summer math packet -...
TRANSCRIPT
Summer Math Packet
Pre Algebra & Math 7
Students who have completed 6th Grade Math and will be taking Pre-Algebra or Math 7.
Topics
1) Whole Numbers: Multiplying & Dividing
2) Order of Operations
3) Decimals: Adding & Subtracting
4) Decimals: Multiplying & Dividing
5) Integers: Adding & Subtracting
6) Integers: Multiplying & Dividing
7) Fractions: Adding & Subtracting
8) Fractions: Multiplying & Dividing
NO CALCULATOR! SHOW ALL WORK!
1) Whole Numbers – Multiplying and Dividing A) 653 x 29 B) 1820 ÷ 28
1
4 2
653
x 29
5877
13060
18937
0
6528 1820
168
140
140
28
x 6
168
28
x 5
140
NO CALCULATOR! SHOW ALL WORK! 1. 975 x 8 2. 23 x 15 3. 471 x 16
4. 73 x 18 5. 981 x 65 6. 2970 ÷ 5
7. 32751 ÷ 9 8. 5472 ÷ 19 9. 42800 ÷ 25
2) Order of Operations
1) Parentheses (Grouping Symbols) (7 – 4)² + 3 • 5
2) Exponents = 3² + 3 • 5
3) Multiply or Divide, from left to right = 9 + 3 • 5
4) Add or Subtract, from left to right = 9 + 15
= 24
NO CALCULATOR! 1. 6 ÷ 3 + 2
2. 5 + 8 • 2 – 4
3. 16 ÷ 8 • 2²
4. 10 ÷ (3 + 2) + 9
5. 7 [(18 – 6) – 6]
6. 3 + (27 ÷ 9) – 5
7. (5 – 3)² + 3 8. [10 + (25 • 2)] ÷ 6
9. (9 • 2) + 18 ÷ 6
3) Decimals – Adding and Subtracting
1) Line up decimal points, if it does not have a one, it is a whole number with the decimal point at the end.
2) Use zeros to hold empty places.
3) Add or subtract vertically.
4) Bring down the decimal point.
4.8 + 3 + 5.6
4 . 8 0 3 . 0 0
+ 5 . 6 1 1 3 . 4 2
$10 – $7.40
10.00 ─ 7.40
2.60
NO CALCULATOR! SHOW ALL WORK!
1. 42.78 + 19.56 2. 0.0997 + 1.4 3. 6.29 + 5
4. $62.74 + $1.75 + $12 5. 0.0674 + 0.12 + 0.0098 6. 6 – 3.8
7. 40.75 – 17. 46 8. 0.95 – 0.68 9. $60 - $31.74
4) Decimals: Multiplying and Dividing
Multiplying
1) Line up digits, starting on the right.
2) Multiply
3) Place the decimal point in the answer by starting at the right and moving a number of places equal to the sum of the decimal places in both numbers multiplied.
(6.432)(4.15) 6.432 (3 decimal places) x 4.15 (2 decimal places) 32160 64320 2572800 26.69280 (5 decimal places)
Dividing
1) If the divisor is not a whole number, move the decimal point to the right to make it a whole number and move the decimal point in the dividend the same number of places.
2) Divide.
3) Bring the decimal point up.
27.216 ÷ 4.8
5.67 48.)272.16
-240 321
-288 336 ─ 336
0 NO CALCULATOR! SHOW ALL WORK!
1. 5.4 x 0.07
2. 5.9 x 1.2
3. 69.3 x 0.15 4. 3.96 x 3.3
5. 9.01 x 0.48 6. 0.24 ÷ 0.8
7. 84.48 ÷ 0.88 8. 6.56 ÷ 4
9. 34.06 ÷ 0.13 10. 147 ÷ 0 .49
5) Integers: Adding and Subtracting
Addition - SAME SIGNS -4 + (-5)
1) Add their absolute values. 4 + 5 = 9
2) Attach the common signs. -4 + (-5) = -9
Addition - OPPOSITE SIGNS 3 + (-9)
1) Subtract the smaller absolute value from the larger.
(9 – 3) = 6
2) Attach the sign of the number with the larger absolute value.
3 + (-9) = -6
Subtraction
1) Adding the opposite of a number is equivalent to subtracting the number.
2) Change all problems to addition and follow the addition rules.
3 – 12 = 3 + (-12) = -(12 – 3) = -9
- 7 – 1 = -7 + (-1) = -(7 + 1) = -8
-4 – (-10) = -4 + 10 = +(10 – 4) = 6
12 – ( -8) = 12 + 8 = 20
NO CALCULATOR! 1. 10 + (-9) = 2. –2 + 15 = 3. 15 – 19 =
4. -7 – (-4) = 5. – 12 – (-5) = 6. 0 – 9 =
7. 0 – (-7) = 8. -9 – 2 = 9. - 5 + 1 =
10. -3 + (-5) = 11. -9 – (-11) + (-4)= 12. -6 – 5 – (-8) =
6) Integers: Multiplying & Dividing
Same Signs: If two numbers have the same sign, their product or quotient is positive.
(-7)(-5) = 35 6 • 8 = 48
Different Signs: If two numbers have opposite signs, their product or quotient is negative
9(-2) = -18 (-3)(4) = -12
NO CALCULATOR! 1. (-7)(3) = 2. (5)(-4) = 3. (20)(-60) = 4. -8 • -5 =
5. -45 ÷ 5 =
6.
=
7. 56 ÷ (-7) = 8.
=
9. (4)(-2)(7) = 10. (-2)(-1)(4)(-6) =
11. -370 ÷ (-10) = 12.
=
13. (11)(-1)(-8)(-3) = 14.
=
15. (-60) ÷ (-12) = 16. (-6)(8)(-2)(5) =
7) Fractions – Adding & Subtracting 3 5
2 54 6
29 4
5
1) Convert to Improper Fractions. 11 35
4 6
9 22
1 5
2) Find LCD. LCD of 4 & 6= 24 LCD of 1 & 5 = 5
3) Change to equivalent fractions. 11 6 66 35 4 140
4 6 245 6 4 24
9 5 45
1 5 5
5) Add or Subtract the Numerators. 66 140 204
24 24
45 22 23
5 5
6) Simplify 204 12 17
24 12 2
7) Convert into a Mixed Number. 17
2
18
2
23
5
34
5
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8) Fractions: Multiplying &Dividing Multiplying 1) Change all mixed numbers to improper fractions. 2) Multiplying across.
3) Simplify
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Dividing 1) Change all mixed numbers to improper fractions. 2) Take the reciprocal. 3) Multiply across.
4) Simplify
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Answers 1) Whole Numbers – Multiplying and Dividing 1. 975 x 8 2. 23 x 15 3. 471 x 16 4. 73 x 18 5. 981 x 65 6. 2970 ÷ 5
7. 32751 ÷ 9 8. 5472 ÷ 19 9. 42800 ÷ 25
2) Order of Operations
1. 6 ÷ 3 + 2 2. 5 + 8 • 2 – 4 3. 16 ÷ 8 • 2²
4. 10 ÷ (3 + 2) + 9 5. 7 [(18 – 6) – 6] 6. 3 + (27 ÷ 9) – 5
7. (5 – 3)² + 3 8. [10 + (25 • 2)] ÷ 6 9. (9 • 2) + 18 ÷ 6
3) Decimals – Adding and Subtracting
1. 42.78 + 19.56 2. 0.0997 + 1.4 3. 6.29 + 5
4. $62.74 + $1.75 + $12 5. 0.0674 + 0.12 + 0.0098 6. 6 – 3.8 7. 40.75 – 17. 46 8. 0.95 – 0.68 9. $60 - $31.74
4) Decimals: Multiplying and Dividing 1. 5.4 x 0.07 2. 5.9 x 1.2 3. 69.3 x 0.15 4. 3.96 x 3.3
5. 9.01 x 0.48 6. 0.24 ÷ 0.8 7. 84.48 ÷ 0.88 8. 6.56 ÷ 4
9. 34.06 ÷ 0.13 10. 147 ÷ 0 .49
5) Integers: Adding and Subtracting 1. 10 + (-9) = 2. –2 + 15 = 3. 15 – 19 =
4. -7 – (-4) = 5. – 12 – (-5) = 6. 0 – 9 = 7. 0 – (-7) = 8. -9 – 2 = 9. - 5 + 1 =
10. -3 + (-5) = 11. -9 – (-11) + (-4)= 12. -6 – 5 – (-8) =
6) Integers: Multiplying & Dividing 1. (-7)(3) = 2. (5)(-4) = 3. (20)(-60) = 4. -8 • -5 =
5. -45 ÷ 5 =
6.
= 7. 56 ÷ (-7) = 8.
=
9. (4)(-2)(7) = 10. (-2)(-1)(4)(-6) =
11. -370 ÷ (-10) = 12.
=
13. (11)(-1)(-8)(-3) = 14.
=
15. (-60) ÷ (-12) = 16. (-6)(8)(-2)(5) =
7) Fractions – Adding & Subtracting
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6. 3
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8) Fractions: Multiplying &Dividing Multiplying 1) Change all mixed numbers to improper fractions. 2) Multiplying across.
3) Simplify
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Dividing 1) Change all mixed numbers to improper fractions. 2) Take the reciprocal. 3) Multiply across.
4) Simplify
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