Student resources
Grades 6-9
Ratios, Rates, and Proportions Guide
Ratios and rates compare quantities. They are useful for recipes, speed, prices, maps, and unit conversions.
Key ideas
- A ratio compares two quantities.
- A rate compares quantities with different units, such as miles per hour.
- A unit rate has a denominator of 1.
- A proportion states that two ratios are equal.
Common Ratio and Rate Ideas
| Idea | Meaning | Example |
|---|---|---|
| Ratio | Compares two amounts | 2 cups flour to 1 cup sugar |
| Rate | Compares different units | 60 miles in 1 hour |
| Unit rate | Rate per 1 unit | $3 per pound |
| Proportion | Two equal ratios | 1/2 = 3/6 |
Practice questions
A car travels 120 miles in 2 hours. What is the speed?
Calculation: 120 / 2 = 60
Answer: 60 miles per hour
A recipe uses 2 cups of water for 1 cup of rice. How much water for 3 cups of rice?
Calculation: 3 x 2 = 6
Answer: 6 cups of water
A 4-pound bag costs $12. What is the unit price?
Calculation: 12 / 4 = 3
Answer: $3 per pound
Are 2/5 and 4/10 proportional?
Calculation: 2/5 x 2/2 = 4/10
Answer: yes