1. Ratios & Unit Rates
6-1

2. VOCABULARY Ratio – a comparison of two quantities by division
Rate – ratio that compares quantities in different units
Unit Rate – a rate that has a denominator of 1

3. WRITING RATIOS Key Concepts:
A ratio compares two quantities through division. You can write a ratio in many different ways.
Statistics: In the United States, about 10 out of every 15 people eligible to vote are registered to vote.
The numbers 10 and 15 form a ratio.
10 to : or 2
Note: When writing in fraction form, always simplify!

4. Example 1
A survey asked students whether they had after-school jobs. Write each ratio as a fraction in simplest form.
Response
Number
Have a job 40
Don’t have a job 60
TOTAL
100
a. Students with jobs to students without jobs
Students with jobs = 40 = 2
Students w/o jobs
b. Students without jobs to all students surveyed
Students w/o jobs = 60 = 3
Students surveyed

5. FINDING RATES AND UNIT RATES
We know that a ratio that compares quantities with different units of measurement is called a rate.
A unit rate is a rate that has a denominator of 1. We will use unit rates when comparing prices, gas mileage, speed, etc.

6. Example 2
Unit Prices: The table shows prices for different sizes of the same dish detergent. Which size has the lowest unit price?
Regular: price = $1.20
volume 12 fl. oz
Size
Volume (fl. oz.)
Price
Regular 12
$1.20
Family 28
$2.24
Economy 40
$3.60
$.10/fl. oz.
Family: price = $2.24
volume 28 fl. oz
$.08/fl. oz.
Economy: price = $3.60
volume 40 fl. oz
Therefore, the family size has the lowest unit price.
$.09/fl. oz.

7. CONVERTING UNITS
Sometimes, you will have to convert units of measurement in order to solve the problem at hand.
Example: convert inches to feet
days to months
ounces to liters

8. Example 3 Convert 10 mi/h to ft/min 10 mi/h = 10 mi 5,280 ft 1h `
1 h mi min 88
10 mi 5,280 ft h `
1h mi min 1
ft = ft
min min
Therefore, 10 mi/h is the same as 880 ft/min