How to Solve Proportions: Cross-Multiplication Made Simple
Published 15 November 2026 · Math
Try it nowProportion Calculator →A proportion states that two ratios are equal, such as 2/5 = 6/15. Whenever one value is missing you can find it with cross-multiplication. Check your answers with the free proportion calculator.
The cross-multiplication rule
Example 1: Recipe scaling
A recipe needs 300 g of flour for 4 people. How much for 10? Write 300/4 = x/10. Cross-multiply: 4x = 3,000, so x = 750 g.
Example 2: Map scale
On a map, 2 cm = 5 km. Two towns are 7.4 cm apart: 2/5 = 7.4/x → 2x = 37 → x = 18.5 km.
Example 3: Best value
If 3 cans cost $4.20, what do 8 cost? 3/4.20 = 8/x → 3x = 33.6 → x = $11.20.
Direct vs inverse proportion
Cross-multiplication works for direct proportion, where both values rise together. In inverse proportion one goes up as the other goes down – for example, more workers finish a job faster. There, multiply instead: 4 workers × 6 days = 24, so 3 workers need 24 ÷ 3 = 8 days.
Quick check
After solving, plug the answer back in. Both ratios should give the same decimal: 300 ÷ 4 = 75 and 750 ÷ 10 = 75. ✔
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15 Nov 2026