fractions

15

13

12 Fractions

Equivalent Fractions look different but hold the same value

34

110

112

112

112

112

112

112

112

112

112

112

112

112

110

12

110

110

110

110

110

110

110

110

18

18

18

18

18

18

18

18

16

16

16

16

16

16

15

15

15

15

15

14

14

14

14

13

13

13

12

1 whole

A B

15

13

12 Fractions


34

12

48

What is the fraction shaded red in each case?

15

13

12 Fractions


34

What fraction of rectangle A is shaded?

A

B

What fraction of rectangle B is shaded?

23

69

15

13

12 Fractions


34

Do rectangles A and B show equivalent fractions?

A

28

B

36

15

13

12 Fractions


34

13

26=

How can I find an equivalent fraction to the one below?

39

13 =

13

412=

x2

x2

x3

x3

x4

x4

Whatever you do to the top you must do to

the bottom andvice versa!

15

13

12 Fractions


34

23 12=

Try these.

x4

x4

8 610 =

÷2 35÷2 416 =

÷4 312÷4

35 35=

x7

x7

21 3240 =

÷8 45÷8 464 =

÷16 348÷16

15

13

12 Fractions

Which fraction is bigger?

34

14

17

This seems obvious with a picture but how do we do it without a picture?

If I can find a common denominator I can compare the fractions

Denominator

Numerator

Which fraction is bigger?

47

35or

The denominator tells us how many pieces the whole has been split into

15

13

12 Fractions 3

4

34

24

is bigger than

Common Denominators

Finding a common denominator

15

13

12 Fractions 3

4

35

47

Easiest way is tomultiply denominators

3535 == 2120

47

35

and

Finding a common denominator

15

13

12 Fractions 3

4

35

23

Easiest way is tomultiply denominators

1515 == 910

23

35

and

- =45

35- = 1

5

+ =17

37+ = 4

7

They must have a common denominator

Adding and Subtracting

15

13

12 Fractions 3

4

=12

13+ = 2

5 +

+What if they have different denominators


15

13

12 Fractions 3

4

A common mistake is shown below

This doesn't make any sense!!

=+12

13+

=


15

13

12 Fractions 3

4

They must have a common denominator

6 6+ Find common denominatorby multiplying 2 by 3

36

26+= Find equivalent fractions

with denominator of 6

= 56

23

15+

= 15+1510 3

= 1513


15

13

12 Fractions 3

4

34

23-

= 12-129 8

= 121

23

12+

46

36+=

= 76

= 161


15

13

12 Fractions 3

4

=

Sometimes you end up witha bigger number on the top.

We can write this another way.

13

13+ =5 2

33 2+ =


15

13

12 Fractions 3

4

16

56+ = 41 2

+ =

Its sometimes easierto visualise fractions

with pictures

45

35+ =5 7

53 2+ = =


15

13

12 Fractions 3

4

35

15- = 13 2

- =

= 6 25

25

What is 1 2 of 1

4 ?

Multiplying Fractions

15

13

12 Fractions 3

4

What is 1 2 of 1

4 ?


15

13

12 Fractions 3

4

What is 1 2 x 1

4 ?

Is there a difference between these questions?

From our work with areas of triangles

12m

9m

Area = x b x h12

Area = x 12 x 912

Area = 6 x 9 Area = 54m2

Therefore 12 of 12 1

2 x 12means and vice versa

Multiply the numerators Multiply the denominators

Rule

1 2 of 1

4 =1 8

1 2 x 1

4 =1 8 or

We can see visually


15

13

12 Fractions 3

4

But can we do this without

drawing a picture?

One eighth

1 3 x 1

5 =1 15


15

13

12 Fractions 3

4

3 4 x 2

3 =6 12

One Fifth

One Third

Solution

Solution

1 2 ÷ 1

4 = 2

Dividing Fractions

15

13

12 Fractions 3

4

If we look firstly at 6 ÷ 2We interpret this as how many 2's are in 6

If we now look at

Dividing is the same as multiplying by the inverse

3 8 ÷ 2

5 = ?

Dividing Fractions

15

13

12 Fractions 3

4

Imagining the diagrams can become complex though

We need a better way!

Often mathematical rules are about spotting patterns

10 ÷ 1 2 = 20 10 x 2

1 = 20

9 ÷ 1 3 = 27 9 x 3

1 = 27

3 ÷ 1 4 = 12 3 x 4

1 = 12

3 8 ÷ 2

5 = ?

Dividing Fractions

15

13

12 Fractions 3

4

Can we now solve this calculation without a diagram?

3 8 ÷ 2

5

= 3 8 x 5

2 = 15

16

4 7 ÷ 1

3

= 4 7 x 3

1= 12

7 = 1 5 7

3 4 ÷ 5

6

= 3 4 x 6

5 = 18

20 =9 10

1 hour

hour1 4

hour1 2

hour3 4

60 mins

15 mins

30 mins

45 mins

=

=

=

=

15

13

12 Fractions 3

4

Fractions of time

What fraction of an hour would 12 mins be?

15

13

12 Fractions 3

4

Fractions of time

Changing minutes into a fraction of an hour

30mins = 30 60 =

3 6 =

1 2

÷10

÷10

÷3

÷3

12mins = 12 60 =

2 10 =

1 5

÷6

÷6

÷2

÷2

36mins = 36 60 =

6 10 =

3 5

÷6

÷6

÷2

÷2

Always simplifyas much as you

are able to

15

13

12 Fractions 3

4

Fractions of time

Changing fractions of an hour into minutes

15 hr = 60mins ÷ 5 = 12mins

13 hr = 60mins ÷ 3 = 20mins

512 hr = 60mins ÷ 12 x 5 = 25mins

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