Lesson 1: Ratios & Proportions
A ratio compares two quantities. A proportion says two ratios are equal. These ideas show up everywhere — recipes, maps, speed, currency exchange, and probability.
Key Concepts
What Is a Ratio?
A ratio compares two values. 3:2, 3/2, and '3 to 2' all mean the same thing. If a recipe calls for 3 cups of flour and 2 cups of sugar, the ratio of flour to sugar is 3:2.
Equivalent Ratios
Multiply or divide both parts by the same number and you get an equivalent ratio. 3:2 = 6:4 = 9:6. Equivalent ratios form a proportion: 3/2 = 9/6.
Solving Proportions
If 3/2 = x/8, cross-multiply: 3×8 = 2×x → 24 = 2x → x = 12. Cross-multiplication works because both sides multiply to the same value.
Unit Rate
A unit rate has 1 in the denominator. 60 miles per 1 hour. $3.50 per 1 pound. Divide both sides by the second quantity to find the unit rate.
🔬 Interactive Lab: Ratios & Proportions Lab
✅ Check Your Understanding
1. What is the simplified form of the ratio 12:8?
2. To solve 4/6 = x/18, cross-multiply to get:
3. A unit rate always has what in the denominator?