RatioLab

Proportion Calculator

Given three, find the fourth.

Solve a/b = c/x → x =

Cross-multiply to find the unknown

What you entered

a: 3b: 4c: 9

1
Cross-multiply: a/b = c/x → a·x = b·c
4 × 9= 36
2
Divide by a to isolate x
36 ÷ 3= 12

Result

Solve a/b = c/x → x =: 12

Solving 3/4 = 9/x gives x = 12.

Solving a proportion for the missing value

Given a over b equals c over x, cross-multiplying gives x equals b times c divided by a.

Proportion	Solved x
2/3 = 8/x	12.0000
1/4 = 5/x	20.0000
3/5 = 12/x	20.0000
5/8 = 20/x	32.0000
2/7 = 6/x	21.0000

Every row scales the first fraction up by a whole-number factor - 2/3 becomes 8/12 by multiplying both parts by 4 - which is what a proportion is: two fractions of equal value. This is the arithmetic behind scaling a recipe, converting between units, working out map distances and resizing images while keeping the aspect ratio. The one thing to check is that the quantities are in matching positions on both sides; swapping numerator and denominator on one side inverts the answer.

Cross-multiplication, explained

When two ratios are set equal (a/b = c/x), cross-multiplying (a·x = b·c) clears the fractions and leaves a simple equation to solve for the unknown.

Where proportions come up

Scaling a recipe up for more guests, converting map distances to real distances, and solving 'if 3 apples cost $2, how much do 7 apples cost?' are all classic proportion problems.

Frequently asked questions

How do I solve a proportion?

Cross-multiply: if a/b = c/x, then a×x = b×c, so x = b×c/a. Example: if 3 apples cost $2, how much do 7? Set up 3/2 = 7/x → 3x = 14 → x = $4.67.

A recipe calls for 2 cups of flour for 12 cookies. How much for 30?

Set up the proportion: 2/12 = x/30. Cross-multiply: 12x = 60, so x = 5 cups. Proportions make recipe scaling foolproof — just keep the ratio constant.

How is a proportion different from a ratio?

A ratio compares two quantities (3:4). A proportion is an equation stating two ratios are equal (3/4 = 6/8). Ratios describe; proportions solve for unknowns. Use the ratio calculator to simplify, and this proportion calculator to find missing values.

What is direct vs inverse proportion?

Direct: as one goes up, so does the other (more hours worked = more pay). Inverse: as one goes up, the other goes down (more workers = less time to finish). Direct uses a/b = c/x; inverse uses a×b = c×x.