How to Simplify a Ratio
Simplifying a ratio means reducing it to its smallest whole number form by dividing all parts by their Greatest Common Divisor (GCD). A simplified ratio expresses the same relationship between quantities using the smallest possible integers.
Step-by-Step Method
- If values are decimals, multiply all parts by a power of 10 to make them whole numbers.
- Find the GCD of all parts of the ratio.
- Divide each part by the GCD.
- The resulting ratio is in its simplest form.
Examples
24 : 16
GCD(24, 16) = 8
24:16 = 3:2
15 : 25 : 35
GCD(15, 25, 35) = 5
15:25:35 = 3:5:7
0.5 : 1.5
Multiply by 10: 5:15, GCD = 5
0.5:1.5 = 1:3
Ratios vs. Fractions
A two-part ratio a:b can be expressed as the fraction a/b. However, ratios can have three or more parts (like 2:3:5), which cannot be directly expressed as a single fraction. Ratios compare multiple quantities simultaneously.
Practical Uses of Ratios
- Cooking recipes (e.g., flour to sugar ratio).
- Map scales (e.g., 1:50000).
- Mixing solutions (e.g., paint colors, concrete).
- Financial analysis (e.g., debt-to-equity ratio).