- Understanding ratios and simplifying them

What Are Ratios?

A ratio is a way to compare two or more quantities, showing how many times one value contains or is contained within the other. Ratios are commonly written using a colon (e.g., 3:2), as a fraction (3/2), or with the word "to" (3 to 2).

Examples of Ratios

• If a recipe uses 4 cups of flour and 2 cups of sugar, the ratio of flour to sugar is 4:2.
• In a classroom with 12 boys and 8 girls, the ratio of boys to girls is 12:8.

How to Simplify Ratios

Simplifying a ratio means expressing it in the smallest whole numbers possible, similar to reducing a fraction. This makes the ratio easier to understand and compare.

Steps to Simplify a Ratio

1. Write the ratio as a fraction. For example, 12:8 becomes 12/8.
2. Find the greatest common divisor (GCD) of both numbers. For 12 and 8, the GCD is 4.
3. Divide both numbers by the GCD. 12 ÷ 4 = 3 and 8 ÷ 4 = 2.
4. Rewrite the simplified ratio. The simplified form of 12:8 is 3:2.

Tips for Simplifying Ratios

• Always use whole numbers in your final answer.
• If the ratio involves more than two numbers, divide all parts by their GCD.
• Check your work by multiplying the simplified ratio back to the original numbers.

Example: Simplify the ratio 18:24.

• GCD of 18 and 24 is 6.
• 18 ÷ 6 = 3, 24 ÷ 6 = 4.
• The simplified ratio is 3:4.

Why Simplify Ratios?

Simplified ratios are easier to interpret and use in real-life situations, such as recipes, maps, and comparing quantities. They help communicate information clearly and efficiently.