7th Grade Math
Pre-algebra concepts, geometry, and statistical thinking for seventh grade students.
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!
Examples
A recipe calls for 2 cups of flour for every 3 cups of sugar.
If you bike 20 miles in 2 hours, your rate is 10 miles per hour.
In a Nutshell
Ratios, rates, and proportions help us compare and scale quantities.