© 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