How Ratios Work and How to Simplify Them
A ratio expresses the relationship between two or more quantities. Ratios appear in cooking recipes, map scales, financial analysis, mixing solutions, and countless other everyday contexts. Simplifying a ratio to its lowest terms makes comparisons clearer — the ratio 24:36 is easier to understand as 2:3.
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Formula
Ratio Calculator
Simplify ratios and find missing values in proportions.
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Worked Example
Given:
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FAQs
How do ratios differ from fractions?
A fraction represents a part of a whole — 2/5 means 2 out of 5. A ratio compares two separate quantities — 2:3 means for every 2 of one thing there are 3 of another. A ratio can be converted to a fraction by treating the first number as numerator and the sum as denominator: ratio 2:3 means 2/5 of the total is A and 3/5 is B.
How do I divide something in a given ratio?
Add the ratio parts together to find the total shares. Divide the total amount by total shares to find one share. Multiply each ratio part by one share. For example, dividing $100 in ratio 3:2: total shares = 5, one share = $20. Parts = $60 and $40.
What are unit rates and how do they relate to ratios?
A unit rate is a ratio expressed with a denominator of 1. For example, 300 km in 3 hours = 100 km per hour (100:1). Unit rates make comparisons easy — $3.60 for 12 eggs vs $4.80 for 18 eggs: unit rates are $0.30/egg vs $0.267/egg, so the 18-pack is better value.