What is proportion?
A proportion shows that two ratios or quantities are equal, or that one amount keeps the same relationship to another.
A proportion compares quantities in a consistent relationship. In everyday maths, it often means two ratios are equal, such as 1:2 being proportional to 3:6.
For example, if a recipe uses 2 parts flour to 1 part sugar, doubling the recipe to 4 parts flour and 2 parts sugar keeps the same proportion.
Why proportions matter
Proportions help you scale recipes, compare prices, split totals, resize measurements and check whether two comparisons are equivalent. They are closely linked to ratios, percentages and unit prices.
Proportion formula
A common way to check a proportion is to compare two ratios. If both sides reduce to the same relationship, they are proportional.
a : b = c : da / b = c / dYou can also cross-multiply: if a × d equals b × c, the two ratios are in proportion.
Need to scale a proportion?
Use the ratio calculator to simplify ratios, scale them up or split a total into proportional parts.
Proportion example
Suppose a drink mix uses 1 part concentrate to 4 parts water. If you use 3 parts concentrate, the water should be 12 parts to keep the same proportion.
| Step | Calculation | Result |
|---|---|---|
| Original ratio | 1 : 4 | 1 part concentrate, 4 parts water |
| Scale factor | 3 ÷ 1 | 3 |
| Scaled proportion | 1 × 3 and 4 × 3 | 3 : 12 |
Proportion and ratios
A ratio compares parts. A proportion shows that two ratios are equal or keep the same relationship. For example, 2:5 and 4:10 are proportional because both simplify to 2:5.
4:10 ÷ 2 = 2:5This is why ratios and proportions often appear together in recipes, scale drawings, unit prices and sharing problems.
Proportion and percentages
A percentage is a proportion expressed out of 100. If 25 out of 100 items are selected, the proportion is 25/100 and the percentage is 25%.
This makes percentages useful when you want to compare proportions using the same base.
Common uses of proportions
- Scaling recipes up or down.
- Checking whether two ratios are equivalent.
- Converting part-to-whole comparisons into percentages.
- Comparing unit prices and value for money.
- Splitting totals fairly between people or categories.
Proportion FAQs
What does proportion mean?
A proportion shows that quantities keep the same relationship. In maths, it often means two ratios are equal.
Is proportion the same as ratio?
No. A ratio compares quantities, while a proportion says two ratios or comparisons are equivalent.
How do you check if two ratios are proportional?
Reduce both ratios to their simplest form or cross-multiply. If the relationship is the same, they are proportional.
Is a percentage a proportion?
A percentage is a proportion expressed out of 100. For example, 25% means 25 out of every 100.