5-1 Ratios and Rates
Learn to identify, write, and compare
ratios and rates.
Course 2
5-1 Ratios
Insert Lesson
Title Here
and Rates
Vocabulary
ratio
rate
unit rate
Course 2
5-1 Ratios and Rates
In basketball practice. Kathlene made 17
baskets in 25 attempts. She compared the
number of baskets she made to the total
number of attempts she made by using the
17
ratio 25 . A ratio is a comparison of two
quantities by division.
Kathlene can write her ratio of baskets made
to attempts in three different ways.
17
25
Course 2
17 to 25
17:25
5-1 Ratios and Rates
Additional Example 1: Writing Ratios
The recommended fuel for Suzanne’s
snowblower is made from 80 quarts of
gasoline and 1 quart of motor oil. Write each
ratio in all three forms.
A. quarts of gasoline to quarts of motor oil
For every 80 quarts of gasoline
80 , 80 to 1, 80:1
there is 1 quart of oil.
1
B. quarts of oil to quarts of fuel mixture
Find the total number of
80 + 1 = 81
1 , 1 to 81, 1:81
81
Course 2
quarts in the mixture.
For each quart of oil there
are 81 quarts of mixture.
5-1 Ratios and Rates
A ratio that compares two quantities
measured in different units is a rate,
which the units must ALWAYS be
labeled. Suppose Ms. Latocki drove 75
miles in 3 hours. Her rate of travel was
75 miles in 3 hours, or 75 mi .
3 hr
Course 2
5-1 Ratios and Rates
If the measure of the second quantity
in a rate is one unit, then the rate is
a unit rate. To change a rate to a unit
rate, divide both the numerator and
denominator by the number in the
denominator.
75 mi = 75 mi ÷ 3 = 25 mi
3 hr
1 hr
3hr ÷ 3
The unit rate 25 miles per hour expresses
the average number of miles Ms. Latocki
drove each hour.
Course 2
5-1 Ratios and Rates
Reading Math
The unit rate 25miles is read as “twenty five
1 hour
miles per hour.”
Course 2
5-1 Ratios and Rates
Additional Example 2A: Writing Rates and Unit Rates
Find the unit rates and write them in both
fraction and word forms.
A. Gordon memorized 560 vocabulary words in
28 days.
560 words
28 days
Rate in fraction
form
560 ÷ 28 = 20 words Unit rate in
28 ÷ 28
1 day
fraction form
Gordon memorized
20 words per day.
Course 2
Unit rate in
word form
5-1 Ratios and Rates
Additional Example 2B: Writing Rates and Unit Rates
Find the unit rates and write them in both
fraction and word forms.
B. Pete added 12 ounces of chocolate chips to a
recipe that yielded 48 cookies.
12 oz
48 cookies
Rate in fraction
form
12 ÷ 48 = 0.25 oz
48 ÷ 48
1 cookie
Unit rate in
fraction form
There is 0.25 ounce of
Unit rate in
chocolate chips per cookie. word form
Course 2
5-1 Ratios and Rates
It is often easy to compare ratios
when they are written as fractions
in simplest form—especially
when they have a common
denominator.
Course 2
5-1 Ratios and Rates
Additional Example 3: Simplifying Ratios to Make
Comparisons
Honey-lemon cough drops come in packages of 30
drops per 10-ounce bag. Cherry cough drops come in
packages of 24 drops per 6-ounce bag. Compare the
ratio of drops per ounces for each bag of cough drops.
Honey-lemon Cherry
Ounces
10
6
Drops
30
24
drops = 30 = 3
Simplify the ratio.
1
ounces
10
drops = 24 = 4 Simplify the ratio.
Cherry:
ounces
6
1
4 is greater than 3 .
1
1
Honey-lemon:
The ratio of drops to ounces is greater in the bag of cherry cough drops.
Course 2
5-1 Ratios and Rates
Try This: Example 3
Jawbreakers come in small packages of 20 per 5 ounce
package and large packages of 24 per 8 ounce package.
Compare the ratio of jawbreakers per ounce for each of
the packages.
Ounces
Jawbreaker
Large
Small
8
5
24
20
jawbreaker = 24 = 3
Simplify the ratio.
1
ounces
8
jawbreaker = 20 = 4 Simplify the ratio.
Small:
ounces
5
1
4 is greater than 3 .
1
1
Large:
The ratio of jawbreakers to ounces is greater in the small package.
Course 2
5-1 Ratios
Insert Lesson
and Rates
Title Here
Lesson Quiz: Part 1
A coin bank contains 16 quarters, 12 dimes,
and 8 nickels. Write the given ratio in all
three forms.
1. nickels to quarters
8 , 8 to 16, 8:16 or 1 , 1 to 2, 1:2
2
16
2. dimes to nickels
12 , 12 to 8, 12:8 or 3 , 3 to 2, 3:2
2
8
3. nickels and dimes to quarters
20 , 20 to 16, 20:16 or 5 , 5 to 4, 5:4
4
16
Course 2
5-1 Ratios
Insert Lesson
and Rates
Title Here
Lesson Quiz: Part 2
4. Find the unit rate and write it in both
fraction and word form.
There are 220 calories in 5 crackers.
44 calories , 44 calories per cracker
1 cracker
5. Kim and Ted work out on treadmills together
at the gym. Kim walked 3.0 miles in 21
minutes, while Ted walked 4.5 miles in 42
minutes. Who walked at the faster rate?
Kim
Course 2
5-1 Ratios
Insert Lesson
and Rates
Title Here
Orange Juice
1.
2.
3.
4.
Count off by A, B, C, D.
Get into A, B, C, D groups in the science room.
With a Sharpie, label 26 Dixie cups with your group letter.
OJ people, measure out the OJ from the can according to
the recipe.
5. Water people, take the OJ container and bowl with OJ and
go to one of the water fountains in the hall (there are 4)
and fill the cup measure with the correct amount of water
and put into bowl.
6. Stirrers, stir the water and OJ together.
7. Pourers, using another cup, ladle out the same amount of
OJ (without spilling) into all 26 cups.
8. Passer Outers- Pass out your cup to everyone.
9. At the end, everyone should have 4 cups, unless you said
pass.
10. DO NOT DRINK until Mrs. Staudohar says to drink!
Course 2