Ratios, Rates, and Proportional Relationships

## Comparing Quantities Ratios compare two quantities, like 3 apples to 4 oranges (written as 3:4). Rates compare quantities with different units, like 60 miles per 2 hours. ### Proportions If two ratios are equal, they form a proportion: \( \frac{3}{4} = \frac{6}{8} \). ### Solving Proportional Problems Cross-multiply to solve: If \( \frac{5}{8} = \frac{x}{24} \), then \( 5 \times 24 = 8 \times x \), so \( x = 15 \). ### Daily Life Connections Proportions help when cooking, shopping, or planning trips. ### Fun Example If 2 pencils cost $1, how much do 10 pencils cost? Set up a proportion to find out!