How to Simplify a Ratio: Step-by-Step With Examples
Learn what a ratio means, a clear two-step method to simplify any ratio to its lowest terms, and where you encounter ratios in everyday life.
What a Ratio Actually Means
A ratio compares two or more quantities and shows their relative sizes. The ratio 3:2 (read as three to two) means for every 3 of the first thing, there are 2 of the second thing. It does not tell you the actual amounts — it tells you the proportion.
Ratios appear everywhere. A recipe calling for 2 cups of flour to 1 cup of sugar is a 2:1 ratio. A map scale of 1:50,000 means one centimeter on the map equals 50,000 centimeters in reality. A classroom with 30 students and 1 teacher has a 30:1 student-to-teacher ratio.
Simplifying a ratio means reducing it to its smallest equivalent form while preserving the proportion. The ratio 6:4 and the ratio 3:2 describe the same proportion — for every 3 of the first item, there are 2 of the second. The simplified form 3:2 is easier to understand and work with.
The Two-Step Method to Simplify Any Ratio
Step one is to find the greatest common divisor (GCD) of the two numbers in the ratio. The GCD is the largest number that divides evenly into both. For the ratio 12:8, the factors of 12 are 1, 2, 3, 4, 6, 12. The factors of 8 are 1, 2, 4, 8. The largest factor that appears in both lists is 4. So the GCD is 4.
Step two is to divide both numbers in the ratio by the GCD. Divide 12 by 4 to get 3. Divide 8 by 4 to get 2. The simplified ratio is 3:2.
The ratio is fully simplified when the GCD of the two numbers is 1 — meaning they share no common factors other than 1. If you divided 12:8 by 2 first to get 6:4, you would need to divide again by 2 to get 3:2. Using the GCD directly gets you to the simplified form in one step.
Examples With Different Types of Numbers
Ratio 15:25: the GCD of 15 and 25 is 5. Divide both by 5 to get 3:5. The simplified ratio is 3:5.
Ratio 100:40: the GCD of 100 and 40 is 20. Divide both by 20 to get 5:2. The simplified ratio is 5:2.
Three-part ratio 6:9:12: find the GCD of all three numbers. The GCD of 6, 9, and 12 is 3. Divide each by 3: 2:3:4. The simplified ratio is 2:3:4. The same two-step approach extends naturally to ratios with more than two parts.
When Ratios Come Up in Real Life
Cooking and baking use ratios constantly. The ratio for a basic vinaigrette is typically 3 parts oil to 1 part acid (vinegar or citrus). Knowing the simplified ratio lets you scale the recipe up or down easily.
Finance and business use ratios to compare performance. A price-to-earnings ratio of 25:1 means a stock's price is 25 times its earnings per share. A debt-to-income ratio of 36:100 simplifies to 9:25. These ratios allow meaningful comparison across companies or time periods of very different scales.
Unit conversions often involve ratios. Converting kilometers to miles uses an approximate ratio of 8:5 — every 8 kilometers is approximately 5 miles. If you know this ratio, you can quickly convert without a calculator: 40 kilometers divided by 8, times 5, equals 25 miles.