Transcript Ratios & Unit Rates

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 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 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.
a. Students with jobs to
students without jobs
Students with jobs = 40 = 2
Students w/o jobs
60
3
b. Students without jobs
to all students surveyed
Students w/o jobs = 60 = 3
Students surveyed 100 5
Response
Number
Have a job
40
Don’t have
a job
60
TOTAL
100
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?
Regular: price = $1.20
Size
volume 12 fl. oz
$.10/fl. oz.
Regular
Volume Price
(fl. oz.)
12
$1.20
Family: price = $2.24
Family
28
$2.24
volume 28 fl. oz
Economy
40
$3.60
$.08/fl. oz.
Economy: price = $3.60
Therefore, the family
volume 40 fl. oz
size has the lowest
unit price.
$.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
1h
5,280 ft 1h
1 mi
60 min
88
10 mi
1h
5,280 ft
1 mi
1h
`
60 min
1
10
88 ft
1
1
1
1 min
=
880 ft
min
Therefore, 10 mi/h is the same as 880 ft/min
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