5. of 621 =
6. of 400ml =
7. of 950km
3
10
2
3
3
5
1
8
3
4
111
Fractions and Decimals 17
Write these fractions as decimals.
1. 15 = 2. 9 = 10 10
3. 25 = 4. 35 = 10 10
5. 30 = 6. 75 = 100 100
7. 95 = 8. 158 = 100 100
9. 7 = 10. 340 = 100 100
11. 350 = 12. 750 = 1000 1000
13. 1245 = 14. 568 = 1000 1000
1·5
112
Fractions and Decimals 18
Write these fractions as decimals. Use a calculator to work them out if you need to.
Write answers to two decimal places.
Example 2 = 1÷5 = 0·20 0·2 × 2 = 0·40 5
1. 1 = 2. 1 = 2 4
3. 1 = 4. 1 = 10 5
5. 3 = 6. 1 = 4 3
7. 1 = 8. 1 = 6 100
9. 1 = 10. 5 = 8 6
11. 7 = 12. 4 = 8 5
113
Fractions and Decimals 19
Write these decimals as fractions.
1. 0·80 = 2. 0·15 =
3. 0·46 = 4. 2·58 =
5. 0·257= 6. 1·634 =
Underline the decimal that is equal to the fraction.
7. 146 1·46 0·146 10·146 14·60
100
8. 24 2·40 0·24 0·024 20·40
100
9. 129 1·29 0·129 10·29 0·0129
1000
10. 937 9·37 93·7 0·937 0·0937
1000
11. 1256 0·1256 1·256 10·1256 0·01256
1000
12. 78 7·8 0·78 0·078 0·0078
1000
114
Fractions and Decimals 20
A. Add these decimals.
1. 0·7 + 0·9 = 2. 0·4 + 0·3 =
3. 1·5 + 0·6 = 4. 1·4 + 1·7 =
5. 0·8 + 0·4 = 6. 2·6 + 0·4 =
7. 1·9 + 0·8 = 8. 1·8 + 1·6 =
9. 6·4 + 3·5 = 10. 3·4 + 4·9 =
B. Add these decimals.
1. 0·17 + 0·92 = 2. 1·45 + 0·31 =
3. 1·42 + 1·43 = 4. 2·34 + 1·77 =
5. 0·82 + 0·46 = 6. 12·61 + 0·43 =
7. 1·97 + 2·87 = 8. 1·93 + 1·88 =
9. 4·49 + 4·59 = 10. 0·47 + 4·96 =
11. 2·15 12. 6·34 13. 2·17 14. 9·57
1·67 2·45 7·23 3·46
+ 3·11 + 3·47 + 3·18 + 12·35
1·6
1·09
115
Fractions and Decimals 21
A. Subtract these decimals.
1. 0·8 - 0·6 = 2. 0·9 - 0·3 =
3. 3·5 - 0·4 = 4. 10·8 - 6·5 =
5. 7·5 - 1·6 = 6. 2·3 - 1·4 =
7. 5·9 - 3·8 = 8. 6·8 - 4·9 =
9. 6·4 - 3·8 = 10. 3·4 - 2·7 =
B. Subtract these decimals.
1. 3·13 - 0·72 = 2. 4·44 - 1·55 =
3. 9·02 - 1·04 = 4. 2·56 - 1·47 =
5. 3·46 - 2·58 = 6. 14·61 - 7·43 =
7. 8·67 - 2·86 = 8. 1·78 - 1·53 =
9. 9·41 - 4·39 = 10. 8·47 - 6·96 =
11. 2·15 12. 6·34 13. 4·17 14. 9·34
-1·67 -3·46 -3·89 -6·58
0·2
2·41
116
Fractions and Decimals 22
Order these decimals from smallest to largest.
1.
2.
3.
4.
5.
2·13 2·78 2·96 2·15 2·75 2·28
6·24 6·2 6·61 6·23 6·5 6·09
38·01 38·12 38·02 38·34 38·30 38·13
1·04 1·40 1·44 1·14 1·004 1·041
0.17 0·017 0·111 0·001 0·710 0·701
117
Fractions and Decimals 23
A. Multiply these tenths by a single digit.
1. 0·6 × 3 = 2. 0·7 × 5 =
3. 3·7 × 2 = 4. 4·8 × 3 =
5. 6·5 × 6 = 6. 5·4 × 4 =
7. 3·1 × 8 = 8. 5·8 × 6 =
9. 3·4 × 9 = 10. 7·8 × 8 =
B. Multiply these hundredth by a single digit.
1. 3·53 × 4 = 2. 1·25 × 7 =
3. 6·32 × 3 = 4. 5·16 × 4 =
5. 5·18 × 2 = 6. 6·34 × 3 =
7. 7·34 × 5 = 8. 3·72 × 4 =
9. 6·07 × 6 = 10. 7·74 × 8 =
11. 3·24 12. 9·78 13. 8·69 14. 6·06
× 5 × 7 × 9 × 8
1·8
14.12
118
Fractions and Decimals 24
A. Divide these tenths by a single digit.
1. 16·6 ÷ 4 = 2. 21·5 ÷ 5 =
3. 12·8 ÷ 2 = 4. 13·6 ÷ 4 =
5. 17·7 ÷ 3 = 6. 16·1 ÷ 7 =
7. 20·8 ÷ 8 = 8. 38·7 ÷ 9 =
9. 13·5 ÷ 9 = 10. 25·2 ÷ 7 =
B. Divide these hundredth by a single digit.
1. 54·06 ÷ 3 = 2. 9·36 ÷ 4 =
3. 30·60 ÷ 5 = 4. 18·72 ÷ 6 =
5. 32·34 ÷ 7 = 6. 28·84 ÷ 4 =
7. 17·82 ÷ 6 = 8. 9·52 ÷ 7 =
9. 15·21 ÷ 9 = 10. 3·04 ÷ 8 =
11. 3 17·04 12. 4 17·96 13. 6 14·28 14. 7 3·22
4·15
18·02
119
Fractions and Decimals 25
Write the equivalent fractions for these percentages.
1. 24% = 2. 30% =
3. 10% = 4. 90% =
5. 75% = 6. 25% =
Order the fractions and decimals from smallest to largest.
7. 12% 0·4 35%
8. 60% 59% 0·54
9. 0·35 40% 50%
10. 99% 0·89 0·98
What is the missing percentage?
11. 50% 12. 75% 13. 64% 14. 12%
2
10 1
4
3
4
7
8
1
3 4
6
9
10 17
20
50%
120
Fractions and Decimals 26
Find the percentages of these amounts. Use the answer
to the first percentage to help you work out the second.
Example
50% of £28 = £28 ÷2 = £14. 25% of £28 = £14÷2=£7
1. 50% of £300= 25% of £300=
2. 50% of £68 = 25% of £68 =
3. 50% of £90 = 25% of £90 =
4. 10% of £70 = 40% of £70 =
5. 10% of £700= 40% of £700=
6. 10% of £26 = 40% of £26 =
7. 5% of £55 = 25% of £55 =
8. 25% of £80 = 12½% of £80=
9. 25% of £28 = 12½% of £28=
10. 10% of £66 = 60% of £66 =
11. 10% of £54 = 60% of £54 =
12. 10% of £78 = 90% of £78 =
121
Fractions and Decimals 27
Match the amounts that are the same.
2
17
100
2·17
217 %
117 %
1·17
1
17
100
1
5
20 %
0·2
9
10
35%
7
20
0·35
90%
0·9
24
25
96%
0·96
5%
0·05
1
20
39
50
78%
0·78
122
Fractions and Decimals 28
Work out these percentage problems. Show your work.
1. There are 50 children in the park.
a. 50% of the children are under 5. How many
children is that?
b. 10% of the children are playing on the climbing
frame. How many children is that?
c. 15 children are wearing boots what percentage is
that?
2. There are 48 people working at the supermarket.
a. 25% work on the tills. How many people is this?
b. 36 of the workers are female.
What percentage of the workers are male?
c. 12·5% of the workers are on the early shift.
How many people is this?
123
Fractions and Decimals 29
Answer these percentage problems.
1. There are 32 children in a class. They did a survey
of favourite fruit. 25% like apples best.
How many children is this?
2. James got 16 spellings right out of 20.
What percentage did he get right?
3. Estimate the percentage of
The rectangle that is
coloured yellow?
4. Melissa’s Dad gives her the choice between getting
20% of £55 or of £30.
You can use a calculator to work out which is more
and by how much?
2
5
124
Ratio and Probability 1
A. Work out the ratio of red to yellow squares.
Example
The ratio is red square to every yellow squares.
1.
The ratio is red squares to every yellow squares.
2.
The ratio is red squares to every yellow squares.
B. Look at the patterns above. Work out the
proportion of the squares which are red.
Example
in every squares are red.
1. in every squares are red,
2. in every squares are red.
1
4
1
3
125
Ratio and Probability 2
Answer these problems involving ratio and proportion.
1. Jill has a bag of 16 sweets. She has 1 orange sweet
for every 3 red sweets.
a. What is the ratio of red to orange sweets? :
b. What proportion of sweets are red? in
c. How many orange sweets are there?
2. A cake recipe needs 1 egg to make 6 cakes.
Tom wants to make 24 cakes.
a. What is the ratio of eggs to cakes? :
b. How many eggs are there?
3. At the zoo, school parties must have a ratio of 1 adult
to every 5 children. The school takes 60 children.
a. How many adults must go on the trip?
b. What proportion of adults are on the trip in
4. Class 6b has 36 children. The ratio of boys to girls
is 2:1.
a. How many boys are in class 6b?
b. What proportion of the class are girls? in
1
3
126
Ratio and Probability 3
Answer these ratio and proportion problems.
1.
+ =
Pink paint is mixed in a ratio 1:6 red to white.
If 1·75 litres red is used, then how much white is used?
2.
a. The ratio yellow to green?
b. The proportion yellow to green?
c. The fraction green?
d. The area of the yellow rectangle is the size of
the green rectangles.
3.
c. The fraction pink?
d. The area of the pink rectangle is the size of the
blue rectangles.
:
1 in every
a. The ratio blue to pink?
b. The proportion pink to blue?
:
1 in every
127
Ratio and Probability 4
Work out the probability that these events will happen.
Example
What is the probability you will pick a heart from a set of
Jacks from a pack of cards?
1 out of 4 = ¼ = 0·25 The probability is 0·25.
1. What is the probability that you will toss heads on a
coin?
2. What is the probability Jim will pick a blue ball
from this bag of balls?
3. What is the probability Jim will pick a red ball?
4. What is the probability Jim will pick a yellow ball?
5. What is the probability Jim will pick a round ball?
128
Ratio and Probability 5
Use the words and phrases below in the sentences to
show the probability of an event happening.
1. If I drop a coin there is an ______________ it will
land heads up.
2. It is ____________ there will be a Tuesday this
week.
3. There is a _________________ that I will see a cat.
4. It is _________________ that there will be 32 days
this month.
5. If a 5 year old runs against a 10 year old a
___________ result should occur.
6. If I choose a card from a pack the result should be
_________________.
7. There is a __________________________ that a
card picked from a pack of 52 cards will be red.
8. It is ______________ I will go to the moon.
equal chance likely Fifty-fifty chance random
biased impossible certain good chance
unlikely
129
Ratio and Probability 6
Answer these probability problems. Give the answer as a
fraction.
1. A bag of sweets has 6 red and 3 orange sweets.
What is the probability that a random sweet taken from
the bag is orange?
2. The School keeps its balls in boxes. Each box
has 10 tennis balls, 4 footballs and 6 basketballs.
Mrs Jones asks Tina to fetch a ball. What is the
chance Tina will bring a football?
130
Ratio and Probability 7
Match the probability of an event occurring on the line,
when rolling an ordinary 1-6 die.
0 0·5 1
evens
Match the probability of an event occurring on the line,
when choosing one of these cards without looking.
0·1 0·2 0·3 0·4 0·5 0·6 0·7 0·8 0·9
evens
A die will roll
an even number. A die will roll a
six A die roll a
zero.
A die roll a
number.
A die roll a one
or two. A die will not
roll a 4.
A die will roll a
seven
A die will roll a
number greater
than three.
A 6 will be
picked. A number from 5
to 9 will be
picked An odd number
will be picked
A 2 or 3 will be
picked.
A ten will be
picked. A 6,7, or 8 will be
picked.
A 2 will not be
picked.
A number above 3
will be picked.
0 1 2 3 4 5 6 7 8 9
certain impossible
impossible certain
1 0
131
Handling Data 1
A. Calculate the mode (the most frequent) of these
numbers.
1. 1, 1, 1, 2, 3
2. 20, 21, 22, 22, 23, 24
3. 100, 101, 102, 100, 103
4. 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 7
5. 2, 8, 4, 7, 8, 4, 3, 2, 1, 7, 8
6. 5, 6, 5 7, 5, 6, 7, 6, 5, 7
B. Calculate the range (the difference between the
highest and lowest) of these numbers.
1. 6, 3, 9, 8, 5
2. 21, 24, 15, 7, 8, 10
3. 3, 3, 7, 7, 8, 9, 10
4. 44, 36, 24, 55, 33
5. 135, 295, 340, 75, 455, 165
6. 66, 44, 22, 55, 77, 44, 55
7. 202, 203, 204, 206, 207
1
9-3=6
132
Handling Data 2
A. Find the median (middle) number from an odd
numbered list.
Order them first from smallest to largest.
1. 5, 4, 8, 3, 4, 7, 6
2. 7, 8, 2, 5, 9, 1, 6
3. 2, 5, 9, 7, 1, 7, 8
4. 2, 14, 6, 11, 8, 12, 15
5. 24, 67, 35
6. 9, 0, 2, 5, 0, 4, 0
B. Find the median number from an even numbered
(halfway between the middle two numbers)
1. 12, 14, 18, 20
2. 1, 2, 6, 6, 4, 8
3. 14, 16, 12, 22
4. 1, 1, 3, 5, 9, 11
5. 1, 1, 7, 7, 9, 9
6. 34, 44, 56, 68, 73, 89
3,4,4,5,6,7,8 = 5
14 + 18 = 32 ÷ 2 = 16
list.
133
Handling Data 3
A. Find the mean (sum of all the numbers divided by
the number of items) number.
1. 6, 4, 9, 7, 8, 2
2. 7, 8, 2, 3, 9, 1
3. 2, 5, 3, 7, 1, 1, 9
4. 20, 14, 6, 11, 8, 1
5. 6, 6, 2, 4, 7, 3, 7
6. 99, 66, 33
7. 4, 0, 2, 3, 0, 4, 1
B. Find the mean of these prices.
1. £1·20, £1·40, £1·90
2. 10p, 22p, 64p, 4p
3. £1·50, £2·40, £1·80
4. £230, £256, £114
5. £2·24, £4·35, £3·01
6. 17p, 11p, 19p, 13p
6+4+9+7+8+2 = 36÷6=6
£1·20 + £1·40 + £1·90 = £4·50 ÷3 = £1·50
134
Handling Data 4
Here are the results for class B’s History test.
Number
of Marks 1 2 3 4 5 6 7 8 Number
of
Children
2 1 3 6 10 4 4 2
Draw a bar chart of the results of class B’s History Test.
12
10
8
6
4
2
0 1 2 3 4
5 6 7 8
Score in History Test
Use the bar chart to answer these questions.
1. How many children took the History test?
2. What is the mode score?
3. What does the shortest bar tell you ?
Number
of children
135
Handling Data 5
Sarah collects data about vehicles going past her school.
She draws a table and bar chart showing her results.
Vehicles 16
14
12
10
8
6
4
2
0 Lorry Bike Car Motorbike Bus Type of Vehicles
1. Write in four pieces of information missing from the
table.
Type of Vehicle Number of Vehicles
Lorry
Bike 0
Car
4
2
2. Which is the mode vehicle?
3. How many vehicles did Sarah record?
Number
Of
Vehicles
136
Handling Data 6
Here is a line graph to show the level of water in a
paddling pool.
10 20 30 40 50 60 70
Time in minutes
Use the graph to answer these questions.
1. What was the highest level of water in the pool?
2. Estimate how long the water was over 10cm?
3. After 40 minutes the children left the pool.
How long were they out of the pool for?
4. If the pool started filling at 2pm.
What time was it completely empty again?
2
4
6
8
10
0 ×
× ×
×
80
×
12
Level of water (cm)
× ×
×
14
137
Handling Data 7
1. Estimate how many children at each school walk to
school.
a.
b.
2. Do more children travel by bus to Star Primary
School or Valley Junior School?
Give a reason for your answer.
______________________________________________
______________________________________________
______________________________________________
Transport to Valley Junior School
bus
bike
walkcar
Transport to Star Primary
bus
bike
walk
car
200 pupils
360 pupils
At Valley Junior pupils walk
At Star Primary pupils walk
138
Handling Data 8
Look at the pie charts and answer the questions
1. Estimate how many children in class G like apples.
2. Estimate how many children in class G like bananas
3. Estimate the the total number of children who like
apples and grapes.
4. Estimate the difference between the number of
children who like apples and strawberries.
Class G's Favourite Fruit
apple
grapes
strawberry
banana
36 pupils
139
Handling Data 9
Here is a line graph for the 4 times table.
1 2 3 4 5 6 7 8 9 10 11 12
Use the graph to answer these questions.
a. 3·5 × 4 = b. 8 × 4 =
c. 2½ × 4 = d. 7·5 × 4 =
e. 12 × 4 = f. 5½ × 4 =
g. 11·5 × 4 = h. 6·5 × 4 =
16
32
8
24
0
0
14
40
48
×
×
×
×
×
×
×
4
12
20
28
36
44
×
×
×
×
×
140
Handling Data 10
Mark in the missing parts of this line graph for the 6
times table.
1 2 3 4 5 6 7 8 9 10 11
Use the graph to answer these questions.
a. 2·5 × 6 = b. 39 ÷ 6 =
c. 8½ × 6 = d. 4·5 × 6 =
e. 45 ÷ 6 = f. 10½ × 6 =
g. 1·5 × 6 = h. 6·5 × 6 =
15
0 12
6
12
×
×
141
Handling Data 11
Draw a line graph for the 8 times table.
Use the graph to answer these questions.
a. 1·5 × 8 = b. 44 ÷ 8 =
c. 7½ × 8 = d. 9·5 × 8 =
e. 92 ÷ 8 = f. 12½ × 8 =
g. 5·5 × 8 = h. 96 ÷ 8 =
142
Handling Data 12
Here is a time and distance graph for a car journey from
Newton to Farl and back again.
10 20 30 40 50 60 70
Time in minutes
Use the graph to answer these questions.
1. How far was the car from Farl after 15 minutes?
2. How far was the car from Farl after 55 minutes?
3. How long did the car stay in Newton?
4. How far was the car from Farl after an hour?
5. How long did the car take to arrive back in Farl?
10
20
30
40
50
0
Distance from Farl
in kilometres
×
× ×
× 80
× ×
60
70
143
Handling Data 13
Draw a time and distance graph for a bus journey from
Jute to Saxon and back again.
Time in minutes Distance from Jute in Kilometres
0 0
15 15
20 20
30 30
35 30
45 20
65 0
10 20 30 40 50 60 70
Time in minutes
Use the graph to answer these questions.
1. How far was the bus from Jute after 20 minutes?
2. How far was the bus from Jute after 34 minutes?
3. How far was the bus from Jute after 55 minutes?
4. How far was the bus from Jute after 1 minute?
10
20
30
40
50
0
Distance from Jute
in kilometres
80
60
70
144
Handling Data 14
This graph converts between gallons and litres.
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Gallons
Convert these to litres.
1. 9 gallons 2. 18 gallons
3. 11 gallons 4. 29 gallons
Convert these to gallons.
5. 40 litres 6. 90 litres
7. 140 litres 8. 70 litres
Complete this table of values.
Gallons Litres(l)
0 0
2 9
4
6
8
10
Litres (l)
20
40
60
80
100
120
32
0
140
32
145
Shape 1
E
A D
B C
Answer these questions about the shape above.
1. Name 2 parallel edges.
2. Name 2 perpendicular edges.
3. Edge DE is parallel to edge
4. Edge AB is perpendicular to edges
G. H.
Answer these questions about the shapes above.
5. How many pairs of parallel faces does shape G.
have?
6. What is the total number of edges on the shapes.
G. H.
D
F
G
AB and
146
Shape 2
Tick the shapes which are nets of a closed cube.
1. 2.
3. 4.
5. 6.
7. 8.
×
147
Shape 3
A parallelogram has its opposite sides equal and parallel.
Draw 4 different parallelograms using the grid below.
.
A rhombus is a parallelogram which has equal sides.
Draw 4 different rhombi using the grid below.
148
Shape 4
A trapezium has one pair of opposite parallel sides
Draw 4 different trapezia using the grid below.
. A kite has two pairs of adjacent sides of equal length.
Draw 4 different kites using the dots below.
149
Shape 5
Look at these quadrilaterals. Draw in the diagonals; tick
the shape if the diagonals intersect at right angles.
Write the name of each shape.
150
Shape 6
1. Look at these shapes and put the right letter in the
statements below.
a b c d e
1. Which shape has reflective symmetry?
2. Which shape has 2 pairs of parallel lines?
3. Which shape is an irregular hexagon?
4. Which shape has angles adding up to 180º?
5. Which shape is an irregular pentagon?
6. Draw a reflection of the shapes in the mirror line.
Mirror line
151
Shape 7
1. Draw a reflection of the shapes in the mirror line
2. Shade in two more squares to make the design
symmetrical about the mirror line.
Mirror line
Mirror line
152
Shape 8
A B
D
C
List the vertices and co-ordinates of the rectangle above.
A (-4, 2) B( , ) C( , ) D( , )
Plot and join these points up in order on the graph below.
A (-5, 2) B( 5, 3 ) C( 2, -2) D( -5, -2)
0
-3
-2
1 2 3 4 5 6 7 8
-
1
0 -1 -2 -3 -4 -5 -6 -7 -8
-1
1
2
3
5
4
8 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 -8
-1
-2
2
3
4
5
6
-4
1
153
Shape 9
A
Plot these points on the grid to make shape B.
( 6, 3) (10, 3) (10, 5) (6, 5)
Shape A has been translated ___to the right, then ___up.
C
Plot these points on the grid to make shape D.
( 3, 1) (7, 1) (5, 5)
Shape C has been translated __ places to the left, then
___down.
1
2
3
4
5
6
0 11 12 13 14 15 10 9 8 7 6 5 4 3 2 1
1 1
2
3
4
5
6
0 11 12 13 14 15 10 9 8 7 6 5 4 3 2 1
154
Shape 10
Look at the pairs of congruent right angle triangles.
. . . . . . . . . . . . . . . .
.A . . . . . B . . . . . . . . .
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . .C . .
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
. .D . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
. . . . . . . . .E . . . . . . .
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .F .
. . . . . . . . . . . . . . . .
Name the shape in each overlap of two congruent
right-angled triangles. Write in which of the
arrangements a triangle is translated and or rotated.
A square, rotated and translated B
C
E
D
F
155
A
B
C
A C
B
Shape 11
Rotate the triangles ABC through 90º about the vertex A.
Repeat the rotations 3 more times.
Write the co-ordinates of C for each rotation.
( , ) ( , ) ( , )
Write the co-ordinates of B for each rotation.
( , ) ( , ) ( , )
-3
-2
1 2 3 4 5 6 7 8 0 -1 -2 -3 -4 -5 -6 -7 -8
-1
1
2
3
4
-4
-3
-2
1 2 3 4 5 6 7 8 0 -1 -2 -3 -4 -5 -6 -7 -8
-1
1
2
3
4
-4
156
Shape 12
Measure and record the marked angles.
1. 2.
3. 4.
Measure and add the angles for each triangle.
5. 6.
+ + = + + =
a
b
c
d
157
Shape 13
Write these angles in the correct column in the chart
below.
1. 27º 2. 89º 3. 105º 4. 270º
5. 180º 6. 90º 7. 310º 8. 145º
9. 11º 10. 190º 11. 125º 12. 256º
acute right obtuse straight reflex
270º
Draw and label angles of these sizes.
13. 90º 14. 108º
15. 43º 16. 157º
Right angle
158
Shape 14
Calculate the size of each missing angle.
1. 2.
44º
3. 4.
78º 131º
5. 6.
222º 162º
90º
270º
159
Shape 15
Measure and record the sizes of angles ABC
1.
B
A C
Measure, then check by working out, the marked angles
on these triangles.
2. 3.
A
B
C
D
D
E
F
E
F
G
H
I
G H I
160
3m
12 cm
3m
5m
Shape 16
Use the formula Perimeter = 2 × (length + breadth) to
work out the perimeter of the rectangles below.
1. 7cm 2. 16 cm
5cm
3. 23cm 4. 19 cm
28cm
These shapes are made by overlapping congruent squares
or rectangles. Work out the perimeter of each green
shape.
6. 6m 7. 2.5m
2m
2.5m
2 × (7+5) cm 2 × 12cm
= 24 cm
4 cm
4m
4m
5m
5m
5m
161
7cm
cmm
m
39cm
mmm 3cmmm
Shape 17
Find the area of each of the shaded shapes in cm²
Work out the area of these shapes. Multiply the length
by breadth.
D. E.
21cm 28cm
F.
9cmmm
A B
C
A. B. C.
D. 21 × 7 = cm²
E.
39cm
F.
162
21cm
4cm
10cm
30cm
20cm
5cm
9cm
8cm
15cm
11cm 9cm 5cm
3cm 3cm
4cm
3cm
10cm 4cm
Shape 18
Work out the area of these shapes. Add or subtract the
area of separate rectangles.
1. 2.
3. 4.
(10cm × 17cm) + (4cm × 5cm)
= 170cm² + 20cm² = cm²
(20cm × 30cm) - (9cm × 8cm)
= 600cm² - 72cm² = cm²
4cm
3cm
163
25cm
6cm
15cm
17cm
11cm
5cm
5cm
20cm
15cm 16cm
7cm
5cm
5cm
26cm
Shape 19
Work out the area of these shapes.
1. 2.
Work out the shaded area of these shapes.
3. 4.
5cm
4cm
20cm
m
6cm
164
4cm
cmm
m
Shape 20
Find the area of each of the shaded right angle triangles
in cm². Multiply the length and breadth then divide by 2.
Work out the area of these triangles.
E. F.
10 cm 8cm
15cm
A
B
C
A. (4×3) ÷ 2 = 6cm²
E
F
D
B.
C. D.
165
Shape 21
Find the area of each of the shaded pentagons in cm².
Draw lines to divide the pentagons into rectangles and
triangles.
Draw two different right angled triangles with an area of
12cm².
A B
A B
166
Shape 22
Here is a rectangular block. (not drawn to scale)
5 5cm
40cm
1.
How many blocks can fit into shape A? blocks
A 40 cm
55cm
What is the area of shape A in cm²
cm²
2.
How many blocks can fit into shape B?
B
120 cm
What is the area of shape B in cm² cm²
25cm
167
Time 1
Look at the timetables and answer the questions below.
1. Swimming lessons
Group Start time Finish time
Beginners 15:40 16:05
Intermediate 16:05 16:35
Advanced 16:35 17:10
a. How long is the advanced swimming lesson?
b. How long is it from the start of the beginners lesson
to the end of the advanced lesson?
c. If the swimming teacher needs 20 minutes to sort
out the swimming pool after the lessons have
finished. Her journey home takes 15 minutes. What
time does the swimming teacher arrive home?
2. Film Times
Film Screen 1 Screen 2 Mr and Mrs Jones 13:30 17:15 The Monsters 15:45 13:55
Space Adventure 17:20 15:30
a. James finishes school at 15:30 and takes 30 minutes
to travel to the cinema. Which film can he not
watch at the cinema?
b. How long is “Mr and Mrs Jones”?
168
Time 2
1. Here is a clock.
How many minutes until this clock shows 5:25?
2. Here is another clock.
What time did the clock show 45 minutes ago?
3. One of the clocks below is 12 minutes fast.
The other is 6 minutes slow.
What is the correct time?
______ minutes
21:26
20:02
169
?
Time 3
The sign shows the opening times for the cake shop.
Answer the questions about shop opening times.
1. How long was the shop open on Thursday
afternoon?
2. How long was the shop shut for lunch on Monday
3. How long is is the shop closed from Sunday to
Monday?
4. Is the shop open longer on Saturday or on
weekdays?
5. How many hours a week is the shop open?
Morning Afternoon
Monday – Friday 9:00 – 12.30 14:00 – 16:00
Saturday 8:30 – 13.00 14:00 – 18:30
Sunday 10:00 – 13.00
170
Time 4
Answer these time questions.
1. Sue goes to the cinema to watch a film at 16:25.
The film is 2 hours 40 minutes long. She has a 15
minute walk home from the cinema. Will she be
home from the cinema by 7:00 pm?
2. Here are the instructions for cooking a fruit cake.
Cook for 25 minutes per 250 g plus 30 minutes.
If the cake mix weighs 750g.
How long will the cake take to cook?
3. Here is a clock
a. How many minutes until this clock shows 4:05?
b. What time did the clock show 50 minutes ago?
Show your working here.
Show your working here.
171
Time 5
Answer the questions about world time.
1. It is 12 noon in London. In which city is the time 7pm?
2. It is 12 noon in London. In which city is the time 9am?
3. It is 12 noon in London. In which city is the time 4am?
4. What is the time difference between New York and
Sidney?
5. What is the time difference between Cape Town and
Perth?
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3+4 +5 +6 +7+8 +9+10+11+12
Time Zones Key
B Bangkok C Cape Town L London
LA Los Angeles NY New York R Rio de Janeiro
T Tokyo P Perth S Sidney
L
. LA
. NY
R . C
. B
. P
. S
. T
Bangkok
.
172
Measuring 1
Convert these units of length.
1. 0·167km into metres.
2. 0·57km into metres.
3. 1·289km into metres.
4. 7823m into kilometres.
5. 5834m into kilometres.
6. 56mm into centimetres.
7. 23mm into centimetres.
8. 1·6m into centimetres.
9. 2·7m into centimetres.
10. 8·5m into kilometres.
11. 1·95m into millimetres.
12. 3·38m into millimetres.
13. 0·456m into millimetres.
14. 64cm into kilometres.
15. 894cm into kilometres.
173
Measuring 2
Use the conversion table to find these equivalent
distances.
a. 8 km = b. 16km =
c. 20 km = d. 30km =
Find the equivalent distance.
e. 17 miles = f. 24 miles =
g. 15 miles = h. 3 miles =
10 15 20
16
32
5
8
24
0
0
miles
kilometers
a
5 miles
c
b
d
27 km
40
36
44
174
Measuring 3
Answer these length problems.
1. Jane is 97cm tall Paul is 1·29m tall What is the difference between their heights
in metres?
2. A family journey includes a 30·8km car drive
followed by a 10·7km bike ride then a 600m walk.
How far do they travel?
3. A snail travelled 456mm in 10 minutes, a tortoise
travelled 6 times as far. Find the length of the
tortoise’s journey in centimetre.
4. How many 65cm pieces of string can be cut from a
20 metre ball of string?
5. How much string will be left over in the previous
question?
6. A ladder is 5m high,the rungs are at 30cm
intervals. Sally climbs up 9 rungs.
What is her height from the ground?
7. How far has Sally still to climb to reach the top of
the ladder?
175
Measuring 4
A B C D
Write the weight of each parcel as kilograms and grams
then as grams only.
A B
C D
Write the number of grams represented by the digit 6 in
each of the parcels.
A B
C D
Round each weight to the nearest tenth of a kilogram.
A B
C D
Find the difference in weight between parcels:
A and C B and D
7·346
kg 4·869 kg
6·088 kg 5·613 kg
7 kg 346g = g
6 grams
7·3kg
176
Measuring 5
1 pound (lb) = 16 ounces 1 pound = 454grams
2 4 6 8 10 12 14 16 18 20 22 24
Use the conversion table to work out these answers.
Round the figures to the nearest ounce or 10 grams.
a. 7 oz = b. 1 lb =
c. 10 oz = d. 4 oz =
e. 100g = f. 150g =
g. 500g = h. 325g =
200
400
100
300
0
0
ounces
grams
g g
g g
oz oz
oz oz
500
600
700
177
Measuring 6
The librarian is moving books to a new shelf.
She has: 30 encyclopaedias weighing 700g each.
42 paperbacks weighing 120g each.
11 hard backs weighing 230g each.
10 hard backs weighing 190g each.
17 hard backs weighing 350g each.
If she can only carry 5kg at a time, work out these
problems you can use a calculator but show your
working.
1. How many journeys must she make with the
encyclopaedias?
2. How many paperbacks can she carry at a time?
3. What is the total weight of all the hardback books?
4. She has a rest when she has moved 30kg of books.
How many more journeys must she make?
178
Measuring 7
A cubic metre of water weighs 1 Tonne.
1 Tonne = 1000kg.
1. How many tonnes of water are in a in a tank
2 metres by 2 metres by 2 metres?
2. How many tonnes of water are in a tank 6 metres by
2 metres by 2 metres?
3. How many tonnes of water are in a swimming pool
10 metres by 5 metres by 1 metre?
4. How many cubic kg of water are in a tank 4 metres
by 2 metres by 1 metre?
5. How many cubic kg of water are in a pool
measuring 6 metres by 8 metres by 2 metres?
1 Tonne
2m × 2m × 2m = 8m³ = 8 tonnes
179
Money 1
To convert pounds (£) into other currencies, multiply the
number of pounds by the exchange rate.
Example
250·0
Australia ($) rate = 1·6 × 1·6
Change £250 = 250 × 1·6 = 150·0
+ 250·0
Answer $400 400·0
1. India (rupees) rate = 65
Change £370
Answer ____________ rupees
2. Japan (yen) rate = 150·2
Change £100
Answer_____________yen
3. France (euro) rate = 1·19
Change £300
Answer______________euro
4. Switzerland (franc) rate = 2·55
Change £150
Answer______________franc
5. USA($) 1·38
Change £450
Answer $______________
180
Money 2
To convert pounds (£) into other currencies, multiply the
number of pounds by the exchange rate.
You can use a calculator to help you.
Give answers to the nearest whole unit of currency.
1. Italy (euro) rate = 1·19
Change £487
Answer ____________ euros
2. USA ($) rate = 1·38
Change £634
Answer $_____________
3. Malaysia (ringgit) rate = 5·79
Change £935
Answer______________ringgit
4. Mexico (peso) rate = 12·92
Change £784
Answer______________peso
5. Norway (krone) rate 13·46
Change £104
Answer ______________krone
6. Canada($) rate 2·27
Change £209
Answer $_______________
181
Money 3
Above are the tourist exchange rates for six countries at
different times of the year.
Work out if the exchange rate has increased ( ) or
decreased ( ) between April and September.
Work out the difference between exchanging £100 in
May or July. Write how much it has increased ( ) or( )
decreased.
Decide when the better time to travel to each country
would be based on this information.
Fill in the table below.
Country Exchange rate
May
Exchange rate
July
or Difference between
changing £100 in May or
July
Best time
to travel
Australia 1 1·69 1 1·791 0·10 1 $10 1 May 1
1
Tourist Rate (May) Tourist Rate (July)
Japan (yen) 157·78 Japan (yen) 157·77
India (rupees) 50·34
India (rupees) 51·26
Denmark (Krone) 12·67
Denmark (Krone) 12·90
Australia ($) 1·69
Australia ($) 1·79
South Africa (rand) 10·36
157.78
South Africa (rand) 11·02
157.78 Thailand (baht) 54·01 Thailand (baht) 53·78
182
Money 4
Above are the tourist exchange rates for six countries.
To convert other currencies into pounds, divide the
amount by the exchange rate.
Work out the cost in English pounds of the items below.
Round each currency rate to the nearest whole number.
1. Mexico 45 peso
2. Israel 144 shekel
3. Norway 132 krone
4. Canada $ 93
5. Hong Kong $152
6. Switzerland 14 francs
7. Mexico 100 peso
8, Canada $ 122
Tourist Rate
Mexico (peso) 14·29
Israel (shekel) 6·87
Hong Kong ($) 12·03
Canada ($) 2·65
Norway (krone) 13·46
Switzerland (franc) 2·55
45 ÷ 14 = £3·00
183
Money 5
Use the information on the hotel price list to answer the
questions.
1. What is the difference in price between a week in a
double room and a week in a Suite?
2. How much would it cost to stay in a double room
for 3 nights?
3. What is the difference in price between staying in a
single room for 4 days or for a week?
4. Work out the cost per night for a week in a suite?
5. Half board (breakfast and dinner) costs 25% of the
cost per night for a single room.
How much does half board cost?
The Grand Hotel
Prices per night week
Double £126 £540
Single £ 74 £336
Suite £168 £931
184
Money 6
Answer these money questions.
1. Sandra saves 5p coins she saves 105 of them.
How much money has Sandra saved?
2. John has saved £8·80 in 20p coins.
How many coins has he saved?
3. James works 36 hours every week.
James is paid £7·25 for every hour.
You can use a calculator to answer these questions.
a. How much does James get paid every week?
James has earned over £900 so far this year.
b. What is the fewest number of hours he has
worked to earn £900?
185
Number Problems 1
Answer these number problems.
1. Fill in the numbers 1-20 in this Venn diagram.
factors of 18 multiples of 3
2. Fill in the numbers below in this Venn diagram.
12 4 25 11 9 16 49 36 5 7
square numbers odd numbers
3. Fill in the numbers 1-30 in this Venn diagram.
square numbers multiples of 2
186
Number Problems 2
Fill in the missing numbers on these addition magic
squares.
1. 2.
Total = Total =
These magic squares are made by multiplying instead of
adding. When the numbers on any side or diagonal are
multiplied they make the same total.
Fill in the missing numbers.
3. 4.
Total = Total = 5. 6.
Total = Total =
36
16
48
3
32
4
16
8
64
12
23
28
27
21
17
71
47
59
5
24
28
2
12
3
6
1
14
4
7
187
Number Problems 3
Fill in the missing numbers on these multiplication
pyramids.
1. 2.
3. 4.
5 6.
92610
126
21
3
735
6
35
7
2
5
6
5
2
4
5
8
9
3
7
6
3
5
6
5
4
2
6
3
9
2
188
Number Problems 4
Fill in the missing numbers in these number sentences.
1. 24 ÷ × 2 × 2 = 12
2. (25 - ) ×3 × 4 = 120
3. 8 × + (5 × 2) = 26
4. 40 ÷ + 6 + 2 = 16
5. (7 × 6) - = 31
6. 54 ÷ ( × 9) × 8 = 24
7. (15 × 3) - = 28
8. ( ÷ 3) + (4 × 8) = 65
Use these symbols to make the number sentences below
true. + - × ÷ ( )
9. 30 6 7 3 = 36
10. 8 3 5 7 = 26
11. (27 9) (7 4) = 31
12. 7 5 6 = 72
13. 9 5 ( 4 3) = 33
14. (12 6) 7 6 = 8
189
Number Problems 5
Work out the answers to these problems. 1. A box of pens holds 64 pens.
a. A school needs 230 pens.
How many boxes must they buy?
b. A shop has 12 boxes of pens.
How many pens is that altogether?
2. In the bookshop sale hardback books cost £7·55
and paperback books cost £4·82.
a. Steven bought a hardback and 3 paperback
books. How much did he spend?
b. Beth bought two hardback books. She paid
with a £20 note. How much change did she get?
c. Mary bought 10 hardback books and was given
a discount of 10%. How much did she pay?
190
Number Problems 6
Work out the answers to these problems. 1. A bag of marbles holds 94 marbles.
They come in boxes of ten bags.
a. How many marbles are in a box?
b. If I have 18 800 marbles.
How many boxes do I have?
c. If I buy 100 boxes.
How many marbles do I have?
2. Cakes are sold in packs of eight. The packs
come in boxes. Each box contains 20 packs.
a. How many cakes does a box hold?
b. If a shop has 5 boxes, how many packs do they
have?
c. If a pack costs 87p, how much does a box cost?
191
Number Problems 7
Work out the answers to these problems. 1. A bottle of mineral water holds 360 ml.
In a week Jack drinks 10·08 litres of mineral
water.
a. How many bottles does Jack drink in a week?
b. If a bottle of mineral water costs 55p. How
much does Jack spend on water in a week?
c. If I buy 6 bottles of water a day.
How many bottles do I buy in two weeks?
2. Lollies are sold in packs of twelve.
a. A pack costs £2·04. How much does each
lolly cost?
b. If Sam buys 10 packs of lollies. How much will
that cost?
c. If Joe buys 4 lollies. How much does he spend?
192
Number Problems 8
Work out the answers to these problems. 1. A mechanic charges £36 per hour.
Car parts cost £48·75.
a. The mechanic gives an estimate of £300·75 to fix
a car. How many hours does he think he will
spend fixing the car?
b. One week he earns £1260 for his work. How
many hours did he work?
c. If the mechanic works for 21 hours and uses
£246 of car parts. How much will it cost?
2. The teacher is sorting out the sports equipment.
The cupboard contains 1200 balls.
a. 25% of the balls are soft foam.
How many balls is that?
b. If 42% of the balls are large. How many is that?
193
Number Problems 9
Work out the answers to these problems. 1. Buns come in packs of 4 or 8. A pack of 4 costs
65p, a pack of 8 costs £1·12.
a. A group of 4 children bought a pack of 8 and
shared them. How much did they each pay?
b. Terry buys 2 packs of 4 buns and Simon buys 1
pack of 8 buns. How much more does Terry pay?
c. Star Playgroup buys 10 packs of 8 buns.
How much do they pay?
2. a. Mrs Jones buys 4 pears. She pays with a £5 note.
She gets £3·20 change. How much is one pear?
b. Ralph buys 10 pears. How much do they cost?
c. I have £2·70. How many pears can I buy?
194
Number Problems 10
1. Joy lives 145 metres from the post office.
If she travelled 870 metres travelling to and from
the post office.
How many times did she visit the post office?
2. Five children time themselves in a skipping race.
Name Paul Tariq Sofia Glen Jade
Time in
seconds
25·8 22·4 21·7 26·4 23·2
a. Who finished the race first?
b. How many seconds faster was Tariq than Glen?
Show your working.
195
Number Problems 11
1. Philip describes a number.
“The number I am thinking of is an odd number.
It is a multiple of 9, is less than 50 and contains
consecutive numbers.”
2. Jayne describes a number.
“The number I am thinking of is a square number.
It is a multiple of 12. It is less than 80.”
3. Tom describes a number.
“The number I am thinking of is a multiple of 8.
It is more than 40 and less than 90. It contains
consecutive numbers.”
4. Winnie describes a number.
“The number is an odd number. It is more than 40
but less than 60. It is a multiple of 7.”
196
Number Problems 12
Answer these number problems
1. a. Write the prime numbers in the following list.
5 7 4 10 21 15 11 23 13
b. Use two of the prime numbers to complete the
following calculation.
+ = = 20
2. a. Write the square numbers in the following list.
4 8 9 10 12 15 16 18 25
b. Use two of the square numbers to complete the
following calculation.
- = = 7
197
Number Problems 13
Answer these number problems
1. a. Write the factors of 64 in the following list.
64 9 2 12 4 1 21 16 8 23 32
b. Use two of the factors of 64 to complete the
following calculation.
× = =
2. a. Write the factors of 360 in the following list.
1 2 3 4 5 6 7 8 9 10 12 15
18 20 22 24 25 30 35 36 40 45 60
72 90 120 144 150 180 360
b. Use two of the factors of 360 to complete the
following calculation.
- = = 78
16
198
Number Problems 14
Here is a thermometer.
1.
a. At 3 pm the temperature is 8ºC.
At 9pm the temperature is 15 degrees lower.
What is the temperature at 9 pm?
b. At 2 am the temperature is - 14ºC.
At 10am the temperature is 17º higher.
What is the temperature at 10 am?
2. Class 6 has been recording the temperature at 9 am
for 5 days.
Here are their results.
Monday Tuesday Wednesday Thursday Friday
-2ºC - 5ºC 2ºC - 6ºC -4ºC
a. What is the mean temperature for that week?
b. What is the temperature range for that week?
____________________________________________________________________
- 20 -15 -10 -5 0 5 10 15 20 25 30 35
ºC
ºC
ºC
ºC
199
Number Problems 15
Use the numbers 1-9 to make these statements correct.
For each number sentence a different letter indicates a
different number.
1. a + a + a = 12 a =
2. b × b × b = 1 b =
3. c + c + c + c = 20 c =
4. 4 × d = 28 d =
5. e + e + e = 45 e =
6. g × g × g = 8 g =
7. 30 - h - h - h = 12 h =
8. i + i + i = j + j i = j =
9. k + k + k = 96 k =
10. l × l × l = 27 l =
11. m × m = 72 – m m =
12. n + n + n + n = 56 n =
13. o × o + o = 42 o =
14. p × 2 = 34 p =
4
200
Number Problems 16
Use the numbers 1-9 to make these statements correct.
For each number sentence a letter indicates a number.
1. 4a = 12 a =
2. 9b = 18 b =
3. 3c + 2 =14 c =
4. d + 5 = 12 d =
5. 7e = 35 e =
6. 2f + 6 = 3f + 3 f =
7. 2g– 9 = g – 3 g =
8. 2h + 2 = h +11 h =
Use different numbers between 1 and 9 for each letter in
these equations. You may find more than one answer.
9. 2j + k = 5 j= k= , j = k =
10. 3m – n = 5 m= n= , m= n=
11. p + 3r = 16 p= r =
12. 3s ÷ t = 2 s= t =
201
Number Problems 17
Write whether the following statements are true or false.
Show your working.
1. (32 × 120) ˃ 4120
2. (1265 + 3987) ˂ 5346
3. (45 × 34) ˃ 1224
4. (12 × 349) ˃ 5502
5. (9435 - 3355) ˂ 7250
6. (4560 ÷ 30 ˃ 125
7. (3270 ÷ 12) ˂ 235
202
Number Problems 18
Put the missing sign in these calculations.
Use
1. 125 5 = 25
2. 5 × 300 1600
3. 12 36 = 432
4. 35 55 = - 20
5. 950 50 = 19
6. 72 × 36 2592
7. 99 3 = 33
8. -49 29 = -20
9. 2480 ÷ 5 490
10. 1035 26 = 1061
11. 6 × 3 11 = 198
12. 5·5 0·25 = 22
13. 7·75 12·5 = -4·75
14. 2·5 1·5 = 3·75
+ - ÷ × ˂ ˃ =
203
5·69
4·14
1·34
Year 6 Answers
Place, value and ordering 1 page 3
1. 800 2. 40 3. 7000 4. 600 5. 200000 6. 60000 7. 4000
8. 70000 9. Fifty seven thousand, eight hundred and twenty six
10. Forty six thousand, three hundred and ten
11. Three thousand, two hundred and ninety
12. Twenty five thousand, eight hundred and ninety one
13. 17120 14. 59206
Place, value and ordering 2 page 4
1. Eight hundredths 2. Seven tenths 3. Nine tenths 4. Four hundredths
5. Two thousandths 6. 5·09 5·95 7·73 9·45 9·55
7. 1·61 1·62 1·68 1·86 1·87 8. 0·53 2·05 2·35 2·53 20·15
9. 1·007 1·07 1·117 1·17 1·71
Place, value and ordering 3 page 5
1. 1·2 1·21 1·22 1·23 1·24 1·25 1·26 1·27 1·28 1·29 1·3 1·31 1·32 1·33
2. 5·55 5·56 5·57 5·58 5·59 5·60 5·61 5·62 5·63 5·64 5·65 5·66 5·67 5·68
3. 4·0 4·01 4·02 4·03 4·04 4·05 4·06 4·07 4·08 4.09 4·10 4·11 4·12 4·13
4. 1·35 1·351 1·352 1·353 1·354 1·355 1·356 1·357 1·358 1·359 1·360
1·361 1·362 1·363 1·364
5. 4·03 4·031 4·032 4·033 4·034 4·035 4·036 4·037 4·038 4·039 4·040
4·041 4·042 4·043 4·044
6. 2·890 2·891 2·892 2·893 2·894 2·895 2·896 2·897 2·898 2·899 2·900
2·901 2·902 2·903 2·904
Place, value and ordering 4 page 6
1. 4·13 3·009 2. 15·07 16·13 3. 23·21 23·01
4. 124·60 123·09 5. 0·002 0·1
6. 7. 8. 9. 377
10. 11.
12.
400
Ninety five thousand, eight hundred and two Ninety five thousand, six hundred and sixty- two
4000 4/10
0239 9320
204
Place, value and ordering 5 page 7
1. £12245 £12425 £12634 £13967 £14900 £14908
2. £12·75 £12·50 £12·15 £12·02 £11·06 £11·05
3. 9·6kg 9·06kg 8·07kg 7·08kg 0·76kg 0·75kg
2.7 3.0 25 26 27 28 29 30 31
Place, value and ordering 6 page 8
1. 45900 2. 2360 3. 5600 4. 90460
5. 15800 6. 1400 7. 39000 8. 40300
9. 135000 10. 1000 11. 87000 12. 56000
13. 25 14. 16 15. 9 16. 11
17. 45 18. 24 19. 15 20. 1
Place, value and ordering 7 page 9
1. 67 460 2. 15 890 3. 62 130 4. 34 590 5. 47 600
6. 25 000 7. 12 900 8. 31 500 9. 83 300 10. 77 000
11. 20 000 12. 100 000 13. 289 000
Place, value and ordering 8 page 10
1. -4◦C 2. -5◦C 3. 10◦C 4. -9◦C 5. 10◦C 6. 13◦C
Place, value and ordering 9 page 11
1. -10 -7 -4 -2 4 8 2. -22 -14 -9 -3 0 2
3. -22 -13 -12 -5 15 20 4. -28 -19 -18 -9 -8 3
5. -2 6. -5 7. 8 8. -18 9. -19 10. 4
Place, value and ordering 10 page 12
A
1. 10 2. 10 3. 6 4. 11 5. 11 6. 15 7. 20 8. 3 9. 17 10. 9
B
1. -92 2. -170 3. -103 4. -79 5. 62 6. -171 7. -102 8. -22 9. -116 10. 296
Place, value and ordering 11 page 13
A
1. 16 2. 81 3. 49 4. 1 5. 144 6. 4
7. 25 8. 64 9. 100 10. 121 11. 36 12. 169
B
1. 22 2. 91 3. 155 4. 73 5. 20 6. 15
7. 112 8. 100 9. 72 10. 41 11. 119 12. 113
13. 32 14. 50 15. 88 16. 130
2·7 2·8 2·95 3·0 3·1 3·25 3·4
205
Place, value and ordering 12 page 14
1. 118, 124, 130 The rule is add 6 2. 460, 465, 470 The rule is add 5
3. -44, -41, -38 The rule is subtract 3 4. -12, -24, -36 The rule is subtract 12
5. 75, 50, 25 The rule is subtract 25 6. 12, 36, 60 The rule is add 24
7. 63, 72, 81 The rule is add 9 8. -45, -65, -85 The rule is subtract 20
Place, value and ordering 13 page 15
1. The sum of odd numbers is odd. Examples include: 3 + 5 + 9 = 17
7+ 17 + 11 = 35 15 + 9 + 7 = 31
2. The sum of 2 even numbers is even. Examples include: 20 + 2 = 22
28 + 8 = 36 10 + 4 = 14
3. The sum of an odd number and and even number is odd. Exampes include:
20 + 7 = 27 3 + 2 = 5 28 + 11 = 39
4. The difference between two even numbers is even. Examples include:
20 – 2 =18 28 – 8 = 20 16 – 4 = 12
Place, value and ordering 14 page 16
1. The product of 3 odd numbers is odd. Examples include:
9 × 1 × 7 = 63 7 × 5 × 3 =105 3 × 11 × 7 = 231
2. The product of 2 even numbers is even. Examples include:
9 × 12 = 108 8 × 6 = 48 4 × 6 = 24
3. The product of 2 odd numbers is odd. Examples include:
9 × 7 = 63 11 × 7 = 77 5 × 5 = 15
4. The product of 1 even number and 1 odd number is even. Examples include:
2 × 9 = 18 12 × 7 = 84 10 × 5 = 50
Addition 1 page 17
1. 325 + 278 = 300 +200 = 500 2. 167 + 164 = 100 + 100 = 200
20 + 70 = 90 60 + 60 = 120
5+ 8 = 13 = 603 7 + 4 =11 = 331
3. 456 + 234 = 400 +200 = 600 4. 645 + 357 = 600 + 300 = 900
50 + 30 = 80 40 + 50 = 90
6+ 4 = 10 = 690 5 + 7 = 12 = 1002
5. 552 + 268 = 500 +200 = 700 6. 785 + 247 = 700 + 200 = 900
50 + 60 = 110 80 + 40 = 120
2+ 8 = 10 = 820 5 + 7 = 12 = 1032
7. 156 + 69 = 156 +70 = 156 + 70 8. 456 + 89 = 456 + 90 = 546
= 226 -1= 225 = 546 – 1 = 545
9. 433 + 102 = 433 + 100 = 10. 391 + 99 = 391 + 100
533 + 2 = 535 491 - 1= 490
206
Addition 2 page 18
1. 3568 2. 8501 3. 7494 4. 3464 5. 2784 6. 6891
+ 455 + 178 + 267 + 389 + 246 + 567
4023 8679 7761 3853 3030 7458 1 1 1 1 1 1 1 1 1 1 1 1
7. 2879 8. 8936 9. 3406 10. 8501 11. 7494 12. 3464
+ 352 + 957 + 3589 + 2673 +4761 + 3678
3231 9893 6995 11174 12255 7142 1 1 1 1 1 1 1 1 1 11 1 1 1
13. 7649 14. 6832 15. 9452 16. 3764 17. 1388 18. 8501
+ 8463 +6945 +7902 +7902 38 3490
16112 13777 17354 11666 239 594
1 1 1 1 1 1 1 1 + 2784 + 4891
4449 17476 1 2 2 2 2
19. 7494 20. 3464 21. 1449 22. 9502 23. 6491 24. 4462
96 2389 247 693 3479 593
2385 784 5937 8462 2845 6936
+ 3570 + 2754 +7461 + 794 + 6743 + 8931
13545 9381 15094 19451 19558 20922 1 3 1 2 2 2 2 1 2 2 2 1 1 2 1 2 2 1
Addition 3 page 19
1. 63377 2. 141603 3. 759127 4. 408033 5. 225145
6. 818207 7. 1025 291 8. 134 861
Addition 4 page 20
1. 28031 2. 17012 3. 42248 4. 72514 5. 107685
6. 109066 7. 107783 8. 100555
Addition 5 page 21
1. 41·76 2. 920·965 3. 325·433 4. 6807·366 5. 5504·797
6. 204·445 7. 1888·477 8. 763·379
Addition 6 page 22
1. 133·13 2. 114·714 3. 100·626 4. 313·28 5. 110·773
6. 46·621 7. 92·026 8. 911·845
207
Addition 7 page 23 1. 2. 3. 4.
1 5 9 0 3 5 6 7 5 7 2 8 3 5 6 7
+ 2 5 1 + 1 7 4 5 + 7 2 3 + 4 9 1 3
1 8 4 1 5 3 1 2 6 4 5 1 84 8 0 5. 6. 7. 8.
1 6 ·3 5 2 5 4· 7 2·5 7 3 1 9· 2 5
+ 3 ·2 6 + 7 4· 2 + 0·8 4 2 + 7 4· 3 6
1 9·6 1 3 2 1·5 3·4 1 5 9 3· 6 1
Addition 8 page 24
1. 57 + 21 = 78 2. 78 + 65 = 143
570 + 210 = 780 780 + 650 = 1430
5700 + 2100 = 7800 7800 + 6500 = 14 300
0·57 + 0·21 = 0·78 0·78 + 0·65 = 1·43
5·70 + 2·10 = 7·80 7·80 + 6·50 = 14·30
0·057 + 0·021= 0·078 0·078+0·065 = 0·143
3. 98 + 24 = 122 4. 56 + 75 = 131
980 + 240 = 1220 560 + 750 = 1310
9800 + 2400 = 12200 5600 + 7500 = 13100
0·98 + 0·24 = 1·22 0·56 + 0·75 = 1·31
9·80 + 2·40 = 12·20 5·60 + 7·50 = 13·10
0·098+ 0·024 = 0·122 0·056+0·075 = 0·131
Addition 9 page 25
1. 8200 2. 9800 3. 7700 4. 13800 5. 4200 6. 10700
7. 15000 8. 17100 9 12500 10. 14500 11. 13100 12. 9500
13. 18800 14. 2300 15. 4900 16. 4200 17. 1600 18. 7600
19. 2900 20. 6500 21. 4700 22. 13100 23. 14000 24 2100 Addition 10 page 26
1. 0·09 2. 0·09 3. 0·08 4. 0·08 5. 0·03 6. 0·07
7. 0·03 8. 0·09 9. 0·18 10. 1·07 11. 0·04 12. 0·3
13. 0·7 14. 0·8 15. 0·45 16. 0·54 17. 0·17 18. 0·8
19. 0·09 20. 0·88 21. 0·97 22. 0·44 Addition 11 page 27
1. 0·56 2. 0·92 3. 0·77 4. 0·38 5. 2·17 6. 2·44
7. 9·44 8. 8·28 9. 12·04 10. 1·872 11. 7·639 12. 2·146
13. 1·111 14. 12·16
208
Addition 12 page 28
1. 175 325 2. 250 100 3. 350 450
4. 150 250 425 5. 125 275 200
Addition 13 page 29
1. 7624 + 3957 = 7624 + 7 + 50 + 900 + 3000 = 11581
+ 7 +50 + 900 +3000
7624 7631 7681 8581 11581
2. 1357 + 297 = 1357 + 7 + 90 + 200 = 1654
+ 7 +90 + 200
1357 1364 1454 1654
3. 5724 + 562 = 5724 + 2 + 60 + 500 = 6286
+ 2 +60 + 500
5724 5726 5786 6 286
4. 7534 + 1582 = 7534 + 2 80 + 500 + 1000 = 9116
+ 2 +80 + 500 +1000
7534 7536 7616 8116 9116
209
Addition 14 page 30
1. 9241 + 5176 = 9241 + 6 + 70 + 100 + 5000 = 14417
+ 6 +70 + 100 +5000
9241 9247 9317 9417 14417
2. 4276 + 247 = 4276 + 7 + 40 + 200 = 4523
+ 7 +40 + 200
4276 4283 4323 4523
3. 3793 + 493 = 3793 + 90 + 400 = 4286
+ 3 +90 + 400
3793 3796 3886 4286
4. 5056 + 3873 = 5056 + 3 + 70 + 800 + 3000 = 8929
+ 3 +70 + 800 +3000
5056 5059 5129 5929 8929
Subtraction 1 page 31
1. 403-67= 3+30+300+3= 336
+ 3 +30 + 300 +3
67 70 100 400 403
2. 309-94= 6+200+9= 215 + 6 + 200 +9
94 100 300 309
3. 713-83= 7+10+600+13= 630
+ 7 +10 + 600 +13
83 90 100 700 713
4. 521-78= 2+20+400+21=443 + 2 +20 + 400 +21
78 80 100 500 521
210
Subtraction 2 page 32
41 8 1 41 6 1 2 1 3 1 8 1 7 1 5 1 8 1
1. 5697 2. 5134 3. 7634 4. 4494 5. 2845 6. 6793
- 749 - 623 - 805 - 865 - 783 - 985
4948 4511 6829 3629 2062 5808
1 9 1 1 3 1 5 21 2 1 1 7 1 011 5 61 7. 2942 8. 8634 9. 3049 10. 8467 11. 1123 12. 4678
- 836 - 459 - 2457 - 6734 - 1034 - 2489
2106 8175 592 1733 89 2189 1 1 1
6 2 41 7 2 61 2 101 4 151 2 1 71421
13. 7356 14. 8469 15. 8374 16. 8312 17. 56345 18. 98534
- 4378 -7356 - 4286 - 4295 - 7891 - 34697
2978 1113 4088 4017 48454 63837
1 1 1 9 15 31 4 21351 8 1 1 1 11 1 716 1 8 1 4 1 1
19. 16474 20. 53464 21. 89321 22. 12567 23. 23870 24. 90501
- 7891 -34897 - 6712 - 7834 - 12671 - 67232
8583 18567 82609 4733 11199 23269
Subtraction 3 page 33
1. 3388 2. 556 3. 59587 4. 37844 5. 71587 6. 11032
7. 804479 8. 25793
Subtraction 4 page 34
1. 21·999 2. 644·99 3. 420·36 4. 6613·134 5. 667·987
6. 77·676 7. 116·835 8. 783·585
Subtraction 5 page 35
1. 2. 3. 4. 5.
3 2 9 0 5 3 2 4 6 3 2 7 8 6 19 2 2 · 1 7
- 5 3 8 - 3 3 7 0 - 2 6 8 3 - 5 0 2 3 5 · 3 9
2 7 5 2 1 9 5 4 3 6 4 4 3 5 9 6 1 6 · 7 8
6. 7. 8.
621· 6 6· 3 7 2 4 9 · 1 6
- 275· 9 - 5· 1 3 4 - 2 4 · 4 8
345· 7 1·2 3 8 2 4 · 6 8
211
9. ×10 10. × 1000 11. × 100 12. × 1000
Subtraction 6 page 36
1. 87 - 25 = 62 2. 74 - 35 = 39 3. 92-37 = 55 4. 76-29= 47
870 - 250 = 620 740 -350 =390 920-370 = 550 760-290=470
8700 - 2500 = 6200 7400 -3500 =3900 9200-3700=5500 7600-2900=4700
0·87 - 0·25 = 0·62 0·74 -0·35 =0·39 0·92-0·37=0·55 0·76-0·29=0·47
8·70 - 2·50 = 6·2 7·4 -3·5 =3·9 9·2- 3·7=5·5 7·6-2·9=4·7
0·087 - 0·025=0·062 0·074 - 0·035=0·039 0·092-0·37=0·055 0·076-0·029=0·047
Subtraction 7 page 37
1. 8700 - 6000 = 6100 2. 6300 -5400 = 900 3. 5800 - 2700 = 3100
4. 8300 - 5800 = 2500 5. 7300 - 2900 = 4400 6. 2900 -2200 = 700
7. 9600 - 3700 = 5900 8. 9500 - 7700 = 1800 9. 6400 – 4900 = 1500
10. 11700 - 8700 = 3000 11. 12400 - 3800 = 8600 12. 22800 – 11700 =11100
13. 19200 - 15600 = 3600 14. 9600 – 6200 = 3400 15. 7400 – 4700 = 2700
16. 9400 – 1800 = 7600 17. 2400 – 500 = 1900 18. 5500 – 1800 = 3700
19. 11000 – 4300 = 6700 20. 8200 – 3500 = 4700 21. 18700 – 9500 = 9200
22. 7400 – 700 = 6700 23. 6600 – 2800 = 3800 24. 9800 – 5900 = 3900
Subtraction 8 page 38
1. 0·7 2. 0·1 3. 0·15 4. 0·72 5. 0·43 6. 0·24
7. 5·07 8. 2·18 9. 1·68 10. 0·93 11. 6·985 12. 0·016
13. 1·028 14. 4·211
Subtraction 9 page 39
1. -1·5, 1·5 2. 3·5, -4·5 ` 3. -8·8, 3·2 4. -1·5, -1·0
5. 1·75, 2·5 Multiplication 1 page 40
1. 560 2. 78 3. 2360 4. 6000 5. 39120 6. 528910
7. 130 8. 26890 9. 2400 10. 1400 11. 78900 12. 40000
13. 451000 14. 4681300 15. 229600 16. 3589100 17. 10 18. 3700
19. 10 20. 9900 21. 50 22. 10 23. 12400 24. 10
Multiplication 2 page 41
1. 100, 4500 2. 100, 8900 3. 1000, 24000 4. 100, 32100
5. 1000, 90000 6. 1000, 305000 7. × 10 8. × 100
212
Multiplication 3 page 42
1. 550 2. 1200 3. 1450 4. 2500 5. 1800
6. 500 7. 400 8. 1250 9. 850 10. 1200
Multiplication 4 page 43
1. 224 2. 352 3. 240 4. 512 5. 672
6. 144 7. 336 8. 360 9. 1200 10. 1008
Multiplication 5 page 44
1. a. 182 b. 104 c. 234 2. a. 192 b. 320 c. 512
3. a. 192 b. 336 c. 432
Multiplication 6 page 45
1. (30 × 3) + (7 × 3) = 90 + 21 = 111 2. (60 ×4) +(5×4) = 240 + 20 = 260
3. (40 × 7) + (3 × 7) = 280 + 21 = 301 4. (50 ×8) +(9×8) = 400 + 72 = 472
5. (70 × 9) + (6 × 9) = 630 + 54 = 684 6. (80 ×6) +(7×6) = 480 + 42 = 522
7. (50 × 7) + (8 × 7) = 350 + 56 = 406 8. (70 ×8) +(9×8) = 560 + 72 = 632
Multiplication 7 page 46
1. (60 × 6) + (5 × 6) = 360 + 30 = 390 2. (40 ×9) +(5×9) = 360 + 45 = 405
3. (70 × 7) + (2 × 7) = 490 + 14 = 504 4. (40 ×9) +(9×9) = 360 + 81 = 441
5. (60 × 8) + (7 × 8) = 480 + 56 = 536 6. (50 ×6) +(4×6) = 300 + 24 = 324
7. (90 × 7) + (8 × 7) = 630 + 56 = 686 8. (70 ×8) +(3×8) = 560 + 24 = 584
Multiplication 8 page 47
1. 7 2. 4 3. 3 4. 6 5. 7 6. 6
7. 7 8. 8 9. 76 10. 82 11. 95 12. 77
13. 27 14. 28 15. 78
Multiplication 9 page 48
1. 6 × 49 = (6 × 50) - 6 = 300 - 6 = 294 2. 4 × 49 = (4 × 50)-4 = 200-4 = 196
3. 15 × 49 = (15 × 50)-15 = 750-15 = 735 4. 8 × 49 = (8×50)-8 = 400-8 =392
5. 26 × 49 = (26 × 50)-26 = 1300-26 =1274 6. 33×49 = (33×50)-33 =1650-33 = 1617
7. 49×49 = (49×50) -49 = 2500-49 =2401 8. 94 ×49= (94×50)-94 = 4700-94 =4606
Multiplication 10 page 49
1. 5 × 51= (5 × 50) + 5 = 250 + 5 = 255 2. 7 × 51 = (7 × 50) + 7= 350 + 7 = 357
3. 9 × 51= (9 × 50) + 9 = 450 + 9 = 459 4. 12 ×51=(12×50) +12 =600 +12 = 612
5. 24×51=(24 × 50)+24=1200 + 24 =1224 6. 36×51= (36×50)+36=1800+36 =1836
7. 78×51= (78×50)+78 =3900 +78 =3978 8. 53×51= (53×50)+53= 2650+53 = 2703
213
Multiplication 11 page 50
1. 465 × 5 = 400 60 5 = 2325
5
2. 748 × 6 = 700 40 8 = 4488
6
3. 734 × 3 = 700 30 4 = 2202
3
4. 876 × 9 = 800 70 6 = 7884
9
5. 978 × 8 = 900 70 8 =7824
8
Multiplication 12 page 51
1. 2461 × 4 = 2000 400 60 1 = 9844
4
2. 3255 × 5 = 3000 200 50 5 = 16275
5
3. 6328 × 3 = 6000 300 20 8 = 18984
3
4. 1289 × 7 = 1000 200 80 9 = 9023
7
5. 4196 × 8 = 4000 100 90 6 = 33568
8
8000 1600 240 4
15000 1000 250 25
18000 900 60 24
7000 1400 560 63
32000 800 720 48
4200
300 25 2000
240 48
2100 90 12
7200 630 54
7200 560 64
214
Multiplication 13 page 52
1. 4256 × 3 = 4000 200 50 6 = 12768
3
2. 3728 × 6 = 3000 700 20 8 = 22368
6
3. 6146 × 7 = 6000 100 40 6 = 43022
7
4. 4578 × 9 = 4000 500 70 8 = 41202
9
5. 7552 × 8 = 7000 500 50 2 = 60416
8
12000 600 150 18
18000 4200 120 48
42000 700 280 42
36000 4500 630 72
56000 4000 400 16
215
Multiplication 14 page 53
1. 126×5 125 × 5 = 600 2. 756 × 4 750 ×4 = 3000
126 756
× 5 × 4
500 (100×5) 2800 (700×4)
100 ( 20 ×5) 200 ( 50×4)
30 ( 6 ×5) 24 ( 6×4)
630 (126×5) 3024 (756×4)
3. 453x5 450 × 5 = 2250 4. 691 × 6 700 × 6 = 4200
453 691
× 8 × 6
3200 (400×8) 3600 (600×6)
400 ( 50 ×8) 540 ( 90×6)
24 ( 3 ×8) 6 ( 1×6)
3624 (453×8) 4146 (691×6)
5. 728×9 720 10 = 7200 6. 847 × 8 850 × 8 = 3400
728 847
× 9 × 4
6300 (700 ×9) 6400 (800×8)
180 ( 20 ×9) 320 ( 40×8)
72 ( 8 ×5) 56 ( 7×8)
6552 (728×5) 6776 (847×8)
+ +
+ +
+ +
216
5622
Multiplication 15 page 54
1. 1526 × 5 1500 × 5 = 7500 2. 2715 × 3 2700 × 3 = 8100
1526 2715
× 5 × 3
5000 (1000 ×5) 6000 (2000×3 )
2500 ( 500 ×5) 2100 ( 700×3 )
100 ( 20 ×5) 30 ( 10×3 )
30 ( 6 ×5) 15 ( 3×5 )
7630 8145 (2715×3)
3. 3642 × 5 3500 × 5 = 17500 4. 7367 × 3 7300 × 3 = 22000
3642 7367
× 5 × 3
15000 (3000 ×5) 21000 (7000 ×3 )
3000 ( 600 ×5) 900 ( 300 ×3 )
200 ( 40 ×5) 180 ( 60 ×3 )
10 ( 2 ×5) 21 ( 7 ×3)
18210 22101 (7367 ×3)
5. 4318 × 7 4000 × 7 = 28000 6. 6967 × 8 7000 × 8 = 56000
4318 6967
× 7 × 8
28000 (4000 ×7) 48000 (6000 ×8)
2100 ( 300 ×7) 7200 ( 900 ×8)
70 ( 10 ×7) 480 ( 60 ×8)
56 ( 8 ×7) 56 ( 7 ×8)
30226 55736 (6967 ×8)
Multiplication 16 page 55
1. 597 2. 736 3. 268 4. 947 5. 783 6. 937
× 6 × 6 × 6 × 8 × 7 × 6
3582 4416 1608 7576 5481 5 4 23 4 4 3 5 52 24
Multiplication 17 page 56
1. 4895 2. 6309 3. 1297 4. 3437 5. 4779 6. 9786
× 6 × 4 × 5 × 6 × 7 × 8
29370 25236 6485 20622 33453 78288 5 53 1 3 1 4 3 2 2 4 5 5 6 6 6 4
+ +
+ +
+ +
217
Multiplication 18 page 57
1. 18904 2. 13390 3. 22074 4. 31302
Multiplication 19 page 58
1. 8·26 × 4 (8 ×4)= 32 2. 4·81 × 5 (5×5)=25
8·00 × 4 = 32·00 4·00 ×5 = 20·00
0·20 × 4 = 0·80 0·80 × 5 = 4·0
0·06 × 4 = 0·24 0·01 × 5 = 0·05
33·04 24·05
3. 5·17 × 6 (5×6)= 30 4. 6·35 × 4 (6×4)=24
5·00 ×6 = 30·00 6·00 × 4 = 24·00
0·10 × 6 = 0·60 0·30 × 4 = 1·20
0·07 ×6 = 0·42 0·05 × 4 = 0·20
31·02 25·40
5. 6·84 × 7 (7×7)=49 6. 9·68 × 8 (10×8)=80
6·00 × 7 = 42·00 9·00 × 8 = 72·00
0·80 × 7 = 05·60 0·60 × 8 = 4·80
0·04 × 7 = 00·28 0·08 × 8 = 0·64
47·88 77·44
Multiplication 20 page 59
1. 7·54 ×7 (8 × 7 )=56 2. 9·78 × 6 (10×6) = 60
7·00 × 7 = 49·00 9·00 × 6 = 54·00
0·50 × 7 = 03·50 0·70 × 6 = 4·20
0·04 × 7 = 00·28 0·08 × 6 = 0·48
52·78 58·68
3 6·05 × 8 (6 × 8 )= 48 4. 5·73 × 9 (6 × 8) = 48
6·00 × 8 = 48·00 5·00 × 9 = 45·00
0·05 × 8 = 00·40 0·70 × 9 = 06·30
48·40 0·03 × 9 = 0·27
51·57
5. 12·24 × 3 (12 ×3)=36 6. 24·72 × 4 (25×4) = 100
12·00 × 3 = 36·00 24·00 × 4 = 96·00
0·20 × 3 = 00·60 00·70 × 4 = 02·80
0·04 × 3 = 00·12 00·02 × 4 = 00·08
36·72 98·88
7. 16·82 × 5 (17 ×5)=85 8. 23·06 × 6 (236)=138
16·00 × 5 = 80·00 23·00 × 6 = 138·00
00·80 × 5 = 4·00 00·06 × 6 = 00·36
00·02 × 5 = 0·10 138·36
84.10
218
Multiplication 21 page 60
1. 150 2. 177 3. 200 4. 340 5. 500 6. 450 7. 400 8. 600
Multiplication 22 page 61
1. 476 × 15 = × 400 70 6 =
2. 694 × 24 = × 600 90 4 =
3. 829 × 37 = × 800 20 9 =
4. 497 × 68 = × 400 90 7 =
4000 700 60
2000 350 30
4760
2380
7140 1 1
+
5 10
0
12000 1800 80
2400 360 16
13880
2776
16656 1 1
+
4
20
0
5
24000 600 270
5600 140 63
24870
5803
30673 11
+
5 30
0
24000 5400 420
3200 720 56
29820
3976
33796 1 1
+
8
60
0
7
219
Multiplication 23 page 62
1. 3472 × 25 = × 3000 400 70 2 =
2. 6193 × 32 = × 6000 100 90 3 =
3. 3831 × 53 =
× 3000 800 30 1 =
4. 8456 × 24 = × 8000 400 50 6 =
8000 1400 40
2000 350 10
69440
17360
86800 1 1
+
20
0
11
5
60000
15000
3000 2700 90
200 180 6
185790
12386
198176 11
+
30
0
2
180000
00 12000
11 40000 1500 50
2400 90 3
191550
11493
203043 1 1 1
+
50
3
150000
00 9000
11 8000 1000 120
1600 200 24
169120
33824
202944 11
+
20
0 4
160000
00 32000
220
7 0 2 3 8
4 3
3
5 0 1
7 1
7 0 2 1
)
5
5
5
3
×
×
×
0 3 0
4 0
( 5
4 7
4
0 1 0 3
1 7 2
5 2
3
3
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4
4
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5 ×
×
0 ( 7 0
( 4 0
( 6
5
5
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5
5
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3
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6
3
0
0
8
Multiplication 24 page 63
1. 345 × 35 = 12075
`
2. 746 × 43 = 32078
1
1 1
1 4 0
×
3
(
(
×
)
0
)
)
221
2 2
4
0 4 8
5 2
8
×
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4
4
4
2
2
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× 0
6 ×
( ×
6
2
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6
2
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5
5
5
× 0
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3
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2
0 5
0
0
0
0
1
0 1 7 4 3
4
3
2
Multiplication 25 page 64
1. 262 × 42 = 11004
2. 756 × 36 = 27216
3. 534 × 65 = 34710
Multiplication 26 page 65
1. 2 2. 3 3. 4 4. 5 5. 7 6. 5 7. 8 8. 5
(
(
1 1
6
6
6
2
×
6
6
6
1 1
222
Factors and Multiples 1 page 66
1. 18 1,2,3,6,9,18 2. 40 1, 2,4,5,8,10,20,40 3. 64 1,2,4,8, 16,32 64
4. 20 1,2,4,5,10,20 5. 36 1,2, 3,4, 6, 9,12, 18
6. 48 1,2,4,6,812,16,24,48 7. 24 1,2,4,6,8,12,24
Answers include:
8. 12 × 15 12 × 3 5, 15 × 6 × 2, 15 × 3 × 4 = 180
9. 16 × 12 16 × 3 × 4, 16 × 2 × 6, 12 × 4 × 4 = 192
10. 24 × 18 6 × 4 × 9 × 2, 12 × 2 × 9 × 2, 6 × 4 × 3 × 6 = 432
11.33 × 16 33 × 4 × 4, 33 × 8 × 2, 16 × 11 × 3 = 528
12. 27 × 18 27 × 9 × 2, 27 × 3 × 6, 18 × 3 × 9 = 486
13. 25 × 16 25 × 4 × 4, 25 × 2 × 8, 16 × 5 × 5 = 400
14. 24 × 25 24 × 5 × 5, 25 × 8 × 3, 25 × 6 × 4 = 600
223
Factors and Multiples 2 page 67
Number Factors Number of Factors
1 1 1
2 1 2 2
3 1 3 2
4 1 2 4 3
5 1 5 2
6 1 2 3 6 4
7 1 7 9 2
8 1 2 4 8 4
9 1 3 9 3
10 1 2 5 10 4
11 1 11 2
12 1 2 3 4 6 12 6
13 1 13 2
14 1 2 7 14 4
15 1 3 5 15 4
16 1 2 4 8 16 5
17 1 17 2
18 1 2 3 6 9 18 6
19 1 19 2
20 1 2 4 5 10 20 6
224
Factors and Multiples 3 page 68
Number Factors Number of Factors
21 1 3 7 21 4
22 1 2 11 22 4
23 1 23 2
24 1 2 3 4 6 8 12 24 8
25 1 5 25 3
26 1 2 13 26 4
27 1 3 9 27 4
28 1 2 4 7 14 28 6
29 1 29 2
30 1 2 3 5 6 10 15 30 8
31 1 31 2
32 1 2 4 8 16 32 6
33 1 3 11 33 4
34 1 2 17 34 4
35 1 5 7 35 4
36 1 2 3 4 6 9 12 18 36 9
37 1 37 2
38 1 2 19 38 4
39 1 3 13 39 4
40 1 2 4 5 8 10 20 40 8
41 1 41 2
42 1 2 3 6 7 14 21 42 8
43 1 43 2
44 1 2 4 11 22 44 6
45 1 3 5 9 15 45 6
225
Factors and Multiples 4 page 69
1. a. 2 3 5 7 11 13 17 19 23 29 31 37 41 43 b. Prime numbers
2. 9 25 3. Odd Square numbers
Factors and Multiples 5 page 70
1. Composite numbers 2. 13 31 17 71 19 91 37 73
3. 845 ends in 5 so it is divisible by 5 a prime number is only divisible by 1 or itself.
4. 266 is an even number a prime number is always odd.
5. Examples such as 23 12 14 16 25
Factors and Multiples 6 page 71
1. 2 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 3 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
2. 5 5,10,15,20,25,30,35,40,45,50 4 4, 8,12,16,20,24,28,32,36,40
3 3 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 9 9, 18, 27, 36, 45, 54, 63, 72,81, 90
4. 5 5,10,15,20,25,30,35,40,45,50 7 7, 14,21,28,35, 42, 49,56, 63, 70
5. 4 4, 8,12,16,20,24,28,32,36,40 10 10,20,30,40,50,60,70,80,90,100
6. 6 6,12,18,24,30,36,42,48,54,60 9 9, 18, 27, 36, 45, 54, 63, 72,81, 90
Factors and Multiples 7 page 72
1. 6 6, 12,18,24,30,36,42,48,54,60 2. 3 3,6,9,12,15,18,21,24,27,30
3 3,6,9,12,15,18,21,24,27,30 6 6,12,18,24,30,36,42,48,54,60
5 5,10,15,20,25,30,35,40,45,50 8 8,16,24,32,40,48,56,64,72,80
3. 5 5,10,15,20.25,30,35,40,45,50 4. 4 4,8,12,16,20,24,28,32,36,40
6 6,12,18,24,30,36,42,48,54,60, 6 6,12,18,24,30,36,42,48,54,60
10 10,20,30,40,50,60,70,80,90,100 9 9,18,27,36,45,54,63,72,81,90
5. 9 9,18,27,36,45,54,63,72,81,
8 , 8,16,24,32,40,48,56,64,72,80
12 12,24,36,48,60,72,84,96,108,120
226
Factors and Multiples 8 page 73
1. 24, 48, 72, 96, 120, 144 2. 30
3. . 42, 84, 126
4. 72 5. 28 days 6. 90 beads
Factors and Multiples 9 page 74
1. 13, 26, 39, 52, 65, 78, 91, 104 2. 84
3. Answers include 305, 310, 315, 320, 325, 330, 335, 340, 345, 350
4. a. 25, 50, 75, 100, 125, 150, 175, 200, 225, 250
b. They all end in 25, 50, 75 or 00
5. 11,22,33,44,55,66,77,88,99,110,121,132,143,154,165,176,187,198, 209, 220,
231,242,253,264,275
Division 1 page 75
1. 24 2. 369 3. 13 4. 34 5. 450 6. 4670
7. 123 8. 7820 9. 66 10. 4 11. 23 12. 1
13. 67 14. 923 15. 22 16. 546 17. 10 18. 9
19. 10 20. 56 21. 4300 22. 10 23. 12 24. 100
Division 2 page 76
1. 100, 4 2. 100, 45 3. 1000, 9 4. 100, 800 5. 100, 9.34
6. 1000 3.215 7. 1000, 0.456 8. ÷10 9. ÷100 10. ÷10
11. ÷100 12. ÷1000 13. ÷1000
Division 3 page 77
1. 32 1,2,4,8,16,32 2. 25 1, 2,5,25 3. 48 1,2,3,4,8,16,24,48
4. 54 1, 2,3,6,9,27,54 5. 60 1,2,3,4,5,6,10,12,15,30,60
6. 100 1,2,4,5,10,25,50,100 7. 108 1, 2, 3,4,6,9,12,18,27,54,108
Answers include:
8. 168 ÷ 12 (168÷3)÷4, (168÷6) ÷2,(84÷12)+(84÷12)=14
9. 180 ÷ 15 (180÷3)÷5, (180÷5) ÷3, (90÷15)+(90÷15)= 12
10. 60 ÷ 15 (60÷3)÷5, (60÷5) ÷3, (30÷15)+(30÷15)= 4
11. 120 ÷ 24 (120÷6)÷4, (120÷12) ÷2, (120÷8) ÷3= 5
12. 800 ÷ 16 (800÷8)÷2, (800÷4) ÷4, (400÷16)+(400÷16)= 50
13. 108 ÷ 27 (108÷3)÷9, (108÷9) ÷3, (54÷27)+(54÷27)= 4
14. 390 ÷ 15 (180÷3)÷5, (180÷5) ÷3, (90÷15)+(90÷15)= 12
227
4 5
2 7
1
2
2 4
1
5
1
5
4
5
4 5
3
7
3 7
1
6
1
3
1 9
6
7
Division 4 page 78
1. √ 2. √ 3. √ 4. × 5. √ 6. √ 7. × 8. √
9. × 10. × 11. √ 12. √ 13. × 14. √ 15. × 16. √
Division 5 page 79
1. 246 ÷ 4 240 ÷ 4 = 60 2. 566÷5 550 ÷ 5 = 110
61 113
4 246 5 566
240 (60 × 4) 550 ( 110 × 5)
6 16
4 ( 1 ×× 4) 15 ( 3 × 5 )
2 1
Answer 61 Answer 113
3. 294 ÷5 290 ÷ 5 = 58 4. 451÷7 420 ÷ 7 = 60
58 64
5 294 7 451
290 ( 58 ×5 ) 420 ( 60 ×7)
4 31
28 ( 4 × 7 )
3
Answer 58 Answer 64
Division 6 page 80
1. 149 ÷ 7 140 ÷ 7 = 20 Answer 21
2. 325 ÷ 6 300 ÷ 6 = 50 Answer 54
3. 230 ÷ 6 180 ÷ 6 = 30 Answer 38
4. 259 ÷ 5 250 ÷ 5 = 50 Answer 51
5. 748 ÷ 9 720 ÷ 9 = 80 Answer 83
6.. 685 ÷ 7 630 ÷ 7 = 90 Answer 97
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
228
Division 7 page 81
1. 46·2 42 ÷ 7 = 6 2. 11·75 ÷ 5 10 ÷ 5 =2
6·6 2·35
7 46·2 5 11·75
42 (6 × 7) 10 (2 × 5)
4·2 ( 0·6 ×7) 1·75
Answer 6·6 1·5 (0·3 × 5)
0·25 (0·05 × 5)
Answer 2·35
3. 25·9 ÷2 24 ÷ 2 = 12 4. 18·9 ÷ 9 2
12·95 2·1
2 25·9 9 189
24 ( 12 × 2) 18 ( 2 × 9 )
1·9 0·9 (0·1 × 9)
1·8 ( 0·9 × 2 )
0· 10 (0·05 × 2)
Answer 12·95 Answer 2·1
Division 8 page 82
1. 84·6 ÷ 9 9 2. 32·5 ÷ 5 30 ÷ 5 =6
9·4 6·5
9 84·6 5 32·5
81·0 ( 9 × 9) 30 ( 6 × 5)
3·6 (0·4 ×9) 2·5 (0·5 × 5)
Answer 9·4 Answer 6·5
3. 47·4 ÷ 5 45 ÷ 5 = 9 4. 24·72 ÷ 2 24 ÷ 2 =12
9·48 12·36
5 47·4 2 24·72
45·0 ( 9 × 5) 24 ( 12 × 2 )
2·4 0·72 (0·36 × 2)
2·0 ( 0·4 × 5 )
0·40 (0·08 × 5)
Answer 9·48 Answer 12·36
5. 28·2 ÷ 6 24÷6= 4 6. 60·8 ÷ 8 56 ÷ 8 = 7
4·7 7·6
6 28·2 8 60·80
24 ( 4 × 6) 56 ( 7 × 8)
4·2 ( 0·7 ×6) 4·8 (0·6 × 8)
Answer 4·7 Answer 7·6
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
~
229
Division 9 page 83
1. 2156 123 470 140 678 467 998 1002 771 43
2. 12 66 94 104 236 126 282 398 448 732 512
3. 1025 1660 3450 36 775 240 900 3335 11175 45
6700 385 67 450 24 200 6590 1100 750 6648 175
4. 6800 216 4256 444 816 612 2680 3156 796
Division 10 page 84
1. a. yes b. no c. yes
2. yes Half of 864 is 432 which is divisible by 4.
3. yes 3500 ends in 00 so it is divisible by 25.
4. no 86 is not divisible by 4.
Division 11 page 85
1. 6500 219 4250 445 805 610 2681 3156 790
2. 68 99 123 672 560 742 919 678 145 252 2106 178 471 142 6765
465 981 1002 771 43
3. 69 72 94 1242 236 99 282 398 448 732 512 4. 68 900 609 504 112 799 75 810 702 333
Division 12 page 86
1. Answers include 302, 304, 306, 308, 312,314 398
2. Answers include 1505, 1510, 1515,1520, 1525 1995
3. Answers include 603, 606, 609, 612, 615,618 699
4. Answers include 906, 912, 918, 924, 930,936 1194
5. Answers include 2004,2008,2012,2016, 2024 2096
6. Answers include 1503,1512,1521,1530, 1539 1998
7. Answers include 1608,1616,1624,1632, 1640 1992
8. Answers include 410, 420, 430, 440, 450,460 790
9. Answers include 1008, 1017, 1026, 1035,1044 1395
10. Answers include 704, 712, 720, 728, 736,744 996
Division 13 page 87
1. 38 74 2. 89 53 3. 48 93 4. 79 40 5. 36 92
Division 14 page 88
1. 150 2. 366 3. 270 4. 125 5. 425 6. 400
7. 762 8. 500
Division 15 page 89
1. 437 ÷ 19 440 ÷ 20 = 22 Answer 23
2. 648 ÷ 24 650 ÷ 25 = 26 Answer 27 ~
~
~
~
230
3. 459 ÷ 17 459 ÷ 17 = 30 Answer 27
4. 546 ÷ 14 540 ÷ 15 = 36 Answer 39
5. 522 ÷ 29 510 ÷ 30 = 17 Answer 18
6. 663 ÷ 13 660 ÷ 10 = 66 Answer 51
Multiplication and Division 1 page 90
1. £24 2. Brighton 3. £20 4. £40 5. £68 £70
Multiplication and Division 2 page 91
1. 4 + 8 7 + 6 = (4 + 8) × 7 + 6 = 12 × 7 + 6 = 90
=4 +( 8 × 7) + 6 = 56 + 4 + 6 = 66
=4 + 8 × (7 + 6) = 13 × 8 + 4 = 108
=(4 + 8) × (7 + 6) = 12 × 13 = 156
2. 64 ÷ 8 × 4 × 3 =(64 ÷ 8) × 4 × 3 = 8 × 4 × 3 = 96
=64 ÷ (8 × 4) × 3 = 64 ÷32 ×3 = 6
3. 100 ÷ 5 × 5 +4 =(100 ÷ 5) × 5 + 4 = 20 × 5 + 4 = 104
=100 ÷ (5 × 5) + 4 = 100 ÷ 25 + 4 = 8
=(100 ÷ 5) × (5 + 4) = 20 × 9 = 180
4. 56 ÷ 4 × 2 × 7 =(56 ÷ 4) × 2 × 7 = 14 × 2 × 7 = 196
=56 ÷ (4 × 2) × 7 = 56 ÷ 8 ×7 = 49
=56 ÷ (4 × 2 × 7) = 56 ÷ 56 = 1
5. 3 + 7 5 + 6 =(3 + 7 ) × 5 + 6 = 10 × 5 + 6 = 56
=3 + (7 × 5) + 6 = 35 + 3 + 6 = 44
=3 + 7 × (5 + 6) = 11 × 7 + 3 = 80
=(3 + 7) × (5 + 6 )= 10 × 11 = 110
Multiplication and Division 3 page 92
1. 56 – 24 ÷ 8 = (56 – 24) ÷ 8 = 32 ÷ 8 = 4
2. 48 + 15 ÷ 3 + 7 =48 + (15 ÷ 3) + 7 = 48 + 5 + 7 = 60
3. 13 × 4 × 2 - 20 =(13 × 4) × 2 - 20 = 52 × 2 -20 = 84
4. 56 ÷ 8 + 6 = 56 ÷ (8 + 6) = 56 ÷ 14 = 4
5. 47 - 11 × 12 ÷ 3 =(47 – 11) × 12 ÷ 3 = 36 × 12 ÷ 3 = 144
6. 7 × 7 + 9 × 3 = (7 × 7) + ( 9 × 3) = 49 + 27 = 76
7. 13 + 7 × 14 -9 = (13 + 7) × (14 -9) = 20 × 5 = 100
8. 14 + 6 × 9 + 32 =14 + (6 × 9) + 32 = 54 + 32 +14 = 100
9. 26 + 24 × 16÷8 =(26 + 24) × (16÷8) = 50 × 2 = 100
10. 28 × 2 – 31 × 4 = (28 × 2) – 31 × 4 =( 56 -31) × 4 =100
11. 56 ÷ 2 + 8 × 9 =(56 ÷2) + ( 8 × 9) = 28 + 72 =100
12. 5 × 12 × 4-28 =5 × (12 × 4) – 28 = (48 -28) ×5 = 100
Multiplication and Division 4 page 93
1. 27 2. 29 3. 6 4. 8 5. 41 6. 26 7. 61 8. 33 9. 32
10. 97 11. 10 12. 13 13. 5 14. 55 15. 230 16. 18 17. 1952 18. 79
19. 40 20. 288
~
~
~
~
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231
3 8
1 6
4
9
37
100
3 5
1 8
37
8
1
4
215 100
31
12
43
10
315
100 26
9
1
19
Multiplication and Division 5 page 94
1. 900 2. 350 3. 390 4. 100 5. 755 6. 250
7. 500 8. 201
Fractions and Decimals 1 page 95
A
1. 1 2. 2 3. 2 4. 1 5. 2 6. 1
7. 1 8. 7
B
1. 2. 3. 4. 5. 6.
Fractions and Decimals 2 page 96
1. is three times 2. is twice 3. is six times
4. is four times
Fractions and Decimals 3 page 97
1. is twice 2. is three times 3. is twice
4. is four times
Fractions and Decimals 4 page 98
1. ½ 2. ¼ 3. ⅜
Fractions and Decimals 5 page 99
1. 2. 3.
Fractions and Decimals 6 page 100
1. 2. 3. 4. 5. 6.
7. 8. 9. 10. 11. 12.
Fractions and Decimals 7 page 101
1. 2. 3. 4. 5. 6.
7. 8. 9. 10. 11. 12.
1
2 1
6
1
3
1
6
1
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1
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20
10
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9
12
Fractions and Decimals 8 page 102
1. 15 12 8 2 6 3 2. 3 5 4 1 2 5
20 20 20 5 10 4 6 6 6 2 3 6
3. 6 3 4 1 2 1 4. 3 6 4 1 1 1
18 18 18 6 9 3 12 12 12 4 3 2
5. 6 7 4 1 3 7 6. 12 21 20 2 2 7
8 8 8 2 4 8 30 30 30 5 3 10
7. 7 4 6 2 1 7 8. 16 21 14 1 4 3
18 18 18 9 3 18 28 28 28 2 7 4
9. 15 6 16 6 5 2
24 24 24 24 8 3
Fractions and Decimals 9 page 103
1. 3 + 4 = 7 2. 5 + 4 = 9 3. 3 + 2 = 5
12 12 12 20 20 20 6 6 6
4. 1 + 6 = 7 5. 5 + 3 = 8 6. 7 + 2 = 9
9 9 9 12 12 12 10 10 10
7. 9 + 8 = 17 8. 5 + 12 = 17
20 20 20 18 18 18
Fractions and Decimals 10 page 104
1. + = 2. + = 3. + =
4. + = 5. + = 6. + =
7. + = 8. + =
Fractions and Decimals 11 page 105
1. 6 - 3 = 3 2. 2 - 1 = 1 3. 4 - 1 = 3 = 1 4. 3 - 2 = 1
10 10 10 4 4 4 6 6 6 2 4 4 4
5. 9 - 6 = 3 6. 5 - 4 = 1 7. 7 - 6 = 1 8. 9 - 8 = 1
10 10 10 12 12 12 10 10 10 12 12 12
=
=
=
=
=
=
=
=
1
19
24
4 10
1
8 12
9 12
1
5
14 3
14
1
7 12
1
9
15 10
15
1
4
15
1
17
20
1
3
20
233
2
12
1
10
1
2
1
8
3
8
10
15
1
6
Fractions and Decimals 12 page 106
1. 5 - 4 = 1 2. 8 - 3 = 5 1 3. 8 - 3 = 5
6 6 6 10 10 10 or 2 12 12 12
4. 7 - 2 = 5 5. 11 - 9 = 2 1 6. 13 - 6 = 7
8 8 8 12 12 12 or 6 15 15 15
7. 9 - 6 = 4 2 8. 19 - 15 = 4 1
10 10 10 or 5 20 20 20 or 5
Fractions and decimals 13 page 107
1. 1 2. 1 3. 1 4. 2 5. 2
6. 1 7. 1 8.
Fractions and decimals 14 page 10
1. 2. 3. 4. 5. 6.
1. 2. 3. 4. 5. 6.
Fractions and decimals 15 page 109
1. £34 2. 84 3. 14 4. 140 5. 36km 6. 69
Fractions and decimals 16 page 110
1. £6 2. 72 3. 60cm 4. 1290g 5. 414 6. 28ml 7. 570k
Fractions and Decimals 17 page 111
1. 1·5 2. 0·9 3. 2·5 4. 3·5 5. 0·3 6. 0·75
7. 0·95 8. 1·58 9. 0·07 10. 3·40 11. 0·350 12. 0·750
13. 1·250 14. 0·568
Fractions and Decimals 18 page 112
1. 0·50 2. 0·25 3. 0·10 4. 0·20 5. 0·75 6. 0·33 7. 0·17 8. 0·01
9. 0·13 10. 0·83 11. 0·88 12. 0·80
Fractions and Decimals 19 page 113
1. 2. 3. 4. 5. 6.
7. 1·46 8. 0·24 9. 0·129 10. 0·937 11. 1·256 12. 0·078
5
20
22
24
8
10
46
100
258 100
15
100
1634
1000
257
1000
1
6
1
8
1
16
6
1
3
4
15
1
15
1
9
1
20
1
4
1
18
1
10
234
Fractions and decimals 20 page 114
A.
1. 1·6 2. 0·7 3. 2·1 4. 3·1 5. 1·2 6. 3·0
7. 2·7 8. 3·4 9. 9·9 10. 8·3
B
1. 1·09 2. 1·76 3. 2·85 4. 4·11 5. 1·28 6. 13·04
7. 4·84 8. 3·81 9. 9·08 10. 5·43 11. 6·93 12. 12·26
13. 12·58 14. 25·38
Fractions and decimals 21 page 115
A.
1. 0·2 2. 0·6 3. 3·1 4. 4·3 5. 5·9 6. 0·9
7. 2·1 8. 1·9 9. 2·6 10. 0·7
B
1. 2·41 2. 2·89 3. 7·98 4. 1·09 5. 0·88 6. 7·18
7. 5·81 8. 0·25 9. 5·02 10. 1·51 11. 0·48 12. 2·88
13. 0·28 14. 2·76
Fractions and decimals 22 page 116
1. 2·13 2·15 2·28 2·75 2·78 2·96 2. 6·09 6·2 6·23 6·24 6·5 6·61
3. 38·01 38·02 38·12 38·13 38·30 38·34 4. 1·004 1·04 1·041 1·14 1·4 1·44
5. 0·001 0·017 0·111 0·17 0·701 0·710
Fractions and decimals 23 page 117
A.
1. 1·8 2. 3·5 3. 7·4 4. 14·4 5. 39 6. 21·6
7. 24·8 8. 34·8 9. 30·6 10. 62·4
B
1. 14·12 2. 8·75 3. 18·96 4. 20·64 5. 10·36 6. 19·02
7. 36·7 8. 14·88 9. 36·42 10. 61·92 11. 16·2 12. 68·46
13. 78·21 14. 48·48
Fractions and Decimals 24 page 118
A.
1. 4·15 2. 4·3 3. 6·4 4. 3·4 5. 5·9 6. 2·3
7. 2·6 8. 4·3 9. 1·5 10. 3·6
B
1. 18·02 2. 2·34 3. 6·12 4. 3·12 5. 4·62 6. 7·21
7. 2·97 8. 1·36 9. 1·69 10. 0·38 11. 5·68 12. 4·49
13. 2·38 14. 0·46
235
2
5
2
5
Fractions and Decimals 25 page 119
1. 2 3.. 4. 5. 6. 6.
7. 12% 35% 0.4 8. 0·54 59% 60%
9. 0·35 40% 50% 10. 0 0·89 0·98 99%
11. 50% 12. 25% 13. 36% 14. 88%
Fractions and decimals 26 page 120
1. £150 £75 2. £34 £17 3. £45 £22·5 4. £7 £28
5. £70 £280 6. £2·60 £10.4 7. £2·75 £13·75 8. £20 £10
9. £7 £3·5 10. £6·60 £39·60 11. £5·40 £32·40 12. £7·80 £70·20
Fractions and Decimals 27 page 121
2.17 217% 1.17 117%
0.2 20% 0.96 96%
0.05 5% 0.35 35%
0.78 78%
Fractions and Decimals 28 page 122
1. a. 25 children b. 5 children c. 30%
2. a. 12 people b. 25% c. 6 people
Fractions and Decimals 29 page 123
1. 8 children 2. 80% 3. 20%
4. 20% of £55 = £11. of £30 = £12 . So of £30 is more by £1.
24
100
30
100 1 10
2
10
3
4
1
4
1
4
3
4 7
8
1 3
4 6
17 20
9
10
9
10
2
17
100 1
17
100
1
5
24
25
1
20 7
20
39
50
236
1
5
Ratio and Probability 1 page 124
A 1. The ratio is 2 red squares to every 3 yellow squares.
2. The ratio is 2 red squares to every 2 yellow squares.
B 1. 2 in 5 are red 2. 2 in 4 are red
Ratio and Probability 2 page 125
1. a. 1:3 b. 3 in 4 c. 4
2. a. 1:6 b. 4
3. a. 12 b. 1 in 6
4. a. 24 b. 1 in 3
Ratio and Probability 3 page 126
1. 1·75 × 6 = 10·5 litres of white paint.
2. a 1: 2 b. 1 in every 3 c. d. .
3. a 1: 4 b. 1 in every 5 c. d.
Ratio and Probability 4 page 127
1 out of 2 = = = 0·5 2. 5 out of 10 = = 0·5
3. 1 out of 10 = = 0.1 4. 4 out of 10 = = 0·4
5. 10 out of 10 = = 1
Ratio and Probability 5 page 128
1. equal chance 2. certain 3. good chance 4. impossible 5. biased
6. random 7. fifty-fifty chance 8. unlikely
Ratio and Probability 6 page 129
1. = 2. =
1
10
=-
1
2
=-
1 2
=- 4 10
=- 10
10
=-
2
3
1 2
1
4
3
9
=-
1
3
=-
4
20
=-
1
5
=-
237
Ratio and Probability 7 page 130
0 0·5 1
evens
0 0·1 0·2 0·3 0·4 0·5 0·6 0·7 0·8 0·9
evens
Handling Data 1 page 131
A. 1. 1 2. 22 3. 100 4. 4 5. 8 6. 5
B. 1. 9-3=6 2. 24-7=17 3. 10-3=7 4. 55-24= 31
5. 455- 75= 380 6. 77-22=55 7. 207-202=5
Handling Data 2 page 132
A 1. 3,4,4,5,6,7,8 = 5 2. 1,2,5,6,7,8,9 =6 3. 1,2,5,7,7,8,9 =7
4. 2,6,8,11,12,14,15=11 5. 24, 35,67=35 6. 0,0,0,2,4,5,9 =2
B 1. 14 + 18 = 32 ÷ 2 = 16 2. 4+6=10 ÷ 2 = 5 3. 14 + 16 = 30 ÷2=15
4. 3+5=8÷2=4 5. 7+7=14÷2=7 6. 56+68= 124÷2=62
A die will roll
an even number. A die will roll a
six A die roll a
zero.
A die roll a
number.
A die roll a one
or two. A die will not
roll a 4.
A die will roll a
seven A die will roll a
number greater
than three.
A 6 will be
picked. A number from 5
to 9 will be
picked An odd number
will be picked
A 2 or 3 will be
picked.
A ten will be
picked. A 6,7, or 8 will be
picked.
A 2 will not be
picked.
A number above 3
will be picked.
impossible certain
1
certain impossible
238
Handling Data 3 page 133
A. 1. 36÷6=6 2. 30÷6=5 3. 28÷7=4
4. 60÷6=10 5. 35÷7=5 6. 198÷3=66
7. 14÷7=2
B. 1. £4·50÷3=£1.50 2. £1·00÷4=25p 3. £5·70÷3=£1·90
4. £600÷3=£200 5. £9·60÷3 6. 60p÷4=15p
Handling Data 4 page 134
1. 32 2. 5 3. Only 1 Child scored 2
Data Handling 5 page 135
Type of Vehicle Number of Vehicles
Lorry 7
Bike 0
Car 15
Motor bike 4
Bus 2
2. Car 3. 28
Handling Data 6 page 136
1. 13 cm 2. 28 minutes 3. 15 minutes 4. 3:05 pm
Handling Data 7 page 137
1. a. At Valley Junior school 50 pupils walk.
b. At Star Primary school 90 pupils walk.
2. At Valley Junior school about one third of the pupils catch the bus this is around
66 pupils. At Star Primary school about a quarter of the pupils catch the bus this
is around 90 pupils. So more children catch the bus to Star Primary School.
Handling Data 8 page 138
1. 8 children 2. 12 children 3. 12 children 4. 4 children
Handling Data 9 page 139
a. 14 b. 32 c. 10 d. 30 e. 48 f. 22 g. 46 h. 26
Handling Data 10 page 140
a. 15 b. 6.5 c. 51 d. 27 e. 7.5 f. 63 g. 9 h. 39
239
Handling Data 11 page 141
a. 12 b. 5.5 c. 60 d. 76 e. 11.5 f. 100 g. 44 h. 12
Handling Data 12 page 142
1. 20 km 2. 25 km 3. 5 minutes 4. 20 km 5. 75 minutes
Handling Data 13 page 143
10 20 30 40 50 60 70
Time in minutes 1. 20 km 2. 30 km 3. 10km 4. 1km
Handling Data 14 check page 144
1. 40 litres 2. 80 litres 3. 45 litres 4. 130 litres
5. 9 gallons 6. 20 gallons 7. 31.5 gallons 8. 16 gallons
Gallons Litres(l)
0 0
2 9
4 18
6 27
8 36
10 45
Shape 1 page 145
1. AB and DC
2. Includes BC and DC or CF and EF or AB and BC or DC and AD or GE and EF
3. CF 4. AD or BC 5. 5 6. 24 7. 9
10
20
30
40
50
0
Distance from Jute
in kilometres
×
×
× 80
×
× ×
×
60
70
240
Shape 2 page 146
1. × 2. × 3 × 4. √ 5. √ 6. × 7. √ 8. √
Shape 3 page 147
Four parallelograms such as the ones below.
Four rhombi such as the ones below.
241
Shape 4 page 148
Draw 4 different trapezia such as the ones below.
. 4 different kites such as the ones below.
242
Shape 5 page 149
rectangle square √
parallelogram traprzium √
kite √
rhombus √
243
Shape 6 page 150
1. b 2. c 3. a 4. d 5.
6.
Shape 7 page 151
1.
Mirror line
Mirror line
244
2.
Shape 8 page 152
A (-4,2) B(1,2) C(1,-1) D(-4,-1)
5
4
B
A
3
2
1
-8 -7 -6 -5 -4 -3 -2 -1
1
1 2 3 4 5 6 7 8
-2
D
- 3
C
-4
0 0
Mirror line
245
Shape 9 page 153
Shape A has been translated 5 to the right, then 2 up.
Shape C has been translated 7 places to the left, then 1 down.
Shape 10 page 154
A square, rotated and translated B right-angle triangle, translated
C pentagon, rotated and translated D right-angle triangle, rotated and translated
E right-angle triangle, translated F Hexagon, rotated
Shape 11 page 155
( 0 , -3 ) ( -3 ,0 ) ( 0 , 3)
( 3, -2 ) ( -2 , -3) ( -3 , 2)
Shape 12 page 156
1. 30º 2. 65º 3. 50º 4. 125º 5. 37 º 63 º 80 º = 180º
6. 21º 54º 105º = 180º
Shape 13 page 157
acute right obtuse straight reflex
27º 90º 105º 180º 270º
11º 145º 310º
89º 125º 190º
256º
13. right angle 14. obtuse 15. acute 16. obtuse
Shape 14 page 158
1. 270º 2. 136º 3. 102º 4. 49º 5. 138 6. 18º
Shape 15 page 159
1. A 36º B 108 º C 36 º 2. D 100º E 34 º F 46 º
3. G 58 º H 45 º I 77 º
Shape 16 page 160
1. 2 × (7+5)cm 2×12cm=24cm 2. 2 × (16+4)cm 2×20cm=40cm
3. 2 × (23+28)cm 2×51cm=102cm 4. 2 × (19+12)cm 2×31cm=62cm
6. 6m-4m=2m, 3m-2m=1m 2×(2+1)m = 6m
7. 5m-2·5m = 2·5m = 2×(2·5+2·5)m = 10m
246
min
Shape 17 page 161
A. 14cm² B 17cm² C 17cm² D 147cm² E 252 cm² F 117 cm²
Shape 18 page 162
1. 190cm² 2. 600 cm²- 72cm²=528cm² 3. 135cm²-55cm²= 80cm²
4. 100cm- 12cm²-12cm²=76cm²
Shape 19 page 163
1. 375cm²-60cm²= 315 cm² 2. 187cm²² – 35cm²=152 cm²
3. 300cm² -20cm² =280 cm² 4. 416cm²-120cm²=296 cm²
Shape 20 page 164
A 6cm² B 18cm² ÷2= 9cm² C 24cm² ÷2= 12 cm² D 28cm² ÷2=14 cm²
E 40cm² ÷2=20 cm² F 120cm² ÷2= 60 cm²
Shape 21 page 165
A 27cm² B 33cm²
Shape 22 page 166
1. 11 blocks 2200cm² 2. 15 blocks 3000 cm²
Time 1 page 167
1. a. 35 minutes b. 1 hr 30 minutes c. 17:45 2. a. The monsters b. 2hrs 15
Time 2 page 168
1. 1:45 2. 20:41 3. 8:08 (20:08)
Time 3 page 169
1. 2 hours 2. 1 hr 30 min 3. 20 hours 4. Saturday 5. 39 hrs 30 min
Time 4 page 170
1. No she will be home at 7.20 pm
2. 3 × 25min = 75 min + 30 min = 1 hour 45 minutes
3. a. 35 minutes b. 2.35
Time 5 page 171
1. Bangkok 2. Rio de Janeiro 3. Los Angeles 4. 15 hours 5. 7 hours
247
Measuring 1 page 172
1. 167m 2. 570m 3. 1289m 4. 7·823km 5. 5·834km
6. 5·6cm 7. 2·3cm 8. 160cm 9. 270cm 10. 0·0085km
11. 1950mm 12. 3380mm 13. 456mm 14. 0·00064km 15. 0·00894km
Measuring 2 page 173
a. 5miles b. 10miles c. 12miles d. 19miles e. 27km f. 38km
g. 24km h. 5km
Measuring 3 page 174
1. 0·32m 2. 42·1km 3. 273·6cm 4. 30 5. 50cm 6 2·7m
7. 2·3m
Measuring 4 page 175
A. 7 kg 345g = 6345g B. 4kg 869g = 4869g C. 6kg 88g= 6088g
D. 5 kg 613g = 5613g
A. 6g B. 60g C. 6000g D. 600g
A 7·3 kg B. 4·9 kg C. 6·1 kg E. 5·5kg
The difference between A and C = 1·258kg
The difference between B and D = 0·744kg
Measuring 5 page 176
a. 200g b. 450g c. 280g d. 110g e. 4oz f. 5oz
g. 19oz h. 11oz
Measuring 6 page 177
1. 700g × 30 = 21000g = 21kg. 21÷5 = 4·2 Answer 5 journeys. 2. 5000 ÷ 120 = 41.66 Answer she can carry 41 paperbacks.
3. 11 × 230g = 2·53kg 10 × 190g = 1.90kg 17 × 350g = 5·95kg Total = 10·38kg
4. Hardbacks 10.38kg + paperbacks 5·04kg + encyclopaedias 21kg = 36·42 kg
36·42 – 30 kg = 6·42 Answer 2 journeys left.
Measuring 7 page 178
1. 2m × 2m × 2m = 8m³=8 tonnes 2. 6m × 2m × 2m = 24m³=24tonnes
3. 10m × 5m × 1m = 50m³=50tonnes 4. 4m × 2m × 1m = 8m³ × 1000 = 8000 kg³
5. 6m × 8m ×2m = 96m³ × 1000 = 96000 kg³
Money 1 page 179
1. 24050 rupees 2. 15020 yen 3. 357euro 4. 382·5 franc 5. $621
248
Money 2 page 180
1. 580 euro 2. $ 875 3. 5414 ringitt 4. 10129 peso
5. 1400krone 6. $474
Money 3 page 181
Country Exchange
rate May
Exchange
rate July
or Difference between
changing £100 in
May or July
Best
time to
travel
Australia 1·69 1·79 0·10 $10 May
Denmark 12·67 12·9 0·23 23 krone May
India 50·34 51·26 0·92 92 ruppees May
Japan 157·78 157·77 0·01 1 yen July
South Africa 10·36 11·02 0·66 66 rand May
Thailand 54·01 53·78 0·23 23 baht July
Money 4 page 182
1. 45 ÷ 14 = £3.00 2. 144 ÷ 7 = £21 3. 132 ÷ 13 = £10
4. 93 ÷ 3 = £31 5. 152 ÷ 12 = £13 6. 14 ÷ 3 = £5
7. 100 ÷ 14 = £7 8. 122 ÷ 3 = £41
Money 5 page 183
1. £391 2. £378 3. £40 5. £133 6. £18·50
Money 6 page 184
1. £5·25 2. 44coins 3. a. £261 b. 125 hours
249
Number Problems 1 page 185
1. factors of 18 multiples of 3
2. square numbers odd numbers
3. square numbers multiples of 2
Number Problems 2 page 186
1. 2.
Total =
Total = Total =
3. 4.
Total =
Total = Total =
36
16
1
48
3
32
4
4
1
16
16
2
8
64
12
144
9
4
23
28
22
27
21
17
89
71
113
47
29
101
59
5
24
26
20
25
72
512
1728
177
1 2
6
3
9 18 12 15
4 16 36
25
9
49 11 5 7
9
25
2 6 8 10 12 14
18 20
22 24 26 28 30
3 5 7 11 13
15 17 19 21
23 27 29
4 5 7 8 11
13 14 16 17
19 20
12
16
4
1
250
5. 6.
Total = Total =
Number Problems 3 page 187
1. 2.
3. 4.
5. 6.
Number Problems 4 page 188
1. 8 2. 15 3. 2 4. 5 5. 11 6. 2 7. 17 8. 99
9. ÷ + × 10. × - + 11. ÷ + × 12. ( + ) × 13. × - × 14. ÷ × -
28
49
98
2
2
12
36
3
4
18
9
1
14
196
4
7
1
2744
6
216
92610
735
126
6
21
35
7
5
3
2
6
5
2
4
30
10
8
80
300
24000
216000
300
720
24
30
10
5
2
6
4
6
3
9
2
18
27
18
486
486
236196
1728000
960
1800
45
40
24
8
3
5
9
7
6
3
5
42
18
15
270
756
204120
251
Number Problems 5 page 189
1. a. 4 boxes b. 768 2. a. £22·01 b. £4·90 c. £67·95
Number Problems 6 page 190
1. a. 940 marbles b. 20 boxes c. 94000
2. a. 160 cakes b. 100 packs c. £17·40
Number Problems 7 page 191
1. a. 28 b. £15·40 c. 84 bottles
2. a. 17p b. £20·40 c. 68p
Number Problems 8 page 192
1. a. £300·75 - £48·45 = £252 ÷ 36 = 7 hours.
b. £1260 ÷ 36 = 35 hours.
c. 21 × £36 = £756 + £246 = £1002
2. a. 300 balls b. 1% = 12 12 × 42 = 504 balls
Number Problems 9 page 193
1. a. 28p b. 18p c. £11·20
2. a. £5- £3·20 = £1·80 ÷ 4 = 45p b. £4·50 c. £2·70 ÷,45 = 6 pears
Number Problems 10 page 194
1. 870 ÷145 = 6 visits 2. a. Sofia b. 4 seconds
Number Problems 11 page 195
1. 45 2. 36 3. 56 4. 49
Number Problems 12 page 196
1. a. 5 7 11 23 13 b. 7 + 13 = 20 2. a. 4 9 16 25 b. 16-9=7
Number Problems 13 page 197
1. a. 64 2 4 1 16 8 32 b. 16 × 4 = 64
2. a. 1 2 4 5 6 8 9 10 12 15 18 30 36 40 45 60 72 90 120 180 360
b. 180-72=108
Number Problems 14 page 198
1. a. -7ºc b. 3ºc 2. a. -3ºc b. 8ºc
252
Number Problems 15 page 199
1. a=4 2. b=1 3. c=5 4. d=7 5. e=15 6. g=2 7. h=6
8. i = 2 j=3 or i = 4 j = 6 or i = 6 j = 9
9. k= 32 10. l=9 11. m=8 12. n =14 13. o= 6 14. p=17
Number Problems 16 page 200
1. a = 3 2. b = 2 3. c = 4 4. d = 7 5. e = 5 6. f = 3 7. g = 6 8. h =9
9. j = 1 k = 3 or j = 2 k = 1 10. m = 2 n = 1 or m = 4 n = 7
11. p = 1 r = 5 12. s = 4 t = 6
Number Problems 17 page 201
1. False 2. True 3. True 4. False 5. True 6. True 7. False
Number Problems 18 page 202
1. ÷ 2. ˂ 3. × 4. - 5. ÷ 6. = 7. ÷ 8. + 9. ˃ 10. +
11. × 12. ÷ 13. - 14. ×
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