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. [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]
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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