How to solve or simplify a ratio
- To solve a proportion, fill in three of A, B, C and D and leave the unknown one empty. The boxes read A : B = C : D.
- To simplify a ratio, enter A and B and leave C and D empty.
- Read the missing value with the full proportion under it, or the simplified ratio with its decimal, 1 : x form and A's share of the total.
Scaling a recipe with a proportion
Proportions are the quickest way to scale anything that has to keep the same balance. Say a recipe uses 250 g of flour to serve 4 and you’re cooking for 6. Write it as flour : people = flour : people:
- A = 250, B = 4, C is empty, D = 6
- C = 250 × 6 ÷ 4 = 375
So you need 375 g of flour. Run the same proportion for each ingredient, or work out the scale factor once (6 ÷ 4 = 1.5) and multiply everything by it. The same method scales a map distance, mixes paint or fuel at a fixed ratio, or converts a price for one size into another.
Reading the results
When you simplify, you get four views of the same ratio. For 18 : 24:
| Result | Value | What it means |
|---|---|---|
| Simplified ratio | 3 : 4 | Smallest whole numbers in the same proportion |
| As a decimal | 0.75 | A divided by B |
| As 1 : x | 1 : 1.333333 | How much B there is for every 1 of A |
| A as a share of the total | 42.86% | A divided by A + B |
The 1 : x form is handy for mixing instructions, such as 1 : 4 for a cordial or 1 : 50 for two-stroke fuel. A ratio can be turned around too: 3 : 4 and 4 : 3 describe the same pair of numbers, but order matters, so keep the parts in the same order on both sides of a proportion.