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Simplify ratios and solve proportions

Ratio calculator

Reduce a ratio to lowest terms or find a missing value in an equivalent proportion.

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Formula and steps included

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Formula

Ratio and proportion formulas

Equivalent ratios: a:b = c:d when a × d = b × c; Simplified ratio = (a ÷ g):(b ÷ g), where g = GCF(a, b)

A ratio compares two quantities in a fixed order. Dividing both terms by the same nonzero factor changes their size but not the relationship between them.

A proportion states that two ratios are equivalent. Their cross products are equal, which provides a direct equation for solving one missing term.

How to use the formula

  1. Keep the terms in order

    Identify what the first and second terms represent and use the same order on both sides of a proportion.

  2. Simplify with the GCF

    For a single ratio, divide both whole-number terms by their greatest common factor.

  3. Cross-multiply a proportion

    Multiply diagonally to turn two equal ratios into one equation.

  4. Solve and check

    Isolate the missing value, then verify that the two cross products match.

Worked examples

Ratio calculator examples

Simplify a ratio

The GCF of 18 and 24 is 6, so 18:24 simplifies to 3:4.

Solve an equivalent ratio

For 5:8 = x:40, use 5 × 40 = 8x. Then 200 = 8x, so x = 25.

Common questions

Ratio calculator FAQ

What is the difference between a ratio and a proportion?

A ratio compares two quantities. A proportion is an equation stating that two ratios have the same value.

Do ratio terms need the same units?

Convert comparable quantities to the same units before simplifying. A part-to-part ratio can compare different categories, but its labels and order must remain clear.

Can a ratio contain zero?

A ratio can have zero as its first term, but a zero second term cannot be treated as a finite quotient. Proportions involving zero also need to avoid division by zero.

Does the ratio calculator store my values?

Your values are not saved by default or uploaded. You can opt into Remember on this device or download a local JSON backup.