© t madas. imagine two identical cakes we slice each of them into equal portions the slices in the...
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© T Madas
© T Madas
Imagine two identical cakes
We slice each of them into equal portions
The slices in the first cake are bigger
Some of the cake is taken away
What portion has been taken away from each cake?
13
39
© T Madas
Imagine two identical cakes
These fractions are called Equivalent FractionsThey are in fact the same fraction
13
39
13
39=
© T Madas
Let’sFindSomeEquivalentFractions
© T Madas
The fraction of has been shaded on
several diagrams below:
12
12
24
36
48
510
612
1530
50100
© T Madas
The fraction of has been shaded on
several diagrams below:
13
13
26
39
515
824
1030
2060
412
© T Madas
The fraction of has been shaded on
several diagrams below:
25
25
410
615
820
1025
1640
2050
40100
© T Madas
How do we find equivalent fractions without diagrams?
??
14 =
x 2
x 2
82 ?
?14 =
x 3
x 3
123 ?
?14 =
x 4
x 4
164
© T Madas
How do we find equivalent fractions without diagrams?
??
23
=
x 2
x 2
64 ?
?23
=
x 5
x 5
1510 ?
?23
=
x 7
x 7
2114
© T Madas
?23 18=
x 6
x 6
12
What is the missing numerator so that the two fractions are equivalent?
?45 20=
x 4
x 4
16
© T Madas
?34 20=
x 5
x 5
15
What is the missing numerator so that the two fractions are equivalent?
?45 30=
x 6
x 6
24
© T Madas
?27 21=
x 3
x 3
6
What is the missing numerator so that the two fractions are equivalent?
?18 72=
x 9
x 9
9
© T Madas
Now we start with a fraction with “big” numerator and denominator.
We will try to find an equivalent fraction with smaller numerator and denominator.
This is called cancelling down
© T Madas
What is in its simplest form?
1520
1520 = 3
4
© T Madas
What is in its simplest form?
812
812
= 23
© T Madas
Cancel down these fractions, to their simplest form:
??
612
=
÷ 6
÷ 6
21 ?
?4
12=
÷ 4
÷ 4
31 ?
?315 =
÷ 3
÷ 3
51
© T Madas
Cancel down these fractions, to their simplest form:
??
812
=
÷ 4
÷ 4
32 ?
?820
=
÷ 4
÷ 4
52 ?
?1215 =
÷ 3
÷ 3
54
© T Madas
Cancel down these fractions, to their simplest form:
??
912
=
÷ 3
÷ 3
43 ?
?1230
=
÷ 6
÷ 6
52 ?
?2530
=
÷ 5
÷ 5
65
© T Madas
We can cancel down in stages.
[usually with bigger numbers]
??
3048
=
÷ 2
÷ 2
1524
??
=
÷ 3
÷ 3
58
÷ 6
÷ 6
© T Madas
??
24120
=
÷ 2
÷ 2
1260
??
=
÷ 2
÷ 2
630
We can cancel down in stages.
[usually with bigger numbers]
??
=
÷ 2
÷ 2
315
??
=
÷ 3
÷ 3
15
÷ 24
÷ 24
© T Madas
Fraction Wall
© T Madas
© T Madas
© T Madas
1 whole
1/2
1/3
1/4
1/5
1/6
1/7
1/8
1/9
1/10
1/11
1/12
1/13
1/14
1/15
1/16
© T Madas
1 whole
© T Madas
1 whole
1/2
2/4
3/6
4/8
5/10
6/12
7/14
8/16
© T Madas
1 whole
1/2
1/3
1/4
1/5
1/6
1/7
1/8
1/9
1/10
1/11
1/12
1/13
1/14
1/15
1/16
© T Madas
1 whole
1/3
2/6
3/9
4/12
5/15
© T Madas
1 whole
1/2
1/3
1/4
1/5
1/6
1/7
1/8
1/9
1/10
1/11
1/12
1/13
1/14
1/15
1/16
© T Madas
1 whole
1/4
2/8
3/12
4/16
© T Madas
© T Madas
4 ?7 21
=12
What is the missing numerator so that the two fractions are equivalent?
3 ?5 20
= 12 2 ?9 18
= 4 4 ?7 14
=8
x3
x3
x4
x4
x2
x2
x2
x2
© T Madas
5 ?6 18
= 15
What is the missing numerator so that the two fractions are equivalent?
2 ?5 25
= 10 3 ?8 32
= 12 2 ?7 35
= 10
x3
x3
x5
x5
x4
x4
x5
x5
© T Madas
5 ?6 36
= 30
What is the missing numerator so that the two fractions are equivalent?
4 ?5 35
= 28 3 ?8 72
= 27 2 ?7 56
= 16
x6
x6
x7
x7
x9
x9
x8
x8
© T Madas
4 ?7 28
=16
What is the missing numerator so that the two fractions are equivalent?
3 ?5 15
= 9 2 ?9 81
= 18
4 ?7 35
= 20
x4
x4
x3
x3
x9
x9
x5
x5
© T Madas
5 ?6 36
= 30
What is the missing numerator so that the two fractions are equivalent?
2 ?5 20
= 8 3 ?8 24
= 9 2 ?7 42
=12
x6
x6
x4
x4
x3
x3
x6
x6
© T Madas
5 ?7 42
=30
What is the missing numerator so that the two fractions are equivalent?
4 ?9 63
= 28 3 ?4 36
= 27 2 ?3 24
= 16
x6
x6
x7
x7
x9
x9
x8
x8
© T Madas
5 ?6 12
= 10
What is the missing numerator so that the two fractions are equivalent?
2 ?5 15
= 6 3 ?8 40
= 15 3 ?10 40
=12
x2
x2
x3
x3
x5
x5
x4
x4
© T Madas
2 ?3 21
= 14
What is the missing numerator so that the two fractions are equivalent?
3 ?5 50
= 30 2 ?9 45
= 10
4 ?7 49
= 28
x7
x7
x10
x10
x5
x5
x7
x7
© T Madas
5 ?6 36
= 30
What is the missing numerator so that the two fractions are equivalent?
4 ?5 60
= 48 3 ?8 56
= 21 2 ?7 63
= 18
x6
x6
x12
x12
x7
x7
x9
x9
© T Madas
4 ?7 21
=12
What is the missing numerator so that the two fractions are equivalent?
3 ?5 30
= 18
2 ?9 45
= 10
4 ?7 28
= 16
x3
x3
x6
x6
x5
x5
x4
x4
© T Madas
5 ?6 42
= 35
What is the missing numerator so that the two fractions are equivalent?
2 ?5 15
= 6 3 ?8 72
= 27 2 ?7 56
=16
x7
x7
x3
x3
x9
x9
x8
x8
© T Madas
1 ?2 28
= 14
What is the missing numerator so that the two fractions are equivalent?
2 ?3 36
= 24 2 ?3 39
= 26 3 ?4 44
=33
x14
x14
x12
x12
x13
x13
x11
x11
© T Madas
© T Madas
1221
=4
Cancel down each of the following fractions to their simplest form
7
1220
=3
5
418
=2
9
814
=4
7÷3
÷3
÷4
÷4
÷2
÷2
÷2
÷2
© T Madas
1518
=5
Cancel down each of the following fractions to their simplest form
6
1025
=2
5
1232
=3
8
1035
=2
7÷3
÷3
÷5
÷5
÷4
÷4
÷5
÷5
© T Madas
3036
=5
Cancel down each of the following fractions to their simplest form
6
2835
=4
5
2772
=3
8
1656
=2
7÷6
÷6
÷7
÷7
÷9
÷9
÷8
÷8
© T Madas
1628
=4
Cancel down each of the following fractions to their simplest form
7
915
=3
5
1881
=2
9
2035
=4
7÷4
÷4
÷3
÷3
÷9
÷9
÷5
÷5
© T Madas
3036
=5
Cancel down each of the following fractions to their simplest form
6
820
=2
5
924
=3
8
1242
=2
7÷6
÷6
÷4
÷4
÷3
÷3
÷6
÷6
© T Madas
3042
=5
Cancel down each of the following fractions to their simplest form
7
2863
=4
9
2736
=3
4
1624
=2
3÷6
÷6
÷7
÷7
÷9
÷9
÷8
÷8
© T Madas
1012
=5
Cancel down each of the following fractions to their simplest form
6
615
=2
5
1540
=3
8
1240
=3
10
÷2
÷2
÷3
÷3
÷5
÷5
÷4
÷4
© T Madas
1421
=2
Cancel down each of the following fractions to their simplest form
3
3050
=3
5
1045
=2
9
2849
=4
7÷7
÷7
÷10
÷10
÷5
÷5
÷7
÷7
© T Madas
3236
=8
Cancel down each of the following fractions to their simplest form
9
4860
=4
5
2156
=3
8
1863
=2
7÷4
÷4
÷12
÷12
÷7
÷7
÷9
÷9
© T Madas
1221
=4
Cancel down each of the following fractions to their simplest form
7
1830
=3
5
1045
=2
9
1628
=4
7÷3
÷3
÷6
÷6
÷5
÷5
÷4
÷4
© T Madas
3542
=5
Cancel down each of the following fractions to their simplest form
6
615
=2
5
2772
=3
8
1656
=2
7÷7
÷7
÷3
÷3
÷9
÷9
÷8
÷8
© T Madas
1428
=1
Cancel down each of the following fractions to their simplest form
2
2436
=2
3
2639
=2
3
3344
=3
4÷14
÷14
÷12
÷12
÷13
÷13
÷11
÷11
© T Madas
© T Madas
4 ?7 21
=12
What is the missing numerator so that the two fractions are equivalent?
3 ?5 20
= 12 2 ?9 18
= 4 4 ?7 14
=8
x3
x3
x4
x4
x2
x2
x2
x2
5 ?6 18
= 15 2 ?5 25
= 10 3 ?8 32
= 12 2 ?7 35
= 10
x3
x3
x5
x5
x4
x4
x5
x5
© T Madas
4 ?7 21
=12 3 ?
5 30= 1
82 ?9 45
= 10
4 ?7 28
= 16
x3
x3
x6
x6
x5
x5
x4
x4
5 ?6 36
= 30
What is the missing numerator so that the two fractions are equivalent?
4 ?5 35
= 28 3 ?8 72
= 27 2 ?7 56
= 16
x6
x6
x7
x7
x9
x9
x8
x8
© T Madas
5 ?6 36
= 30 2 ?5 20
= 8 3 ?8 24
= 9 2 ?7 42
=12
x6
x6
x4
x4
x3
x3
x6
x6
4 ?7 28
=16
What is the missing numerator so that the two fractions are equivalent?
3 ?5 15
= 9 2 ?9 81
= 18
4 ?7 35
= 20
x4
x4
x3
x3
x9
x9
x5
x5
© T Madas
5 ?6 12
= 10 2 ?5 15
= 6 3 ?8 40
= 15 3 ?10 40
= 12
x2
x2
x3
x3
x5
x5
x4
x4
5 ?7 42
=30
What is the missing numerator so that the two fractions are equivalent?
4 ?9 63
= 28 3 ?4 36
= 27 2 ?3 24
= 16
x6
x6
x7
x7
x9
x9
x8
x8
© T Madas
5 ?6 36
= 30 4 ?5 60
= 48 3 ?8 56
= 21 2 ?7 63
= 18
x6
x6
x12
x12
x7
x7
x9
x9
2 ?3 21
= 14
What is the missing numerator so that the two fractions are equivalent?
3 ?5 50
= 30 2 ?9 45
= 10
4 ?7 49
= 28
x7
x7
x10
x10
x5
x5
x7
x7
© T Madas
5 ?6 42
= 35 2 ?5 15
= 6 3 ?8 72
= 27 2 ?7 56
=16
x7
x7
x3
x3
x9
x9
x8
x8
1 ?2 28
= 14 2 ?3 36
= 24 2 ?3 39
= 26 3 ?4 44
=33
x14
x14
x12
x12
x13
x13
x11
x11
What is the missing numerator so that the two fractions are equivalent?
© T Madas
© T Madas
1518
=5
6
1025
=2
5
1232
=3
8
1035
=2
7÷3
÷3
÷5
÷5
÷4
÷4
÷5
÷5
1221
=4
Cancel down each of the following fractions to their simplest form
7
1220
=3
5
418
=2
9
814
=4
7÷3
÷3
÷4
÷4
÷2
÷2
÷2
÷2
© T Madas
1628
=4
7
915
=3
5
1881
=2
9
2035
=4
7÷4
÷4
÷3
÷3
÷9
÷9
÷5
÷5
3036
=5
Cancel down each of the following fractions to their simplest form
6
2835
=4
5
2772
=3
8
1656
=2
7÷6
÷6
÷7
÷7
÷9
÷9
÷8
÷8
© T Madas
3042
=5
7
2863
=4
9
2736
=3
4
1624
=2
3÷6
÷6
÷7
÷7
÷9
÷9
÷8
÷8
3036
=5
Cancel down each of the following fractions to their simplest form
6
820
=2
5
924
=3
8
1242
=2
7÷6
÷6
÷4
÷4
÷3
÷3
÷6
÷6
© T Madas
1421
=2
3
3050
=3
5
1045
=2
9
2849
=4
7÷7
÷7
÷10
÷10
÷5
÷5
÷7
÷7
1012
=5
Cancel down each of the following fractions to their simplest form
6
615
=2
5
1540
=3
8
1240
=3
10
÷2
÷2
÷3
÷3
÷5
÷5
÷4
÷4
© T Madas
1221
=4
7
1830
=3
5
1045
=2
9
1628
=4
7÷3
÷3
÷6
÷6
÷5
÷5
÷4
÷4
3236
=8
Cancel down each of the following fractions to their simplest form
9
4860
=4
5
2156
=3
8
1863
=2
7÷4
÷4
÷12
÷12
÷7
÷7
÷9
÷9
© T Madas
1428
=1
2
2436
=2
3
2639
=2
3
3344
=3
4÷14
÷14
÷12
÷12
÷13
÷13
÷11
÷11
3542
=5
Cancel down each of the following fractions to their simplest form
6
615
=2
5
2772
=3
8
1656
=2
7÷7
÷7
÷3
÷3
÷9
÷9
÷8
÷8
© T Madas
© T Madas
1 10 2 52 15 6 10
4 5 1 48 20 4 20
2 4 2 28 12 3 6
4 1 5 210 5 10 10
50 1 10 11000 100 100 10
6 3 6 1216 4 8 15
4 2 1 210 5 20 10
4 2 3 26 15 6 3
© T Madas
7 10 2 514 15 6 10
4 4 1 48 20 5 16
2 1 2 29 3 3 6
4 1 5 410 5 10 20
1 5 10 12 100 100 20
6 3 9 1212 4 12 15
10 2 1 225 5 20 10
8 2 3 212 9 6 3
© T Madas
3 12 2 56 15 6 10
4 5 2 48 20 8 10
2 4 1 108 12 3 15
4 2 5 39 6 10 15
5 12 9 615 20 15 10
6 9 6 1216 12 8 15
4 6 5 810 15 20 30
8 2 3 1012 15 6 15
© T Madas
© T Madas
1 10 2 52 15 6 10
4 5 1 48 20 4 20
2 4 2 28 12 3 6
4 1 5 210 5 10 10
50 1 10 11000 100 100 10
6 3 6 1216 4 8 15
4 2 1 210 5 20 10
4 2 3 26 15 6 3
© T Madas
7 10 2 514 15 6 10
4 4 1 48 20 5 16
2 1 2 29 3 3 6
4 1 5 410 5 10 20
1 5 10 12 100 100 20
6 3 9 1212 4 12 15
10 2 1 225 5 20 10
8 2 3 212 9 6 3
© T Madas
3 12 2 56 15 6 10
4 5 2 48 20 8 10
2 4 1 108 12 3 15
4 2 5 39 6 10 15
5 12 9 615 20 15 10
6 9 6 1216 12 8 15
4 6 5 810 15 20 30
8 2 3 1012 15 6 15
© T Madas
© T Madas
1 4 2 52 8 6 10
4 5 1 48 20 4 16
2 4 1 29 12 3 6
4 1 5 220 5 10 10
100 1 10 11000 100 100 10
6 3 6 1216 4 8 16
4 2 8 210 5 20 10
4 10 3 26 15 6 3
© T Madas
12 3 2 620 5 6 10
20 15 5 1224 18 6 16
2 4 4 109 27 18 45
8 2 7 628 7 28 21
500 5 25 11000 100 500 20
8 4 28 1220 5 35 15
3 27 21 98 72 56 32
5 15 10 359 27 36 63
© T Madas
20 4 2 1245 9 3 27
15 55 5 1833 121 11 44
2 6 4 107 21 28 35
35 7 21 2840 8 24 36
50 4 20 11000 100 500 25
27 3 28 1845 5 35 30
21 56 28 724 72 36 9
5 12 4 249 21 7 42
© T Madas
© T Madas
1 4 2 52 8 6 10
4 5 1 48 20 4 16
2 4 1 29 12 3 6
4 1 5 220 5 10 10
100 1 10 11000 100 100 10
6 3 6 1216 4 8 16
4 2 8 210 5 20 10
4 10 3 26 15 6 3
© T Madas
12 3 2 620 5 6 10
20 15 5 1224 18 6 16
2 4 4 109 27 18 45
8 2 7 628 7 28 21
500 5 25 11000 100 500 20
8 4 28 1220 5 35 15
3 27 21 98 72 56 32
5 15 10 359 27 36 63
© T Madas
20 4 2 1245 9 3 27
15 55 5 1833 121 11 44
2 6 4 107 21 28 35
35 7 21 2840 8 24 36
50 4 20 11000 100 500 25
27 3 28 1845 5 35 30
21 56 28 724 72 36 9
5 12 4 249 21 7 42
© T Madas