What is a ratio and how is it different from a fraction?

A ratio compares two or more quantities, showing their relative sizes. While similar to fractions, ratios can compare more than two values (e.g., 2:3:5) and often represent different units. The ratio 2:3 can be written as 2/3 as a fraction, but conceptually represents 'for every 2 of one thing, there are 3 of another.'

How do you simplify ratios?

To simplify a ratio, divide all parts by their greatest common divisor (GCD). For example, 12:18 simplified: find GCD(12,18) = 6, then divide both by 6 to get 2:3. Simplified ratios maintain the same proportional relationship while using the smallest possible whole numbers.

How do you scale ratios?

To scale a ratio, multiply or divide all parts by the same number. If a recipe uses a 2:3 ratio of flour to sugar and you want 8 cups of flour, multiply both parts by 4: (2×4):(3×4) = 8:12, meaning you need 12 cups of sugar. This maintains the proportional relationship.

What are some common applications of ratios?

Ratios are used everywhere: cooking recipes (ingredient proportions), mixing paint or concrete, financial analysis (debt-to-equity ratios), map scales, gear ratios in machinery, aspect ratios in screens and images, and student-teacher ratios. They're fundamental for maintaining consistent proportions when scaling quantities.

How do you convert ratios to percentages?

To convert a ratio to a percentage, first find the total of all parts, then divide each part by the total and multiply by 100. For example, in the ratio 2:3, the total is 5. First part: (2/5) × 100 = 40%, second part: (3/5) × 100 = 60%. This shows what percentage each part represents of the whole.

Math

Ratio Calculator

Simplify and calculate ratios.

If the ratio is 4:3, then for every 8 on the left, you need ? on the right.

How to Use This Calculator

Enter the ratio values

Input the numbers that make up your ratio. You can enter two or more values separated by colons (e.g., 4:6 or 2:3:5). The calculator accepts whole numbers, decimals, and fractions.

Choose your operation

Select whether you want to simplify the ratio, scale it to a specific value, convert it to percentages, or compare it with another ratio. Each operation serves different practical purposes.

Review results and applications

The calculator shows the simplified ratio, equivalent forms, and may provide the total parts and individual percentages. This comprehensive view helps you apply the ratio in practical situations.