Cross Multiplication Calculator

How to Solve Proportions with Cross Multiplication

Cross multiplication is a fundamental mathematical technique used to solve proportions. When you have two ratios set equal to each other in the form a/b = c/d, cross multiplication lets you find the unknown value quickly and accurately. Our Cross Multiplication Calculator handles this automatically with step-by-step solutions.

The Cross Multiplication Formula

Starting from the proportion $a/b = c/d$, cross multiplication gives $a \times d = b \times c$. From this equation, you can solve for any single unknown. For example, to solve for c you would use $c = (a \times d) / b$, and to solve for a you would use $a = (b \times c) / d$.

Real-World Applications

Cross multiplication appears in many everyday situations. Scale a recipe by finding how much flour you need for 16 servings when 3 cups makes 4 servings. Convert map distances using the scale ratio. Find unknown side lengths in similar triangles. Compare unit prices across different package sizes. Our calculator handles all of these scenarios.

Step-by-Step Example

To solve $3/4 = x/16$, first cross multiply to get $3 \times 16 = 4 \times x$, which simplifies to $48 = 4x$. Then divide both sides by 4 to find $x = 12$. You can verify the answer by checking that $3/4 = 0.75$ and $12/16 = 0.75$.

For more fraction and ratio tools, check out the Ratio Simplifier, Equivalent Fractions Calculator, and Fraction to Decimal Calculator.