Dimensional Analysis in Mathematics

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