A ratio is a way of comparing two or more quantities, showing how much of one there is for each amount of another. It is usually written with a colon, so 3:2 is read as “3 to 2”. If a recipe uses 3 cups of flour for every 2 cups of sugar, the ratio of flour to sugar is 3:2, whether you make one batch or ten.
Ratios come up constantly at work, from staffing levels to budgets, and they are a regular feature of any free numerical reasoning test.
Ratio definition
In mathematics, a ratio is a comparison of quantities of the same kind that tells you their relative size. Each number in a ratio is called a term or a part. The ratio 3:2 has two parts: 3 of the first thing for every 2 of the second.
A ratio does not tell you the actual amounts, only how they compare. A team with a ratio of 2:3 could have 2 and 3 people, 20 and 30, or 200 and 300. What stays fixed is the relationship.
Three things to remember:
- Order matters. Managers to staff of 1:6 is not the same as staff to managers of 1:6.
- The units must match. You cannot compare 30 minutes with 2 hours as 30:2. Convert first, to 30:120, which is 1:4.
- A ratio can have more than two parts. A budget split 2:3:5 compares three amounts at once.
How a ratio is written
The same ratio can be written in several ways, and tests use all of them:
- With a colon: 3:2
- In words: 3 to 2, or 3 for every 2
- As a fraction: 3/2, when comparing the first quantity to the second
Phrases such as “per”, “for every” and “out of” in a question are often a sign that a ratio is involved.
Ratio examples
Ratios appear in many everyday places.
- Recipes. Two parts squash to five parts water is 2:5. Make more by keeping the ratio the same.
- Map scales. A scale of 1:25,000 means 1 cm on the map stands for 25,000 cm, or 250 metres, on the ground.
- Screen shapes. A 16:9 screen is 16 units wide for every 9 units high, whatever its actual size.
- Staffing. A warehouse with 84 operatives and 12 supervisors has a supervisor to operative ratio of 12:84, which simplifies to 1:7.
- Mixing materials. A mortar mix of 1 part cement to 4 parts sand is 1:4.
Part-to-part and part-to-whole ratios
Most ratios compare one part with another. Some questions need you to compare a part with the whole.
Take a team of 10 with 4 men and 6 women. The part-to-part ratio of men to women is 4:6, which simplifies to 2:3. To get the part-to-whole share, add the parts: 2 + 3 = 5. Men make up 2/5 of the team and women make up 3/5.
Mixing these up is one of the most common errors in tests. A ratio of 2:3 does not mean the first group is 2/3 of the total. Our guide on how to convert a ratio into a fraction explains this step in detail.
Equivalent ratios and simplest form
Ratios that describe the same relationship are called equivalent. 2:3, 4:6, 10:15 and 200:300 are all equivalent, because each is the first multiplied or divided by the same number on both sides.
The simplest form is the version with the smallest whole numbers. To get there, divide every part by the largest number that goes into all of them. 6:9 divided by 3 gives 2:3. Our guide on how to simplify ratios works through harder cases.
Ratio, fraction and proportion
These three ideas are closely linked, which is why they are easy to confuse.
- A ratio compares parts with each other: 2 men to 3 women is 2:3.
- A fraction compares a part with the whole: men are 2/5 of the team.
- A proportion says two ratios are equal: 2:3 is in proportion to 20:30.
For a fuller comparison, read our guide to ratio vs proportion.
Ratios in a numerical reasoning test
Ratio questions in tests usually ask you to do one of three things: write two amounts as a ratio, share a total in a given ratio, or use a ratio to find a missing amount. The method behind all three is to find the value of one part.
Example. A firm employs 120 people, split between office and field roles in the ratio 5:3. How many work in the field?
- Add the parts: 5 + 3 = 8.
- Find one part: 120 ÷ 8 = 15.
- Field roles are 3 parts: 3 × 15 = 45 people.
Check: office roles are 5 × 15 = 75, and 75 + 45 = 120.
For step-by-step methods covering every type, see our guide on how to calculate a ratio. Then try ratio questions alongside percentages and data tables in a timed numerical reasoning test.