Proportion Calculator - Solve for Unknown X

About the Proportion Calculator & Missing Variable Solver

A proportion is a mathematical statement demonstrating that two ratios or fractions are completely equal: A / B = C / D. When one of the four terms is unknown (commonly designated as x), a proportion solver uses the fundamental property of cross-multiplication to find the missing value.

Our Proportion Calculator allows you to find any missing number across all four positions (numerator or denominator on either side). It delivers instant step-by-step cross-multiplication workings, identifies the scale factor multiplier, and illustrates the proportion with high-contrast diagrams.

Proportion & Cross-Multiplication Formulas

All proportion solving is founded on the Means-Extremes Property (Cross-Multiplication):

How to Solve a Proportion Step-by-Step

1. Write the Proportion Equation: Set up the two fractions with the unknown quantity written as x (e.g. 3/4 = x/20).
2. Cross-Multiply Diagonally: Multiply the numerator of each fraction by the denominator of the opposite fraction: 3 × 20 = 4 × x.
3. Form a One-Step Linear Equation: Simplify the products: 60 = 4x.
4. Isolate the Variable: Divide both sides by the coefficient (4): x = 60 ÷ 4 = 15.

Worked Example: To solve 3/4 = x/20: Multiply 3 × 20 = 60. Then divide by 4: 60 ÷ 4 = 15. Therefore, x = 15.

Frequently Asked Questions (FAQ)

What is a proportion in math?

A proportion states that two fractions or ratios are mathematically equivalent, written as A/B = C/D or A:B = C:D.

How does cross-multiplication work?

Cross-multiplying multiplies the top of one fraction by the bottom of the other (A × D and B × C). Because both fractions are equal, their diagonal cross-products must also be equal.

Can x be a decimal or fraction?

Yes! If the product does not divide evenly by the coefficient, the solution can be written as an exact simplified fraction, mixed number, or rounded decimal.