Cross Multiplication Calculator

About Cross Multiplication Calculator

The Cross Multiplication Calculator is a free online tool that solves proportions quickly and accurately. Whether you are scaling a recipe, working with map distances, solving similar triangle problems, or handling any scenario involving equivalent ratios, this calculator finds the unknown value in an \(\frac{a}{b} = \frac{c}{d}\) equation and shows the complete step-by-step cross multiplication process with a visual diagram.

What is Cross Multiplication?

Cross multiplication is a mathematical technique used to solve proportions — equations that state two ratios are equal. Given the proportion:

Cross multiplication involves multiplying the numerator of each fraction by the denominator of the other fraction, producing a simple equation without fractions:

This transformation makes it straightforward to isolate and solve for any unknown value.

The Cross Multiplication Formula

Starting from the proportion \(\frac{a}{b} = \frac{c}{d}\), cross multiplication gives:

From this equation, you can solve for any single unknown:

• Solve for a: \(a = \frac{b \times c}{d}\)
• Solve for b: \(b = \frac{a \times d}{c}\)
• Solve for c: \(c = \frac{a \times d}{b}\)
• Solve for d: \(d = \frac{b \times c}{a}\)

How to Use This Calculator

1. Enter your known values — Type three of the four values (a, b, c, d) into the proportion fields. The layout shows \(\frac{a}{b} = \frac{c}{d}\).
2. Leave the unknown empty — Leave exactly one field blank. This is the value the calculator will solve for.
3. Click "Solve Proportion" — The calculator applies cross multiplication and displays the result instantly.
4. Review the solution — Examine the step-by-step cross multiplication process, the visual diagram with color-coded pairs, and verification that both cross products are equal.

You can also enter all four values to verify whether a proportion is valid.

Real-World Applications

Step-by-Step Example

Solve: \(\frac{3}{4} = \frac{x}{16}\)

1. Set up: \(\frac{3}{4} = \frac{x}{16}\)
2. Cross multiply: \(3 \times 16 = 4 \times x\)
3. Simplify: \(48 = 4x\)
4. Divide: \(x = \frac{48}{4} = 12\)
5. Verify: \(\frac{3}{4} = 0.75\) and \(\frac{12}{16} = 0.75\) ✓

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