3.1 Using equivalent fractions
Equivalent fractions are fractions that are the same as each other, but are expressed in different ways. The BBC Skillswise website has an explanation of equivalent fractions.
To make an equivalent fraction, you multiply or divide the numerator (top) and denominator (bottom) by the same number. The size of the fraction is not altered. For example:
In the fraction , the numerator is 4 and the denominator is 6.
4 × 2 = 8
6 × 2 = 12
So =
In the fraction , the numerator is 10 and the denominator is 15.
10 ÷ 5 = 2
15 ÷ 5 = 3
So =
Example: Looking at equivalent fractions
Arrange the following fractions in order of size, starting with the smallest:
- , ,
Method
You need to look at the bottom number in each fraction (the denominator) and find the lowest common multiple. In this case, the bottom numbers are 6, 3 and 12, so the lowest common multiple is 12:
- 6 × 2 = 12
- 3 × 4 = 12
- 12 × 1 = 12
Whatever you do to the bottom of the fraction you must also do to the top of the fraction, so that it holds the equivalent value. The third fraction, , already has 12 as its denominator, so we don’t need to make any further calculations for this fraction. But what about and ?
- 2 × means calculating (2 × 3 = 6) and (2 × 6 = 12), so the equivalent fraction is
- 4 × means calculating (4 × 1 = 4) and (4 × 3 = 12), so the equivalent fraction is
Now you can now see the size order of the fractions clearly:
- , ,
So the answer is:
- , ,
Use the examples above to help you with the following activity. Remember to check your answers once you have completed the questions.
Activity 19: Fractions in order of size
- Put these fractions in order of size, with the smallest first:
- , , , ,
Answer
Remember that when the numerator of a fraction is 1, the larger the denominator, the smaller the fraction.
From smallest to largest, the order is:
- , , , ,
- What should you replace the question marks with to make these fractions equivalent?
- =
- =
- =
- =
Answer
- =
- =
- =
- =
- Put these fractions in order of size, with the smallest first:
- , ,
Answer
You need to change to equivalent fractions to compare like-for-like. To do this, you need to look at the bottom numbers of the fractions (3, 5 and 10) and find the lowest common multiple. The lowest common multiple of 3, 5 and 10 is 30:
3 × 10 = 30
5 × 6 = 30
10 × 3 = 30
Whatever you do to the bottom of each fraction, you must also do to the top:
With , you need to multiply the top and bottom numbers by 10 to make .
With , you need to multiply the top and bottom number by 6 to equal .
With , you need to multiply the top and bottom number by 3 to equal.
The order of the fractions from smallest to largest is therefore:
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