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Unit Rates
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What you will learn from this videoWhat you will learn
- 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 go-kart, and make dog treats.
- Discussion Questions
Before Video
Draw a picture to represent the following sentence.
The ratio of red circles to blue circles is 3 : 5.ANSWERStudents 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]ANSWERThese 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 Video
There 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?ANSWERThe 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
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide