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Unit Rates
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 We'll learn that a unit rate is a special type of ratio that compares the first quantity to one unit of the second quantity.
 We will also learn how to calculate unit rates with whole numbers, then decimals and finally fractions.
 And we'll see how this knowledge can help us buy tacos, drive a gokart, and make dog treats.

Discussion Questions

Before VideoDraw a picture to represent the following sentence.
The ratio of red circles to blue circles is 3 : 5.ANSWER
Students may draw something similar to 3 red circles and 5 blue circles.

3 : 5

6 : 7

[ggfrac]1/4[/ggfrac], [ggfrac]2/8[/ggfrac], [ggfrac]8/32[/ggfrac]
[ggfrac]2/3[/ggfrac] and [ggfrac]8/12[/ggfrac]ANSWER
These are equivalent ratios. Each ratio says that for every two of one thing, there are 3 of another. Multiply the numerator and denominator of [ggfrac]2/3[/ggfrac] by 4 to find [ggfrac]8/12[/ggfrac].


After VideoThere are 36 people in 9 cars. There is the same number of people in each car. How can you use equivalent ratios to find the unit rate?ANSWER

The rate is 36 people per 9 cars, or [ggfrac]36/9[/ggfrac].
[ggfrac]36/9[/ggfrac] = [ggfrac]12/3[/ggfrac] = [ggfrac]4/1[/ggfrac]
The unit rate is 4 people per car.

The unit rate is $9.50 per shirt. I found the unit rate by dividing $66.50 by 7.

Tala’s Sporting Goods Store:
[ggfrac]$33/6[/ggfrac] = [ggfrac]$5.50/1[/ggfrac] The unit rate is $5.50 per baseball.
Osher's Sporting Goods Store:
[ggfrac]$24/4[/ggfrac] = [ggfrac]$6/1[/ggfrac] The unit rate is $6.00 per baseball.
Tala’s Sporting Goods Store has a better deal.

[ggfrac]36/8[/ggfrac] = [ggfrac]4.5/1[/ggfrac], so the unit rate is 4.5 hours per day.
4.5 × 20 = 90. Marcos works 90 hours in 20 days.

Rate of flour to sugar: 2[ggfrac]1/4[/ggfrac] / 1[ggfrac]1/2[/ggfrac]
Unit rate of flour to sugar:
2[ggfrac]1/4[/ggfrac] / 1[ggfrac]1/2[/ggfrac] = [ggfrac]9/4[/ggfrac] x [ggfrac]2/3[/ggfrac] = [ggfrac]18/22[/ggfrac] = [ggfrac]3/2[/ggfrac] cups of flour for every cup of sugar
Multiply [ggfrac]3/2[/ggfrac] × 9 to find out how much flour she needs:
[ggfrac]3/2[/ggfrac] x 9 = 13[ggfrac]1/2[/ggfrac] cups of flour
Sandra needs 13[ggfrac]1/2[/ggfrac] cups of flour to make the cookies with 9 cups of sugar.



Vocabulary

Rate
DEFINE
A quantity measured with respect to another quantity.

Fraction
DEFINE
A fraction shows how many parts of a whole you have.

Denominator
DEFINE
The bottom number in a fraction. Shows how many parts are in the whole.

Numerator
DEFINE
The top number in a fraction. Shows how many parts of the whole you have.

Unit rate
DEFINE
A ratio with denominator 1.

Ratio
DEFINE
A comparison between two quantities.

Equivalent ratio
DEFINE
Ratios are equivalent if one can be expressed as a multiple of the other.

Ratio table
DEFINE
A table that shows equivalent ratios.

Rate
DEFINE

Reading Material
Download as PDF Download PDF View as Separate PageWHAT ARE UNIT RATES?A unit rate is a ratio with denominator 1. The speed of a car in miles per hour is an example of a unit rate.
To better understand unit rates…
WHAT ARE UNIT RATES?. A unit rate is a ratio with denominator 1. The speed of a car in miles per hour is an example of a unit rate. To better understand unit rates…LET’S BREAK IT DOWN!
Calculate the Speed of Gokarts
Let’s say you drove a gokart 6 miles in 30 minutes. This is a ratio of 6 miles to 30 minutes. You want to find out how much time it takes you to drive 1 mile. You can find equivalent ratios to figure this out. To find equivalent ratios, multiply or divide both the numerator and denominator in the ratio by the same number. If you divide both numbers in the ratio [ggfrac]30/6[/ggfrac] by 3, you get the equivalent ratio [ggfrac]10/2[/ggfrac]. Divide 2 again to get the ratio [ggfrac]5/1[/ggfrac]. It takes 5 minutes to drive 1 mile, or you drive at a rate of 5 minutes per mile. This ratio is called the unit rate because it has 1 in the denominator. Try this one for yourself. What is the unit rate if you drove a gokart 9 miles in 36 minutes?
Calculate the Speed of Gokarts Let’s say you drove a gokart 6 miles in 30 minutes. This is a ratio of 6 miles to 30 minutes. You want to find out how much time it takes you to drive 1 mile. You can find equivalent ratios to figure this out. To find equivalent ratios, multiply or divide both the numerator and denominator in the ratio by the same number. If you divide both numbers in the ratio [ggfrac]30/6[/ggfrac] by 3, you get the equivalent ratio [ggfrac]10/2[/ggfrac]. Divide 2 again to get the ratio [ggfrac]5/1[/ggfrac]. It takes 5 minutes to drive 1 mile, or you drive at a rate of 5 minutes per mile. This ratio is called the unit rate because it has 1 in the denominator. Try this one for yourself. What is the unit rate if you drove a gokart 9 miles in 36 minutes?Tacos
Let’s say you want to buy some tacos. Dave’s Tacos offers 10 tacos for $30. Jasmine’s Tacos offers 20 tacos for $40. You want to find which is the better deal. Jasmine’s tacos cost $40 for 20 tacos. You can divide by 10 and then by 2 to find a ratio of $2 for 1 taco. You could also divide the numerator and denominator by 20 to get the unit rate of $2 for 1 taco. This is a more efficient way to find the unit rate. Dave's deal is $30 for 10 tacos. Divide by 10 to find that it costs $3 to buy one of Dave's tacos. The best deal is Jasmine’s tacos because $2 per taco is a better deal than $3 per taco. Try this one for yourself. Mita sells 5 hamburgers for $25. Jenell sells 12 hamburgers for $72. Who has a better deal?
Tacos Let’s say you want to buy some tacos. Dave’s Tacos offers 10 tacos for $30. Jasmine’s Tacos offers 20 tacos for $40. You want to find which is the better deal. Jasmine’s tacos cost $40 for 20 tacos. You can divide by 10 and then by 2 to find a ratio of $2 for 1 taco. You could also divide the numerator and denominator by 20 to get the unit rate of $2 for 1 taco. This is a more efficient way to find the unit rate. Dave's deal is $30 for 10 tacos. Divide by 10 to find that it costs $3 to buy one of Dave's tacos. The best deal is Jasmine’s tacos because $2 per taco is a better deal than $3 per taco. Try this one for yourself. Mita sells 5 hamburgers for $25. Jenell sells 12 hamburgers for $72. Who has a better deal?Dog Treats
Let’s say you want to make 36 dog treats. It costs $16.40 for the ingredients to make 8 dog treats. To find out how much it costs for the ingredients to make 36 dog treats, you can first find the unit rate. Since it cost $16.40 for the ingredients for 8 dog treats, you can divide $16.40 by 8 to get $2.05 per dog treat. Now that you know the cost for 1 treat, you can multiply $2.05 by 36 to find the cost for 36. $2.05 × 36 = $73.80. It costs $73.80 to make 36 dog treats. Try this one for yourself. It costs $54 to make 12 cookies. How much does it cost to make 18 cookies?
Dog Treats Let’s say you want to make 36 dog treats. It costs $16.40 for the ingredients to make 8 dog treats. To find out how much it costs for the ingredients to make 36 dog treats, you can first find the unit rate. Since it cost $16.40 for the ingredients for 8 dog treats, you can divide $16.40 by 8 to get $2.05 per dog treat. Now that you know the cost for 1 treat, you can multiply $2.05 by 36 to find the cost for 36. $2.05 × 36 = $73.80. It costs $73.80 to make 36 dog treats. Try this one for yourself. It costs $54 to make 12 cookies. How much does it cost to make 18 cookies?Chocolate Chip Cookie Recipe
You want to use Adesina’s World Famous Chocolate Chip Cookie Recipe to make some cookies. You need 1[ggfrac]1/2[/ggfrac] cups of sugar for every [ggfrac]2/5[/ggfrac] cup of chocolate chips. You have 10 cups of chocolate chips to use. If you want to use all of the chips, how much sugar do you need? First, find how much sugar you need for 1 cup of chips. The ratio of sugar to chips is 1[ggfrac]1/2[/ggfrac] to [ggfrac]2/5[/ggfrac]. To find the unit rate, divide 1[ggfrac]1/2[/ggfrac] by [ggfrac]2/5[/ggfrac]. [ggfrac]3/2[/ggfrac] ÷ [ggfrac]2/5[/ggfrac] = [ggfrac]1/2[/ggfrac] × [ggfrac]5/2[/ggfrac] = [ggfrac]15/4[/ggfrac] = 3[ggfrac]3/4[/ggfrac]. The unit rate is 3[ggfrac]3/4[/ggfrac] cups of sugar per 1 cup of chips. To use all 10 cups of chocolate chips, multiply 3[ggfrac]3/4[/ggfrac] by 10 to find the amount of sugar you need. 10 × 3[ggfrac]3/4[/ggfrac] = 10 × [ggfrac]15/4[/ggfrac] = [ggfrac]150/4[/ggfrac] = 37[ggfrac]1/2[/ggfrac]. You need 37[ggfrac]1/2[/ggfrac] cups of sugar. Try this one for yourself. For a cake recipe you need 2 [ggfrac]1/4[/ggfrac] cups of milk. If you have 15 cups of milk and want to use it all to make cakes, how many cups of flour do you need?
Chocolate Chip Cookie Recipe You want to use Adesina’s World Famous Chocolate Chip Cookie Recipe to make some cookies. You need 1[ggfrac]1/2[/ggfrac] cups of sugar for every [ggfrac]2/5[/ggfrac] cup of chocolate chips. You have 10 cups of chocolate chips to use. If you want to use all of the chips, how much sugar do you need? First, find how much sugar you need for 1 cup of chips. The ratio of sugar to chips is 1[ggfrac]1/2[/ggfrac] to [ggfrac]2/5[/ggfrac]. To find the unit rate, divide 1[ggfrac]1/2[/ggfrac] by [ggfrac]2/5[/ggfrac]. [ggfrac]3/2[/ggfrac] ÷ [ggfrac]2/5[/ggfrac] = [ggfrac]1/2[/ggfrac] × [ggfrac]5/2[/ggfrac] = [ggfrac]15/4[/ggfrac] = 3[ggfrac]3/4[/ggfrac]. The unit rate is 3[ggfrac]3/4[/ggfrac] cups of sugar per 1 cup of chips. To use all 10 cups of chocolate chips, multiply 3[ggfrac]3/4[/ggfrac] by 10 to find the amount of sugar you need. 10 × 3[ggfrac]3/4[/ggfrac] = 10 × [ggfrac]15/4[/ggfrac] = [ggfrac]150/4[/ggfrac] = 37[ggfrac]1/2[/ggfrac]. You need 37[ggfrac]1/2[/ggfrac] cups of sugar. Try this one for yourself. For a cake recipe you need 2 [ggfrac]1/4[/ggfrac] cups of milk. If you have 15 cups of milk and want to use it all to make cakes, how many cups of flour do you need? 
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Science & Math$_{/yr}

Science Only$_{/yr}
40 inches of snow fell over 8 days. What is the unit rate of snow per day? Show how you found the unit rate.
At Yoshira’s Market, 5 pounds of potatoes cost $10. At Luna’s Market, 14 pounds of potatoes cost $35. Which market has a better deal on potatoes? Show how you solved the problem.
For a cookie recipe you need 2[ggfrac]3/4[/ggfrac] cups of flour for every 1[ggfrac]1/2[/ggfrac] cups of sugar. If you have 12 cups of sugar and want to use it all to make cookies, how many cups of flour do you need? Show how you solved the problem.
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