A ratio compares one part with another part, such as 1 manager to every 2 analysts (1:2). A proportion compares one part with the whole, such as managers making up 1/3 of the team. In maths, “proportion” also has a second meaning: a statement that two ratios are equal, such as 1:2 = 4:8. So a ratio is a comparison, and a proportion is either a share of the whole or an equation between two ratios.
Mixing the two up is one of the most common ways to lose marks in a numerical test, so it is worth getting clear before you sit one. You can practise both in a free numerical reasoning test, where they usually appear inside a table or chart.
The difference at a glance
| Ratio | Proportion | |
|---|---|---|
| What it compares | One part with another part | One part with the whole, or two ratios with each other |
| How it is written | With a colon, such as 1:2 or 3:4:5 | As a fraction, decimal or percentage, such as 1/3 or 33.3%, or as an equation such as 1:2 = 4:8 |
| Can it be above 1? | Yes, 5:2 is a valid ratio | A share of the whole cannot be more than 1, or 100% |
| Typical question | “What is the ratio of permanent to temporary staff?” | “What proportion of staff are temporary?” |
The same data as a ratio and as a proportion
A team has 4 managers and 8 analysts, so 12 people in total.
- As a ratio, managers to analysts is 4:8. Dividing both parts by 4 simplifies it to 1:2. For every manager there are 2 analysts.
- As a proportion, managers are 4 out of 12 people, which is 4/12 = 1/3. As a percentage that is about 33.3%.
Notice that the ratio 1:2 does not mean managers are half the team. The 1 is compared with the 2, not with the total. To get the share of the whole, you add the parts of the ratio: 1 + 2 = 3, so managers are 1/3 of the team and analysts are 2/3. This is the trap test writers rely on most, and “50%” will often be one of the wrong answers.
If you want a fuller explanation of ratios on their own, start with what a ratio is.
How to turn a ratio into a proportion
Add the parts of the ratio to find the whole, then put each part over that total.
Example. Sales leads come from online and referral sources in the ratio 2:3. What proportion come from referrals?
- Add the parts: 2 + 3 = 5.
- Referrals are 3 of those 5 parts, so the proportion is 3/5.
- As a percentage: 3 ÷ 5 = 0.6, which is 60%.
This is the same method as converting a ratio into a fraction, which covers three-part ratios and other variations.
How to turn a proportion into a ratio
Work out the share that is left over, then compare the two shares.
Example. 30% of customers pay in cash. What is the ratio of cash payers to non-cash payers?
- The rest pay another way: 100% − 30% = 70%.
- Cash to non-cash is 30:70.
- Divide both parts by 10 to simplify: 3:7.
Proportion as two equal ratios
In maths, a proportion is also an equation that says two ratios are equal, such as 3:5 = 6:10. This is how you scale a ratio up or down, and it is behind most “how many would there be” questions.
Example. A warehouse keeps packing boxes and pallets in the ratio 3:5. It has 40 pallets. How many packing boxes should it have?
- Write the proportion: 3:5 = x:40.
- The pallet figure has gone from 5 to 40, which is a multiplier of 40 ÷ 5 = 8.
- Apply the same multiplier to the other side: 3 × 8 = 24 boxes.
You can also cross-multiply: 3 × 40 = 5 × x, so 120 = 5x and x = 24. Both methods give the same answer, so use whichever feels quicker.
Direct and inverse proportion
Two quantities are in direct proportion when they rise and fall together at the same rate. If 3 machines make 450 units an hour, each machine makes 450 ÷ 3 = 150 units, so 5 machines make 5 × 150 = 750 units an hour.
Two quantities are in inverse proportion when one rises as the other falls. If 4 people take 12 days to finish a job, the job takes 4 × 12 = 48 person-days in total. With 6 people it takes 48 ÷ 6 = 8 days. More people means fewer days.
Before you calculate, ask whether more of one thing should mean more or less of the other. That one check stops you scaling in the wrong direction.
Which one is the question asking for?
Read the wording carefully:
- “Ratio of A to B”, “for every” and “A:B” mean a ratio. Compare part with part, and keep the order the question uses.
- “Proportion of”, “what fraction of”, “what share of” and “what percentage of” mean a share of the whole. Divide the part by the total.
- “If there were 40 of B, how many of A” means two equal ratios. Find the multiplier and apply it to both sides.
Once you have the right type, the arithmetic is usually simple. For questions that ask you to split a total, see how to share an amount in a ratio.
Practise ratio and proportion questions
In a real test these questions rarely say “ratio” or “proportion” in a heading. They sit inside a staffing table, a budget breakdown or a sales chart, and you have to recognise which one is needed. A timed numerical reasoning practice test is the best way to build that recognition until it is automatic.