Proportion Calculator

About Proportion Calculator

A proportion states that two ratios are equal. Cross-multiply and solve for the unknown.

How to use this calculator

1. Enter the known values for a, b, and c in the proportion \(\frac{a}{b} = \frac{c}{x}\).
2. Leave the unknown value as the missing quantity the calculator will solve for, which is \(x\) here.
3. Check that the ratios are set up in the same order on both sides, because the matching positions matter.
4. Click calculate to get \(x\) instantly, along with the proportional relationship used.

The formula explained

The formula \(x = \frac{bc}{a}\) finds the missing term in a proportion by cross multiplying and solving for \(x\). It tells you which value keeps the two ratios equal.

• a = the first term in the left ratio
• b = the second term in the left ratio
• c = the first term in the right ratio
• x = the missing second term in the right ratio

Step by step method

1. Write the proportion as \(\frac{a}{b} = \frac{c}{x}\).
2. Cross multiply to get \(ax = bc\).
3. Divide both sides by \(a\) to isolate the unknown, so \(x = \frac{bc}{a}\).

Worked example

Problem. Solve the proportion \(\frac{4}{6} = \frac{10}{x}\).

1. Cross multiply: \(4x = 6 \cdot 10\).
2. Simplify: \(4x = 60\).
3. Divide by 4: \(x = 15\).

Tips and common mistakes

• Make sure the numerators match each other and the denominators match each other in the same order, because switching terms changes the answer.
• If one number is zero, think carefully, because proportions with a zero denominator are not allowed.

Frequently asked questions