Fractions, Ratios & Proportions

How to Solve a Proportion

A proportion states that two ratios are equal. Cross multiplication converts the proportion into a simple equation.

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Quick answer

A proportion states that two ratios are equal. Cross multiplication converts the proportion into a simple equation.

Formula or method

If a/b = c/d, then ad = bc

Keep units, percentages and time periods consistent. The formula is useful as a transparent check on the calculator result and helps explain why changing one input changes the answer.

Step-by-step

  1. Write the ratios in the same order.
  2. Cross multiply.
  3. Solve the resulting equation.
  4. Substitute the answer back to check.

Worked example

For 3/5 = x/20, 3×20 = 5x, so x = 12.

How to interpret the result

Proportions appear in scaling, rates, maps, recipes and percentage questions.

When the answer is used for a purchase, loan, payroll decision, construction order, school grade, health estimate or other real-world choice, verify the assumptions that matter in that context. Accurate arithmetic still depends on accurate inputs.

Common mistakes

  • Reversing only one ratio.
  • Cross multiplying incorrectly.
  • Mixing units without converting.

Frequently asked questions

Can I solve by scaling instead?

Yes, when the scale factor is obvious.

What if a denominator is zero?

The ratio is undefined.

Are percentages proportions?

Yes; percentages compare to 100.

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