Fractions Re-cap1

Mathematics

Equivalent fractions spider diagram

Cancelling fractions to their lowest termsA fraction is said to be expressed in its lowest terms if the numerator and the denominator have no common factors.

Which of these fractions are expressed in their lowest terms?

14

16

20

27

3

13

15

21

14

35

32

15

Fractions which are not shown in their lowest terms can be simplified by cancelling.

7

8

5

7

2

5

Mixed numbers and improper fractionsWhen the numerator of a fraction is larger than the denominator it is called an improper fraction.

For example,

15

4is an improper fraction.

We can write improper fractions as mixed numbers.

15

4can be shown as

15

4= 3

3

4

Improper fraction to mixed numbers

Convert to a mixed number.378

378

=88

+ + +88

88

88

+58

581 + 1 + 1 += 1 +

= 4 5

8437 ÷ 8 = 4 remainder 5 37

8= 4

5

84This is the number of times 8 divides into 37.

4

This number is the remainder.

5

227733

Mixed numbers to improper fractions

Convert to an improper fraction.273

273 =

271 + 1 + 1 +

=77

+ + +77

77

27

=237

To do this in one step,

=

Multiply these numbers together …

… and add this number …

… to get the numerator.237

Find the missing number

Finding a fraction of an amount

We can see this in a diagram:

23

of £18 = £18 ÷ 3 × 2 = £12

23

of £18?What is

To find of an amount we need to add 1 times the amount to two fifths of the amount.

251

1 × 3.5 m =3.5 m and2

5of 3.5 m = 1.4 m

so, of 3.5 m =2

51 3.5 m + 1.4 m =4.9 m

What is of 3.5m?2

51

Finding a fraction of an amount

We could also multiply by 7

5

MathsBlox

Which is bigger or ?38

512

To compare two fractions convert them to equivalent fractions.

First we need to find the lowest common multiple of 8 and 12.

The lowest common multiple of 8 and 12 is 24.

Now, write and as equivalent fractions over 24. 38

512

38

=24

×3

×3

9and

512

=24

×2

×2

10so,

38

512

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Using equivalent fractions

Ordering fractions