Ratios & Unit Rates

6-1

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

WRITING RATIOSKey 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 15 10:15 10 or 2 15 3

Note: When writing in fraction form, always simplify!

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

b. Students without jobs to all students surveyed

Students with jobs = 40 = 2Students w/o jobs 60 3

Students w/o jobs = 60 = 3Students surveyed 100 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.

Example 2 Unit Prices: The table shows prices for

different sizes of the same dish detergent. Which size has the lowest unit price?

Size Volume (fl. oz.)

Price

Regular 12 $1.20

Family 28 $2.24

Economy 40 $3.60

Regular: price = $1.20 volume 12 fl. oz

Family: price = $2.24 volume 28 fl. oz

Economy: price = $3.60 volume 40 fl. oz

Therefore, the family size has the lowest unit price.

$.10/fl. oz.

$.08/fl. oz.

$.09/fl. oz.

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

Example 3 Convert 10 mi/h to ft/min

10 mi/h = 10 mi 5,280 ft 1h `

1 h 1 mi 60 min

10 mi 5,280 ft 1 h ` 1h 1 mi 60 min

88

1

10 88 ft 1 = 880 ft

1 1 1 min min

Therefore, 10 mi/h is the same as 880 ft/min