Proportion Calculator

This calculator solves algebraic proportions, which are equations involving two equal ratios. To use it, enter three known values and one unknown value (use 'x' or leave the box blank) in the format $A/B = C/D$. The calculator will solve for the missing variable and show the steps.

What is a Proportion?

A proportion is a statement that two ratios or fractions are equal. It is an equation that can be written in two forms:

• Fraction Form: $\frac{A}{B} = \frac{C}{D}$
• Ratio Form: $A : B = C : D$

In both forms, $A$ and $D$ are called the "extremes," and $B$ and $C$ are called the "means." A proportion is used to find a missing value when two quantities scale up or down at the same rate. For example, if you are scaling a recipe or reading a map, you are using proportions.

How to Solve a Proportion (Cross-Multiplication)

The easiest way to solve a proportion is by using **cross-multiplication**. This is also known as the "Means-Extremes Property."

For any proportion $\frac{A}{B} = \frac{C}{D}$, the product of the means equals the product of the extremes:

To solve for an unknown value (like $x$), you can rearrange this formula.

Example: Solve for $x$ in $\frac{2}{5} = \frac{x}{20}$

1. Set up the equation: $A=2$, $B=5$, $C=x$, $D=20$
2. Cross-multiply: $2 \times 20 = 5 \times x$
3. Simplify: $40 = 5x$
4. Isolate $x$: $x = \frac{40}{5}$
5. Solve: $x = 8$

Example: Solve for $x$ in $\frac{3}{10} = \frac{15}{x}$

1. Set up the equation: $A=3$, $B=10$, $C=15$, $D=x$
2. Cross-multiply: $3 \times x = 10 \times 15$
3. Simplify: $3x = 150$
4. Isolate $x$: $x = \frac{150}{3}$
5. Solve: $x = 50$

Algebraic vs. Statistical Proportions

It's important to know that this calculator solves **algebraic proportions** (ratios). This is different from **statistical proportions**, which relate to percentages or fractions of a population (e.g., "60% of voters"). Calculators for statistical proportions are used to find things like confidence intervals or the sample size needed for a survey.

Frequently Asked Questions (FAQ)

','

$A \times D = B \times C$