How do you solve a proportion?

Use cross multiplication. For a/b=c/x, multiply a·x=b·c, then divide by a to get x=bc/a.

What is cross multiplication?

Cross multiplication means multiplying numerator of one fraction by denominator of the other fraction.

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Proportion Calculator

Solve a / b = c / x using cross multiplication

a / b = c / x

Proportion Formula

a/b = c/x → ax = bc → x = bc/a

A proportion states that two ratios represent the same relationship. Cross multiplication works because multiplying both sides by the two denominators removes the fractions without changing equality. Once the diagonal products are set equal, the missing value can be isolated with ordinary algebra. This method is widely used for scale problems, rate comparisons, similar figures, and unit conversions.

⚠Note: a and b cannot be zero in this a/b=c/x form.

What Is a Proportion?

A proportion is an equation that says two ratios are equal. It is one of the most common algebra tools for scaling quantities, comparing rates, solving similar triangle problems, and converting units.

Equal Ratios

If a/b and c/x describe the same relationship, their cross products must be equal.

Cross Products

For a/b=c/x, the diagonal products are ax and bc. Setting them equal gives a simple equation.

Missing Value

The unknown term can be found by isolating it after cross multiplication.

Scale Factor

Proportions often represent a constant multiplier between two related quantities.

💡 Example: 3/4 = 9/x → 3x = 36 → x = 12.

Applications of Proportions

Scale DrawingsSimilar TrianglesRecipesRates

Frequently Asked Questions

What is a proportion calculator?▼

A proportion calculator solves equations where two ratios are equal, such as a/b=c/x.

What is a proportion?▼

A proportion is an equation showing that two ratios are equal.

How does cross multiplication work?▼

For a/b=c/x, multiply diagonally to get ax=bc.

Can denominators be zero?▼

No. Denominators in a proportion cannot be zero.

Where are proportions used?▼

Proportions are used in scale drawings, recipes, rates, similar triangles, maps, and unit conversions.

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