Understanding Ratios
A ratio is a comparison of two quantities that shows the relative size of one quantity to another. Ratios are written in the form A:B and can be simplified by dividing both numbers by their Greatest Common Divisor (GCD).
How to Simplify a Ratio
- Find the GCD of both numbers.
- Divide each number by the GCD.
- The result is the simplified ratio.
Ratio Representations
Colon Notation
The most common way to express a ratio.
A : B (e.g., 3 : 2)
Fraction Form
A ratio can be written as a fraction A/B.
A/B (e.g., 3/2)
Decimal Form
Divide A by B to get the decimal ratio.
A / B (e.g., 1.5)
Percentage
Express one number as a percentage of the other.
(A/B) x 100%
Practical Applications
Ratios are used extensively in cooking (recipe scaling), finance (financial ratios), science (mixing solutions), map scales, and everyday comparisons. Understanding how to simplify and interpret ratios is a fundamental mathematical skill.
Tips
- Always simplify ratios to their lowest terms for clarity.
- Ratios can involve decimals - multiply both parts by a power of 10 to convert to whole numbers first.
- The order of numbers in a ratio matters: 3:2 is different from 2:3.