# Cross Multiplication Calculator

Solve proportions using cross multiplication. Find any missing value in a/b = c/d and verify equality. Free online cross multiplication calculator.

## What this calculates

Solve any proportion using cross multiplication. Enter three values to find the missing fourth, or enter all four to verify whether the proportion is true. A fundamental tool for algebra and ratio problems.

## Inputs

- **Numerator 1 (a)** — The numerator of the first fraction.
- **Denominator 1 (b)** — The denominator of the first fraction.
- **Numerator 2 (c)** — The numerator of the second fraction.
- **Denominator 2 (d)** — The denominator of the second fraction.

## Outputs

- **Missing Value** — The solved missing value.
- **Cross Multiplication Equation** — formatted as text — The cross multiplication step: a x d = b x c.
- **Complete Proportion** — formatted as text — The full proportion with all four values.
- **Cross Products Equal?** — formatted as text — Verification that the cross products are equal.

## Details

Cross multiplication is the standard technique for solving proportions. Given a/b = c/d, cross multiplication states that a x d = b x c. This transforms a proportion into a simple equation.

How Cross Multiplication Works

Multiply the numerator of each fraction by the denominator of the other. If these cross products are equal, the proportion is valid. If one value is unknown, solve the resulting equation.

For example, 3/4 = x/20: cross multiply to get 3 x 20 = 4 x x, so 60 = 4x, giving x = 15.

When to Use Cross Multiplication

Use it whenever you have a proportion (two equal ratios) with one unknown. Common applications include unit conversions, recipe scaling, map distances, similar triangles, and solving percent problems.

## Frequently Asked Questions

**Q: What is cross multiplication?**

A: Cross multiplication is a method for solving proportions. For a/b = c/d, multiply diagonally: a x d and b x c. If the proportion is true, these products are equal. If one value is missing, set up the equation and solve. For example, x/6 = 10/15: cross multiply to get 15x = 60, so x = 4.

**Q: Why does cross multiplication work?**

A: Cross multiplication works because it is equivalent to multiplying both sides of the equation by both denominators. Starting with a/b = c/d, multiply both sides by b x d to get a x d = b x c. This eliminates the fractions and creates a simple equation. It is a shortcut for fraction clearing.

**Q: Can I cross multiply inequalities?**

A: You can cross multiply inequalities only when both denominators are positive. If a/b < c/d and b > 0 and d > 0, then a x d < b x c. If any denominator is negative, the inequality direction reverses. Always check the sign of the denominators before cross multiplying inequalities.

**Q: How is cross multiplication used in everyday life?**

A: Cross multiplication solves countless practical problems: scaling recipes (if 2 cups serve 4, how many cups for 10?), unit conversions (converting miles to kilometers), map reading (if 1 inch = 50 miles, what distance is 3.5 inches?), and calculating prices (if 3 items cost $12, what do 7 cost?).

**Q: Can cross multiplication be used with more than two fractions?**

A: Cross multiplication directly applies to two fractions. For chains like a/b = c/d = e/f, work with two fractions at a time. You can use the property that if all ratios are equal, a/b = c/d and c/d = e/f, solving pairs sequentially. For simultaneous proportion problems, set up a system of equations.

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Source: https://vastcalc.com/calculators/math/cross-multiply
Category: Math
Last updated: 2026-04-21