To convert a ratio into a fraction, add the parts of the ratio to find the whole, then put each part over that total. In the ratio 3:5 there are 3 + 5 = 8 parts, so the first quantity is 3/8 of the whole and the second is 5/8. Simplify the fraction if you can. The one thing not to do is write 3:5 as 3/5 when the question asks for a share of the whole.
Ratio to fraction conversions come up throughout employer numeracy tests, often as a step towards a percentage or an amount. You can practise them in a free numerical reasoning test.
How to convert a ratio into a fraction, step by step
Example. A team’s staff are full-time and part-time in the ratio 7:3. What fraction of the team is part-time?
- Add the parts of the ratio. 7 + 3 = 10. This is the denominator, the bottom of the fraction.
- Put the part you want over the total. Part-time staff are 3 of the 10 parts, so the fraction is 3/10.
- Simplify if possible. 3 and 10 share no factor except 1, so 3/10 is already in its simplest form.
The full-time fraction is 7/10. The two fractions add up to 1, or 10/10, which is a useful check.
Why 3:5 is not the same as 3/5
A ratio compares one part with another part. A fraction of the whole compares one part with the total. In the ratio 3:5, the 3 is compared with the 5, not with all 8 parts.
Picture 3 red counters and 5 blue counters. There are 8 counters altogether, and 3 of them are red. The red counters are 3/8 of the total, not 3/5.
This is the trap most wrong answers are built on, so it is worth pausing on every time. For more on the difference, see our guide to ratio vs proportion.
When a/b is the right answer
There is one case where 3:5 does become 3/5. If the question asks how big the first quantity is compared with the second, rather than as a share of the whole, you divide one part by the other.
Example. A business has costs and revenue in the ratio 3:5. What fraction of revenue are the costs?
Here the question compares costs with revenue directly, so the answer is 3/5. Costs are 3/5 of revenue, which is 60%. Adding costs and revenue together would make no sense, so there is no “whole” to divide by.
Read the question for the word that follows “fraction of”. If it is the total, the team or the whole, add the parts. If it is the other quantity in the ratio, divide one by the other.
Converting three-part ratios
The method is the same however many parts the ratio has.
Example. A marketing budget is split between digital, print and events in the ratio 2:3:5. What fraction goes on each?
- Add the parts: 2 + 3 + 5 = 10.
- Digital: 2/10, which simplifies to 1/5.
- Print: 3/10.
- Events: 5/10, which simplifies to 1/2.
Check: 2/10 + 3/10 + 5/10 = 10/10 = 1.
Using the fraction to find an amount
Once you have the fraction, multiplying it by a total gives that share. This is the same as sharing an amount in a ratio, just written differently.
Example. The team above has 120 staff, full-time and part-time in the ratio 7:3. How many are part-time?
- Part-time staff are 3/10 of the team.
- 3/10 of 120 = 120 ÷ 10 × 3 = 36.
So 36 staff are part-time and 120 − 36 = 84 are full-time. Check: 84 ÷ 12 = 7 and 36 ÷ 12 = 3, which gives back the ratio 7:3.
Going on to a decimal or percentage
Tests often want the share as a percentage rather than a fraction. Convert the fraction by dividing the top by the bottom, then multiply by 100.
In the ratio 3:5, the first share is 3/8. 3 ÷ 8 = 0.375, which is 37.5%. The second share is 5/8 = 0.625, which is 62.5%. Together they make 100%.
There is more on the middle step in our guide to converting a fraction to a decimal.
Ratios with decimals or large numbers
Simplify the ratio first and the fraction will come out in its simplest form. For 1.5:2.5, multiply both parts by 10 to get 15:25, then divide by 5 to get 3:5. The first share is 3/8.
You can also convert first and simplify afterwards. For 6:4, the total is 10, so the first share is 6/10, which simplifies to 3/5. Both routes give the same answer. Our guide on how to simplify ratios covers the simplifying step in full.
Converting a fraction back into a ratio
To go the other way, take the fraction for one part, work out what is left, and compare the two.
Example. 2/5 of a team are women. What is the ratio of women to men?
- The fraction for women is 2/5, so the whole is 5 parts and women are 2 of them.
- Men are the remaining 5 − 2 = 3 parts.
- The ratio of women to men is 2:3.
Quick reference
| Ratio | Total parts | Fraction for each part |
|---|---|---|
| 1:1 | 2 | 1/2 and 1/2 |
| 1:3 | 4 | 1/4 and 3/4 |
| 3:5 | 8 | 3/8 and 5/8 |
| 7:3 | 10 | 7/10 and 3/10 |
| 2:3:5 | 10 | 1/5, 3/10 and 1/2 |
Practise ratio and fraction questions
In a test, the conversion is rarely the whole question. It is one step in a calculation about staff, budgets or sales, done under time pressure. A timed numerical reasoning practice test is the quickest way to make it automatic.