Ratios and Rates
Grade 6 · Math · Study Guide
Understand how to compare two quantities using ratios and rates.
A ratio is a comparison of two quantities. If you have 3 red marbles and 5 blue marbles, the ratio of red to blue is 3 to 5, which you can write as 3:5 or 3/5. The order matters — 3:5 and 5:3 mean different things.
Ratios can be simplified just like fractions. If a recipe uses 4 cups of flour and 2 cups of sugar, the ratio is 4:2, which simplifies to 2:1. This means for every 2 cups of flour, you use 1 cup of sugar. Equivalent ratios are like equivalent fractions — they represent the same relationship. 3:5 = 6:10 = 9:15.
A rate is a special kind of ratio that compares two quantities with different units. For example, driving 120 miles in 2 hours is a rate. A unit rate shows how much of one quantity exists per one unit of the other. 120 miles in 2 hours = 60 miles per 1 hour, so the unit rate is 60 mph.
Unit rates are incredibly useful in everyday life. If apples cost $3.50 for 5, the unit rate is $0.70 per apple — now you can compare prices at different stores fairly. Whenever you see 'per' — miles per hour, calories per serving, price per ounce — that's a unit rate at work.
| Type | Example | Notes |
|---|---|---|
| Ratio | 3 cats : 4 dogs | Compares same or different units |
| Rate | 150 miles in 3 hours | Always different units |
| Unit Rate | 50 miles per hour | Second quantity is always 1 |
Key terms
- Ratio
- A comparison of two quantities, written as a:b, a to b, or a/b
- Rate
- A ratio that compares two quantities with different units
- Unit Rate
- A rate where the second quantity is 1, such as 60 miles per hour
- Equivalent Ratios
- Ratios that represent the same comparison, like 2:3 and 4:6
Flashcards
- Ratio
- A comparison of two quantities — e.g. 3:5 means 3 for every 5
- Rate
- A ratio comparing quantities with different units — e.g. 60 miles per hour
- Unit Rate
- A rate per 1 unit of the second quantity — e.g. $2.50 per pound
- Equivalent Ratios
- Ratios that simplify to the same value — e.g. 4:6 and 2:3
- Simplifying a Ratio
- Divide both parts by their GCF — e.g. 12:18 → 2:3
- How to find unit rate
- Divide the first quantity by the second — e.g. 150 miles ÷ 3 hours = 50 mph
Practice questions
A class has 12 boys and 18 girls. What is the ratio of boys to girls in simplest form?
- 2:3
- 3:2
- 12:18
- 6:9
Show answer
Answer: 2:3
GCF of 12 and 18 is 6. 12÷6=2, 18÷6=3, so the ratio simplifies to 2:3.
A car travels 240 miles in 4 hours. What is the unit rate?
- 60 miles per hour
- 240 miles per hour
- 4 miles per hour
- 960 miles per hour
Show answer
Answer: 60 miles per hour
240 miles ÷ 4 hours = 60 miles per 1 hour. Unit rates always have 1 as the second quantity.
The ratios 4:6 and 6:9 are equivalent ratios.
Show answer
Answer: True
4:6 simplifies to 2:3 and 6:9 also simplifies to 2:3. Same simplified form = equivalent ratios.
A ratio that compares a quantity to 1 unit of another quantity is called a ___ rate.
Show answer
Answer: unit
A unit rate compares a quantity to exactly 1 unit of another, like 55 words per minute.
Which ratio is equivalent to 5:8?
- 10:16
- 15:20
- 5:16
- 8:5
Show answer
Answer: 10:16
Multiply both parts of 5:8 by 2 to get 10:16. The other options don't maintain the same relationship.
Fun facts
- The golden ratio (about 1.618:1) appears in nautilus shells, sunflower seeds, and even the Parthenon in Greece.
- Your heart beats roughly 70 times per minute — that's a unit rate of about 100,000 beats per day!
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