Ratio and Proportion Guide

What a ratio means

A ratio compares two quantities by division. It can be written as a:b, a to b, or a/b. Ratios are used in recipes, scale drawings, finance, and data analysis.

Simplifying ratios

Simplify ratios by dividing both parts by their greatest common divisor. Example: 24:36 simplifies to 2:3 because 12 divides both numbers.

Proportions and scaling

A proportion is an equation showing that two ratios are equal. If 2:3 equals x:12, then x = 8. You solve proportions with cross multiplication: 2/3 = x/12, so 2 * 12 = 3 * x.

Worked examples

Recipe scaling: A 2:3 sugar-to-flour ratio means for every 2 cups of sugar, use 3 cups of flour. If you need 9 cups of flour, sugar should be 6 cups.

Map scale: If 1 inch represents 5 miles, a 3-inch line represents 15 miles. Ratios make scaling simple.

Ratios to percentages

A ratio a:b can be converted to percentages by dividing each part by the total. For a 2:3 ratio, the total is 5. The first part is 2/5 = 40%, the second is 60%.

Common pitfalls

• Mixing units (always compare like with like).
• Skipping simplification, which hides simple relationships.
• Using totals incorrectly when converting to percentages.

Practical checklist

• Simplify ratios using gcd.
• Convert units before comparing.
• Use cross multiplication for proportions.
• Convert to percentages for easy interpretation.

Recommended calculators

• Ratio Calculator
• Recipe Scaler

References

• Algebra references for ratios and proportions
• Educational resources on gcd and simplification