Understanding Ratios

What Is a Ratio?

A ratio compares two quantities. It tells you how much of one thing there is compared to another.

Ways to Write Ratios

The ratio of 3 dogs to 5 cats can be written:

• $3$ to $5$
• $3 : 5$
• $\frac{3}{5}$

Types of Ratios

• Part to part: 3 dogs to 5 cats
• Part to whole: 3 dogs to 8 total animals
• Whole to part: 8 animals to 3 dogs

Equivalent Ratios

Equivalent ratios show the same relationship: $2 : 3 = 4 : 6 = 6 : 9 = 10 : 15$

To find equivalent ratios, multiply or divide both parts by the same number.

Ratio Tables

| Red Paint | Blue Paint | |-----------|-----------| | 2 | 3 | | 4 | 6 | | 6 | 9 | | 8 | 12 |

The ratio $2 : 3$ is maintained throughout.

Unit Rate

A unit rate has a denominator of 1:

• If 6 apples cost $3, the unit rate is \frac{\3}{6} = $0.50$ per apple

Tape Diagrams

A tape diagram (or bar model) visualizes ratios:

For the ratio $2 : 3$:

• Draw 2 equal boxes for the first quantity
• Draw 3 equal boxes for the second quantity

If the total is 25:

• Each box = $25 \div 5 = 5$
• First quantity = $2 \times 5 = 10$
• Second quantity = $3 \times 5 = 15$

Real world: Recipes use ratios! If a recipe uses 2 cups flour and 1 cup sugar, the ratio is $2:1$. To double the recipe, use $4:2$.