Rate
A rate is a special ratio that compares two quantities with different units of measure. It is a comparison of two measurements that have different units, such as miles per hour or cost per item.
Key Concepts
- Rate: A rate is a comparison of two different kinds of quantities.
- Unit Rate: A unit rate is a rate in which the second quantity in the comparison is one unit.
- Examples: Rates can be expressed in various forms such as miles per hour (mph), cost per item, or words per minute.
Calculating Rate
To calculate a rate, you divide one quantity by the other. For example, to calculate the rate of speed, you divide the distance traveled by the time taken.
Formula
The formula to calculate rate is:
Rate = (Quantity 1) / (Quantity 2)
Unit Rate
A unit rate is a special type of rate where the second quantity in the comparison is one unit. It is often used to compare prices, speeds, or other quantities to a single unit.
Formula for Unit Rate
The formula to calculate unit rate is:
Unit Rate = (Total Quantity) / (Number of Units)
Examples
Here are some examples of rates and unit rates:
- Speed: A car travels 60 miles in 2 hours. The rate of speed is 60 miles / 2 hours = 30 miles per hour (mph).
- Cost: 5 apples cost $10. The unit rate is $10 / 5 apples = $2 per apple.
Practice Problems
1. Calculate the unit rate for the following:
a) 360 miles in 6 hours
b) 24 items for $48
2. Express the following rates as unit rates:
a) 120 words in 3 minutes
b) 500 meters in 5 seconds
3. A car travels 240 miles in 4 hours. Calculate the rate of speed.
4. If 8 cans of soda cost $16, what is the unit rate for one can?
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