Unit Rates, Proportions, and Conversions Study Guide

Unit Rates, Proportions, and Conversions Study Guide

Copy down important notes in your notebook. You will be able to use your notes on the test.

Conversions​

On your test, you will have to use conversion ratios to convert between different units of measurement.​

The easiest way to convert between units is to use a proportion (butterfly method).

​Set your proportion up using the conversion ratio on one side of the equal sign and another fraction using a variable for the unknown measurement.

Multiple Choice

How many inches are in 1 foot?

• 10

• 12

• 24

• none of the above

Multiple Choice

One yard is how many feet?

• 10

• 3

• 5

• 36

Multiple Choice

Since there are 2000 pounds in 1 ton, how many tons is 5000 pounds?

• 2

• 3

• 4

• 2.5

Multiple Choice

3 yards = ______ feet

• 30 feet
• 9 feet
• 10 feet
• 6 feet

Unit Rates​

Remember unit rates are a measurement of 1 of something.​

​To calculate unit rates we divide by the number of the measurement we want to turn into 1.

​Example:

​

​Rita reads 40 pages in 2 hours. What is the unit rate of pages per hour?

​

​40 pages divided by 2 hours = 20 pages per 1 hour.

Multiple Choice

Which rate is equivalent to $9 per hour?

• $27 in 3 hours
• $28 in 4 hours
• $33 in 3 hours

Multiple Choice

Which rate is equivalent to 6 miles per gallon?

• 30 miles to 6 gallons
• 24 miles to 8 gallons
• 18 miles to 3 gallons

Multiple Choice

A unit rate is a rate in which the unit in the denominator is:

• 0

• 3

• 1

• 2

Multiple Choice

How many gallons are there in 12 liters? Use x to solve.

• 4 gallons

• 2 gallons

• 5 gallons

• roughly 3 gallons

​Using Unit Rates to Make Predictions

​If you are given a ratio, and then asked to make a prediction, you can solve by finding the unit rate and then multiplying by the new amount.

​Example:

​Tyler reads 300 pages in 6 hours. How many pages does he read in 8 hours.

​

​1) First find the unit rate: 300 pages in 6 hours = 50 pages in 1 hour.

​2) Multiply the unit rate by the number of hours

​3) 50 pages in 1 hour x 8 hours = 400 pages in 8 hours.

Multiple Choice

Julie can type about 300 words in 5 minutes. At this rate, about how many words can she type in an hour (60 minutes=1 hour)?

• 3000 words in an hour

• 3600 words in an hour

• 60 words in an hour

• 5000 words in an hour

Multiple Choice

If Maya makes $10 an hour at her after school job, how many hours will it take her to earn $150?

• 10 hours

• 1.5 hours

• 15 hours

• 20 hours

Multiple Choice

An athlete can swim

$$\frac{1}{2}$$  mile every $$\frac{1}{3}$$  hour. What is the unit rate of the athlete? (The unit is 1 hour)

• $$\frac{2}{3}miles\ per\ hour$$  

• $$\frac{1}{6}miles\ per\ hour$$  

• $$1\frac{1}{2}\ miles\ per\ hour$$  

• $$1\frac{3}{4}miles\ per\ hour$$  

​Unit Rates and Graphs

​To solve a unit rate with a graph, find a point on the line and divide the y axis buy the x axis. In this graph, the unit rate is 3/4 gallons per minute.

Multiple Choice

Which statement is the correct unit rate?

• 5 seconds per foot

• 5 feet per second

• 2.5 seconds per foot

• 2.5 feet per second

Multiple Choice

What is the unit rate in this proportional relationship?

• 60 miles/1 hour
• 120 miles/ 2 hours
• 1 mile/ 1 hour

Better Buy Problems​

​If a problem asks you to find the better buy, find the unit rate of all the answer choices and the better buy is the LOWEST price.

​

Multiple Choice

Sara Lee Turkey $6.58 per lb.
or
Butterball Turkey $11.16 for 2 lb.
Find the unit price of each and choose the better deal.

• Sara Lee
• Butterball

Multiple Choice

Cheerios $3.68 for 17 oz.
or
Apple Jacks $2.89 for 13 oz.
Find the unit price of each and choose the better deal.

• Cheerios
• Apple Jacks

Multiple Choice

Daisy sour cream $1.49 for 8 oz.
or
Kraft sour cream $2.55 for 16 oz.
Find the unit price of each and choose the better deal.

• Daisy
• Kraft

Multiple Choice

A Hummer that gets 300 miles on 20 gallons of gas or a Camry that gets 495 miles of 15 gallons of gas. Which is the better deal?

• Hummer
• Camry

Multiple Choice

Which option is the better deal?
Doritos
$4.39 for 11.5 oz
or
Cheetos
9.75 oz for $3.24

• Doritos
• Cheetos

Proportions

To solve proportions, you can use the butterfly method. Every question on your test can be solved with a proportion.

​Butterfly Method (Cross Multiplication)

​A proportion says that two fractions are equal. You can solve proportions by cross multiplying.

​Here is an example:

​First, you multiply the two numbers that are across from each other and then divide by the number across from the variable.

Multiple Choice

Solve the following proportion:

• 34

• 8.5

• 15

• 10

Multiple Choice

Solve the following proportion:

ROUND YOUR ANSWER

• 30

• 30.03

• 14.7

Multiple Choice

Solve the following proportion:

ROUND YOUR ANSWER

• 3.33333333

• 4.67

• 5

• 5.2

Multiple Choice

Hunter buys 36 baseball cards for $18. How many baseball cards can Troy buy if he has $9?

• 18 baseball cards

• 4 baseball cards

• 24 baseball cards

• 16 baseball cards

Multiple Choice

Mrs. Sparks has been craving smoothies lately. She buys a 20oz chocolate smoothie for $7. Mrs. Jones also buys a 17oz chocolate smoothie. How much is Mrs. Jones smoothie?

• $5.95

• $6

• 8.24

​Proportional Relationships with Graphs and Tables

​Tables and graphs can be used to represent proportional relationships.

​On graphs and tables you can create ratios using the x and y axes or the different unit labels from the table.

Multiple Choice

What is the total cost of tickets if there are 7 adults?

• $600
• $75
• $500
• $525