🔢 Ratios & Proportions

What is a Ratio?
A ratio is a comparison of two quantities. It tells us how much of one thing there is compared to another.
Example: In a fruit bowl with 3 apples and 2 oranges:
• The ratio of apples to oranges is 3 to 2

Three Ways to Write a Ratio:
FormExampleHow to ReadColon form3:2"3 to 2"Fraction form3/2"3 halves" or "3 to 2"Word form3 to 2"3 to 2"Part-to-Part vs. Part-to-Whole:
TypeMeaningExample (3 apples, 2 oranges, total 5 fruits)Part-to-PartCompare one part to another partApples to oranges = 3:2Part-to-WholeCompare one part to the totalApples to total fruits = 3:5

What are Equivalent Ratios?
Equivalent ratios are ratios that name the same comparison. They are like equivalent fractions!
Example: 1:2 = 2:4 = 3:6 = 4:8
Finding Equivalent Ratios:
• Multiply or divide both terms by the same number
• Just like finding equivalent fractions!

The Proportion Method:
When two ratios are equal, they form a proportion:
3/5 = ?/20

Cross-multiply: 3 × 20 = 5 × ?
60 = 5 × ?
? = 60 ÷ 5 = 12

So 3/5 = 12/20

What is a Ratio Table?
A ratio table is an organized way to list equivalent ratios. It helps you see patterns and solve problems.
Example: Ratio of apples to oranges = 3:2
Apples3691215Oranges246810What is a Double Number Line?
A double number line shows two quantities on parallel lines. It's great for visualizing ratios!
Example: 3 cups flour : 2 cups sugar
Flour: 0 3 6 9 12 15
├────┼────┼────┼────┼────┤
Sugar: 0 2 4 6 8 10