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Transcript of © T Madas. Imagine two identical cakes We slice each of them into equal portions The slices in the...
![Page 1: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/1.jpg)
© T Madas
![Page 2: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/2.jpg)
© 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
![Page 3: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/3.jpg)
© T Madas
Imagine two identical cakes
These fractions are called Equivalent FractionsThey are in fact the same fraction
13
39
13
39=
![Page 4: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/4.jpg)
© T Madas
Let’sFindSomeEquivalentFractions
![Page 5: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/5.jpg)
© T Madas
The fraction of has been shaded on
several diagrams below:
12
12
24
36
48
510
612
1530
50100
![Page 6: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/6.jpg)
© T Madas
The fraction of has been shaded on
several diagrams below:
13
13
26
39
515
824
1030
2060
412
![Page 7: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/7.jpg)
© T Madas
The fraction of has been shaded on
several diagrams below:
25
25
410
615
820
1025
1640
2050
40100
![Page 8: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/8.jpg)
© 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
![Page 9: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/9.jpg)
© 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
![Page 10: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/10.jpg)
© 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
![Page 11: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/11.jpg)
© 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
![Page 12: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/12.jpg)
© 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
![Page 13: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/13.jpg)
© 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
![Page 14: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/14.jpg)
© T Madas
What is in its simplest form?
1520
1520 = 3
4
![Page 15: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/15.jpg)
© T Madas
What is in its simplest form?
812
812
= 23
![Page 16: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/16.jpg)
© T Madas
Cancel down these fractions, to their simplest form:
??
612
=
÷ 6
÷ 6
21 ?
?4
12=
÷ 4
÷ 4
31 ?
?315 =
÷ 3
÷ 3
51
![Page 17: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/17.jpg)
© T Madas
Cancel down these fractions, to their simplest form:
??
812
=
÷ 4
÷ 4
32 ?
?820
=
÷ 4
÷ 4
52 ?
?1215 =
÷ 3
÷ 3
54
![Page 18: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/18.jpg)
© T Madas
Cancel down these fractions, to their simplest form:
??
912
=
÷ 3
÷ 3
43 ?
?1230
=
÷ 6
÷ 6
52 ?
?2530
=
÷ 5
÷ 5
65
![Page 19: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/19.jpg)
© T Madas
We can cancel down in stages.
[usually with bigger numbers]
??
3048
=
÷ 2
÷ 2
1524
??
=
÷ 3
÷ 3
58
÷ 6
÷ 6
![Page 20: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/20.jpg)
© 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
![Page 21: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/21.jpg)
© T Madas
Fraction Wall
![Page 22: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/22.jpg)
© T Madas
![Page 23: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/23.jpg)
© T Madas
![Page 24: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/24.jpg)
© 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
![Page 25: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/25.jpg)
© T Madas
1 whole
![Page 26: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/26.jpg)
© T Madas
1 whole
1/2
2/4
3/6
4/8
5/10
6/12
7/14
8/16
![Page 27: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/27.jpg)
© 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
![Page 28: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/28.jpg)
© T Madas
1 whole
1/3
2/6
3/9
4/12
5/15
![Page 29: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/29.jpg)
© 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
![Page 30: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/30.jpg)
© T Madas
1 whole
1/4
2/8
3/12
4/16
![Page 31: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/31.jpg)
© T Madas
![Page 32: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/32.jpg)
© 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
![Page 33: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/33.jpg)
© 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
![Page 34: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/34.jpg)
© 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
![Page 35: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/35.jpg)
© 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
![Page 36: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/36.jpg)
© 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
![Page 37: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/37.jpg)
© 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
![Page 38: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/38.jpg)
© 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
![Page 39: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/39.jpg)
© 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
![Page 40: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/40.jpg)
© 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
![Page 41: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/41.jpg)
© 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
![Page 42: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/42.jpg)
© 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
![Page 43: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/43.jpg)
© 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
![Page 44: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/44.jpg)
© T Madas
![Page 45: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/45.jpg)
© 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
![Page 46: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/46.jpg)
© 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
![Page 47: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/47.jpg)
© 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
![Page 48: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/48.jpg)
© 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
![Page 49: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/49.jpg)
© 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
![Page 50: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/50.jpg)
© 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
![Page 51: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/51.jpg)
© 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
![Page 52: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/52.jpg)
© 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
![Page 53: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/53.jpg)
© 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
![Page 54: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/54.jpg)
© 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
![Page 55: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/55.jpg)
© 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
![Page 56: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/56.jpg)
© 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
![Page 57: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/57.jpg)
© T Madas
![Page 58: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/58.jpg)
© 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
![Page 59: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/59.jpg)
© 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
![Page 60: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/60.jpg)
© 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
![Page 61: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/61.jpg)
© 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
![Page 62: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/62.jpg)
© 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
![Page 63: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/63.jpg)
© 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?
![Page 64: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/64.jpg)
© T Madas
![Page 65: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/65.jpg)
© 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
![Page 66: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/66.jpg)
© 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
![Page 67: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/67.jpg)
© 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
![Page 68: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/68.jpg)
© 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
![Page 69: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/69.jpg)
© 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
![Page 70: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/70.jpg)
© 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
![Page 71: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/71.jpg)
© T Madas
![Page 72: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/72.jpg)
© 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
![Page 73: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/73.jpg)
© 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
![Page 74: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/74.jpg)
© 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
![Page 75: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/75.jpg)
© T Madas
![Page 76: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/76.jpg)
© 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
![Page 77: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/77.jpg)
© 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
![Page 78: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/78.jpg)
© 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
![Page 79: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/79.jpg)
© T Madas
![Page 80: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/80.jpg)
© 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
![Page 81: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/81.jpg)
© 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
![Page 82: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/82.jpg)
© 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
![Page 83: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/83.jpg)
© T Madas
![Page 84: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/84.jpg)
© 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
![Page 85: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/85.jpg)
© 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
![Page 86: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/86.jpg)
© 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
![Page 87: © 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.](https://reader031.fdocuments.in/reader031/viewer/2022013011/56649f345503460f94c518df/html5/thumbnails/87.jpg)
© T Madas