Unit Rates
MA.6.AR.3.2 Given a real-world context, determine a rate for a ratio of quantities with different units. Calculate and interpret the corresponding unit rate.
Objective: Students will be able to find the unit rate given a real-world scenario.
Unit Rates
What is a unit rate? A unit rate is a ratio that is used for comparing two different kinds of quantities which have different units. Below are some examples of unit rates:
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5 miles per gallon or 5:1
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10 feet per second or 10:1
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100 calories per serving or 100:1
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2 loads for one dollar or 2:1
Watch the following video for an introduction to ratios and rates. The video will explain the difference between a rate and a ratio and will provide examples.
After watching the video on ratios and rates, think of an example of a unit rate that you have seen in the real world. Write your example in your notes.
Next, watch the following video which goes into greater detail about unit rates. Pause the video during the examples and try to solve them yourself!
Example One:
The cost of apples is $8.00 for 4 pounds. How much does 1 pound cost?
Step 1) Identify the ratio and write it in fraction notation.
$8.00
4 pounds
Step 2) To get our unit rate, we need a denominator of 1. In order to get a denominator of 1, we need to divide the denominator of our ratio by itself! When you divide any number by itself, you get 1. Remember, anything you do to the bottom, you must do to the top as well! Divide the numerator by the same number.
$8.00 ÷ 4
4 pounds ÷ 4
Step 3) 8 divided by 4 is 2, and 4 divided by 4 is 1.
$8.00 ÷ 4 = $4.00
4 pounds ÷ 4 = 1 pound
Answer: One pound of apples costs $4.00.
Example Two:
A student types 45 words in 60 seconds. How many words does the student type in 1 second?
Step 1) Identify the ratio and write it in fraction notation. Remember to write it in the same order as the question.
45 words
60 seconds
Step 2) Find the GCF of 45 and 60.
GCF
45 60
1 1
2
3 3 GCF = 15
4
5 5
6
15 15
Step 3) Divide the numerator and the denominator by the GCF.
45 words ÷ 15 = 3 words
60 seconds ÷ 15 = 4 seconds
Answer: words per second
3
4