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Ratios and Rates
Name:
Ratio: A ratio is a comparison of two numbers using __________________. A ratio
that compares a to b (where b  0 ) can be written in three different ways.
1. Words
a to b
a
2. Fraction
b
3. Colon
a:b
Examples: Write each example as a ratio in three different ways. Write the ratio in both
non-simplified and in simplest form.
a. There are 14 boys and 10 girls in class. Compare the number of boys in class to
the number of girls in class.
b. Three out of five dentists prefer Brand X toothpaste. Compare the dentists who
prefer Brand X toothpaste to the number of dentist who do not.
c. 85 people surveyed preferred Jiff peanut butter and 15 people preferred Skippy
peanut butter. Compare the number of people who preferred Jiff to the total
number surveyed.
Equivalent ratios: Equivalent ratios are ratios that have the same _________________.
15
25
15
25
and
 1.25 and
 1.25
For example:
are equivalent ratios because
12
20
12
20
Examples: Determine if the following ratios are equivalent:
18
2
20
and 3 : 1
a.
b.
25 to 2.5 and
c.
10
3
2
15
2 5
and 11 : 2
3
6 6
Rate: A rate is a ratio of two quantities that have different _________________.
Equivalent Rates: Equivalent rates are two rates that have the same ________________.
Examples: Write a rate for each situation and create an equivalent rate with the given
conditions.
a. Sue types 75 words per minute.
a. Write and properly label a rate.
b. How many words per Sue type per hour? Write and properly label an
equivalent rate using unit analysis.
b. Lightning strikes about 100 times per second around the world.
a. Write and properly label a rate.
b. About how many times does lightning strike per minute around the world?
Write and properly label an equivalent rate using unit analysis.
c. Material cost $0.87 for 30 inches
a. Write and properly label a rate.
b. How much money would that be per ft? Write and properly label an
equivalent rate using unit analysis.
d. The object moved 15 meters in 5 minutes.
a. Write and properly label a rate.
b. How many centimeters would that be per hour? Write and properly label
an equivalent rate using unit analysis.
Unit Rate: A unit rate is a rate that has a denominator of ___________ unit. To write an
equivalent rate, find an equivalent rate with a denominator of ____________ unit. To
find a unit rate, _____________ the distance or frequency by the amount of time or
number of units
Examples: Write each situation as a unit rate.
a. 24 pages in 15 minutes
b. 18 degrees in 6 min
c. 3lb for $2
Ratios and Rates
Name:
Answer Key
Essential Vocabulary
Ratio: A ratio is a comparison of two numbers using ________division______. A ratio
that compares a to b (where b  0 ) can be written in three different ways.
1. Words
a to b
a
2. Fraction
b
3. Colon
a:b
Examples: Write each example as a ratio in three different ways. Write the ratio in both
non-simplified and in simplest form.
a. There are 14 boys and 10 girls in class. Compare the number of boys in class to
the number of girls in class.
14 7

Answer:
14 to 10 or 7 to 5
14:10 or 7:5
10 5
b. Three out of five dentists prefer Brand X toothpaste. Compare the dentists who
prefer Brand X toothpaste to the number of dentist who do not.
3
Answer:
3 to 2
3:2
2
c. 85 people surveyed preferred Jiff peanut butter and 15 people preferred Skippy
peanut butter. Compare the number of people who preferred Jiff to the total
number surveyed.
85 17

Answer:
85 to 100 or 17 to 20
85:100 or 17:20
100 20
Equivalent ratios: Equivalent ratios are ratios that have the same ___value_________.
15
25
15
25
and
 1.25 and
 1.25
For example:
are equivalent ratios because
12
20
12
20
Determine if the following ratios are equivalent:
18
2
20
and 3 : 1
a.
b.
25 to 2.5 and
10
3
2
c.
15
2 5
and 11 : 2
3
6 6
Answer:
Yes
18
2
4
 1.8and 3 : 1  1  1.8
10
3
5
Yes
25
20
 10and
 10
2.5
2
No
2
15
 5and 6  4
5
3
2
6
11
Rate: A rate is a ratio of two quantities that have different _____units_______.
Equivalent Rates: Equivalent rates are two rates that have the same __values________.
Examples: Write a rate for each situation and create an equivalent rate with the given
conditions.
a. Sue types 75 words per minute.
a. Write and properly label a rate.
75words
Answer:
1 min ute
b. How many words per Sue type per hour? Write and properly label an
equivalent rate using unit analysis.
75words 60 min utes 4500 words


Answer:
1 min ute
1hour
1hour
b. Lightning strikes about 100 times per second around the world.
a. Write and properly label a rate.
100 strikes
Answer:
1sec ond
b. About how many times does lightning strike per minute around the world?
Write and properly label an equivalent rate using unit analysis.
100 strikes 60 sec onds 6000strikes


1sec ond
1 min ute
1 min ute
c. Material cost $0.87 for 30 inches
a. Write and properly label a rate.
$0.87
Answer:
30inches
b. How much money would that be per ft? Write and properly label an
equivalent rate using unit analysis.
Answer:
$0.87
12inches $10.44 $0.348 $0.35




30inches
1 foot
30 ft
1 ft
1 ft
d. The object moved 15 meters in 5 minutes.
a. Write and properly label a rate.
15meters
Answer:
5 min utes
b. How many centimeters would that be per hour? Write and properly label an
equivalent rate using unit analysis.
15meters
100cm 60 min utes 90,000cm 18000cm




Answer:
5 min utes
1meter
1hour
5hours
1hour
Answer:
Unit Rate: A unit rate is a rate that has a denominator of ____one____ unit. To write an
equivalent rate, find an equivalent rate with a denominator of ____one_____ unit. To
find a unit rate, _____divide__ the distance or frequency by the amount of time or
number of units
Examples: Write each situation as a unit rate.
a. 24 pages in 15 minutes
24 pages
1.6 pages
 24  15  1.6 
15 min utes
1 min ute
b. 18 degrees in 6 min
18 deg rees
3 deg rees
 18  6  3 
Answer:
6 min utes
1 min ute
c. 3lb for $2
3lb
1.5lb
Answer:
 3  2  1.5 
$2
$1
Answer: