How to Solve a Proportion
A proportion is an equation stating that two ratios are equal: a/b = c/d. When three values are known, cross-multiplication finds the fourth: multiply along the diagonals and set the products equal, then divide to isolate the unknown.
missing value = (product of its diagonal pair) ÷ (the value opposite it)
If 3 notebooks cost $7.50, what do 8 notebooks cost? Set up 3/7.50 = 8/x. Cross-multiply: 3x = 7.50 × 8 = 60, so x = $20.
Setting Up Proportions Correctly
The most common mistake is mixing up which quantities belong on top. Keep the same kind of quantity in the same position on both sides: if the left ratio is notebooks over dollars, the right ratio must also be notebooks over dollars. As long as the structure matches, the cross-products will give the right answer.
- Recipes: 2 eggs / 3 cups flour = x eggs / 9 cups flour → x = 6.
- Maps: 1 cm / 4 km = 7.5 cm / x km → x = 30 km.
- Unit prices: $4.20 / 3 lb = x / 5 lb → x = $7.00.
Frequently Asked Questions
What is a proportion?
A proportion is an equation stating that two ratios (or fractions) are equal, written a/b = c/d. If three of the four values are known, the fourth can always be found by cross-multiplication.
How does cross-multiplication work?
In any true proportion a/b = c/d, the cross products are equal: a × d = b × c. To solve for a missing value, multiply the two numbers diagonal to it and divide by the number opposite it. For 3/4 = x/20: x = (3 × 20) ÷ 4 = 15.
What are proportions used for in real life?
Scaling recipes, converting currencies, reading maps, computing medicine doses by body weight, resizing images, and solving “if 3 shirts cost $27, what do 5 cost?” problems — any situation where two quantities grow at the same rate.
What is the difference between direct and inverse proportion?
In direct proportion both quantities rise together (more hours worked, more pay). In inverse proportion one rises as the other falls (more workers, less time). Cross-multiplication as used here applies to direct proportions.
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The CalculatorsGuide Editorial Team. (2026). Proportion Calculator. CalculatorsGuide. Retrieved from https://www.calculatorsguide.com/math/proportion-calculator/