Introduction to Ratios

What is a Ratio?

A ratio compares two quantities by division. It shows how much of one thing there is compared to another.

Ways to Write Ratios

If there are 3 apples and 5 oranges, the ratio of apples to oranges can be written three ways:

1. Using "to": 3 to 5
2. Using a colon: 3:5
3. As a fraction: $\frac{3}{5}$

Simplifying Ratios

Like fractions, ratios should be written in simplest form.

Example: The ratio 6:8 simplifies to 3:4 (divide both by 2)

Part-to-Part vs Part-to-Whole

• Part-to-Part: Compares one part to another part

  • Example: 3 boys to 5 girls → 3:5

• Part-to-Whole: Compares one part to the total

  • Example: 3 boys out of 8 total students → 3:8

Equivalent Ratios

Ratios are equivalent if they represent the same comparison: $2:3 = 4:6 = 6:9 = 8:12$

(Multiply or divide both parts by the same number)