Ratios in everyday life
A ratio compares two amounts: 2 parts paint to 3 parts water, 16 wide to 9 high, 3 teachers for every 40 pupils. A proportion says two ratios are equal, which lets you scale things up or down. Double a recipe, stretch an image, or split a bill in the same shares as last time, and you are working with proportions.
This ratio calculator does the three jobs people need most. It finds the missing number in a proportion, simplifies a ratio to its smallest whole numbers, and shares an amount between two or three people in a given ratio.
How to use it
- Choose Solve a : b = c : x, Simplify a ratio, or Share an amount.
- To solve, enter a, b and c. The calculator finds x so that a : b = c : x.
- To simplify, enter the two numbers. Decimals are fine.
- To share, enter the total and the parts of the ratio. The third part is optional.
- Read the answer and the steps, including a check that the proportion holds.
The ratio rules
a : b = c : x means a ÷ b = c ÷ x
cross-multiply: a × x = b × c, so x = b × c ÷ a
simplify: divide both sides by their greatest common factor
share: one part = total ÷ sum of the partsCross-multiplying is the key move: in a true proportion, the outside numbers multiplied together equal the inside numbers multiplied together. For simplifying, decimals are scaled up to whole numbers first, so 1.5 : 2.25 becomes 150 : 225 and then 2 : 3.
Worked example: 3 : 4 = 15 : x
- Cross-multiply: 3 × x = 4 × 15 = 60
- Divide: x = 60 ÷ 3 = 20
- Check: 3 × 20 = 4 × 15, both 60
So x = 20, and 3 : 4 is the same ratio as 15 : 20. In a kitchen: if 3 cups of flour need 4 eggs, 15 cups need 20 eggs. Switch to Share an amount to split 1,200 in the ratio 2 : 3: one part is 240, so the shares are 480 and 720.
Common ratios
| Ratio | First share | Second share |
|---|---|---|
| 1 : 1 | 50% | 50% |
| 1 : 2 | 33.3% | 66.7% |
| 2 : 3 | 40% | 60% |
| 1 : 3 | 25% | 75% |
| 3 : 7 | 30% | 70% |
| 1 : 4 | 20% | 80% |
Mistakes that trip people up
- Swapping the order. 2 : 3 and 3 : 2 are different ratios; keep the parts in the same order on both sides.
- Treating a ratio as a fraction of the whole. In 2 : 3, the first share is 2 out of 5, not 2 out of 3.
- Mixing units. Compare like with like, such as minutes with minutes.
- For screen and image shapes, the aspect ratio calculator handles pixel sizes directly.
Frequently asked questions
How do I solve a proportion?
Cross-multiply and divide. For 3 : 4 = 15 : x, multiply the outside numbers and the inside numbers: 3x = 60, so x = 20. Choose Solve a : b = c : x above, enter the three numbers you know, and the calculator shows the cross-multiplication and checks the answer.
How do I simplify a ratio?
Divide both numbers by their greatest common factor. 18 : 24 has a common factor of 6, so it simplifies to 3 : 4. If the numbers have decimals, multiply both by 10 or 100 first to make them whole. The calculator does this automatically.
How do I divide an amount in a ratio?
Add the parts of the ratio, divide the total by that sum to get one part, then multiply. To split 1,200 in the ratio 2 : 3, there are 5 parts, so one part is 240, and the shares are 480 and 720. Choose Share an amount above.
What is the difference between a ratio and a proportion?
A ratio compares two amounts, like 3 : 4. A proportion states that two ratios are equal, like 3 : 4 = 15 : 20. You use proportions to scale a ratio up or down while keeping the same balance, which is exactly what the Solve mode does.
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