Rates Study Guide
What is a Rate?
A rate is a special ratio that compares two quantities measured in different units. It is a comparison of two different quantities. For example, miles per hour, price per pound, or words per minute are all examples of rates.
How to Calculate Rate?
To calculate a rate, you need to divide one quantity by the other. The formula for calculating rate is:
Rate = Quantity 1 / Quantity 2
Units in Rates
When expressing a rate, it is important to include the units. For example, if the rate is 60 miles per hour, both "miles" and "hours" should be included to indicate the units being compared.
Unit Rates
A unit rate is a rate with a denominator of 1. It is often used to compare the prices of items. For example, if a 2-pound bag of rice costs $4, the unit rate is $2 per pound.
Proportions and Rates
Rates can be used in proportions to solve problems. For example, if 3 gallons of juice cost $6, you can set up the proportion 3 gallons / $6 = x gallons / $12 to find the cost of 6 gallons.
Real-Life Applications
Rates are used in many real-life situations, such as speed (miles per hour), unit pricing in stores, and performance measures like words per minute in typing or reading speed.
Practice Problems
- Calculate the rate: 360 miles in 6 hours.
- Determine the unit rate: 15 apples for $6.
- Use a proportion to solve: If 5 shirts cost $75, how much would 8 shirts cost?
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