Download Ratios and Unit Rates

PRE-ALGEBRA
Lesson 6-1 Warm-Up
PRE-ALGEBRA
Ratios and Unit Rates (6-1)
What is a “ratio”?
ratio: a comparison of two numbers by division – There are three ways
to compare two numbers:
a
a to b
a:b
b
read as “to”
How do you write a
ratio?
You can write a ratio to compare a part to a part or part to a whole. The
first item being compared is always the first number and the second item
being compared is the second number of the ratio.
Example: A recipe calls for 4 cups of cereal and 2 cups of pretzels.
Write this as a ratio.
PRE-ALGEBRA
Ratios and Unit Rates (6-1)
What is a “rate”?
rate: a ratio that compares two quantities measured in different units.
Example: 120 miles is read as “120 miles ‘per’ or ‘each’ 4 hours”
4 hours
What is a “unit rate”?
unit rate: the rate in which the denominator is 1 (rate ‘per’ 1 unit of a
given quantity) - Unit rate is used in everyday life to determine the best
value. It can be found by simplifying the fraction to a denominator of “1”
or simply dividing the numerator (top number) by the denominator
(bottom number.
Example: 120 miles  4 = 30 miles or 120  4 = 30 mph
1 hours
4 hours  4
The above unit rate is read as “30 miles ‘per’ hour” (30 m/h or 30 mph)
PRE-ALGEBRA
Ratios and Unit Rates
LESSON 6-1
Additional Examples
Find the unit rate for typing 145 words in 5
minutes.
number of words
number of minutes
=
145 words
5 minutes
= 29 words/minute
Write a rate
comparing words
to minutes.
Divide.
The unit rate is 29 words per minute.
PRE-ALGEBRA
Ratios and Unit Rates
LESSON 6-1
Additional Examples
Convert 30 gal/min to cups/second.
30 gal
30 gal/min = 1 min
130
gal
= 1 min
16 c
• 1 gal
816
c
• 1 gal
8c
= s
1 min
• 60 s
•
1 min
260 s
Convert gallons to cups and
minutes to seconds.
Divide the common factors
and units.
1
Simplify.
30 gal/min equals 8 c/s.
PRE-ALGEBRA
Ratios and Unit Rates
LESSON 6-1
Additional Examples
The table shows prices for different packages of index
cards. Which size has the lowest unit cost?
Size
(cards)
Price
100
$2.70
50
$1.30
25
$.75
100 cards:
price
number of cards
$2.70
100 cards
= $.027/card
50 cards:
price
number of cards
$1.30
50 cards
Find the
= $.026/card unit costs.
25 cards:
price
number of cards
$.75
25 cards
= $.03/card
The 50-card pack has the lowest unit cost.
PRE-ALGEBRA
Ratios and Unit Rates
LESSON 6-1
Additional Examples
Painting several rooms will take 36 person-hours.
How long will it take for 4 painters?
It takes 36 persons to complete painting several rooms in
1 hour. To find the number of hours it will take 4 persons
to complete the job, divide.
36 person-hours
= 9 hours
4 persons
Divide the number of person-hours by
the number of workers.
It will take 9 hours for 4 painters to paint the rooms.
Check Since person • hours = hours, the units check.
persons
PRE-ALGEBRA
Ratios and Unit Rates
LESSON 6-1
Lesson Quiz
Find each unit rate.
1. You pay $4.50 for 2 gallons of orange juice.
$2.25/gal
2. You pay $21.60 for a 20-lb bag of dog food.
$1.08/lb
3. A bird flies at a speed of 384 in./s. What is its
1,920 ft/min
speed in units of ft/min?
4. A job takes 96 person-days. How many
workers are needed to complete the job in
24 days?
4
PRE-ALGEBRA