A ratio compares two or more quantities. Written as a:b, it tells you how much of one thing there is relative to another. A recipe calling for 2 cups of flour to 3 cups of sugar has the ratio 2:3. Ratios appear in cooking, construction, finance, and science.
Simplifying ratios
To simplify a ratio, divide both parts by their greatest common divisor (GCD). This gives the smallest whole-number form.
Formula: a : b → (a ÷ GCD) : (b ÷ GCD)
Worked example: Simplify 8:12. The GCD of 8 and 12 is 4. Divide both parts: 8 ÷ 4 = 2, 12 ÷ 4 = 3. The simplified ratio is 2:3. Use the ratio calculator to check your work.
Finding equivalent ratios
Multiply or divide both parts by the same number. To scale 2:3 up to a total of 25 parts: find the factor 25 ÷ (2+3) = 5, then multiply both parts: 10:15. The ratio 2:3, 4:6, 6:9, 10:15 are all equivalent.
Ratio to fraction conversion
A ratio a:b can be written as the fraction a/(a+b). So 2:3 means 2/5 of the whole is the first part and 3/5 is the second. This is useful for dividing quantities in proportion. Use the fraction calculator for the conversion.
Comparing ratios
To compare two ratios, convert each to a decimal by dividing the first number by the second. For example, 3:4 = 0.75 and 6:9 ≈ 0.667. The first ratio is larger. Alternatively, cross-multiply: 3×9 = 27 vs 4×6 = 24, so 3:4 > 6:9.
Part-to-part vs part-to-whole
A ratio of 2:3 compares two parts. The part-to-whole ratio is 2:5 (2 out of 5 total). Converting between the two depends on context. A percentage is always part-to-whole: 2:3 as percentages is 40% and 60%. Use the percentage calculator for this.
The golden ratio
The golden ratio is approximately 1.618:1. It appears in nature (leaf arrangements, spiral shells), art, and architecture. Two quantities are in the golden ratio if their ratio equals the ratio of their sum to the larger quantity. The fractions guide explains how ratios relate to fractions and decimal forms.
Frequently asked questions
What is the difference between a ratio and a fraction? A ratio compares two quantities to each other (a:b); a fraction represents one part of a whole (a/b). They are related: a ratio a:b means the first part is a/(a+b) of the total.
How do I simplify a ratio? Find the greatest common divisor (GCD) of both numbers and divide each by it. For example, 8:12 has GCD 4, so the simplified form is 2:3.
Can ratios have more than two parts? Yes. A ratio like 2:3:5 compares three quantities. To simplify, find the GCD of all three numbers.
How do I scale a ratio up or down? Multiply or divide both parts by the same number. To scale 2:3 up to a total of 25, find the factor 25 ÷ (2+3) = 5, then multiply: 10:15.