Ratios & Rates

Lessons 8.1 & 8.2

Ratios

• A ratio is a comparison of two numbers using division.

• The ratio may be written as an improper fractions for certain situations.

• A ratio can be written in many ways, including as a fraction (which means division).

Ratios

Example 1 – Compare the number of baseballs to the number of basketballs. Write the comparison as a fraction.

There are 4 baseballs

There are 6 basketballs

6

Ratios

Ratios can be reduced just like fractions.

=

2 to 3

2 out of 3

2:3

These are equivalent ratios.

Your Turn

Question #1 – Compare the number of green trucks to the number of red cars. Write the comparison as a fraction in simplest form.

​

There are 8 green trucks

There are 6 red cars

=

6

Your Turn

Question #2 – Compare the number of apples to the number of oranges. Write the comparison as a fraction in simplest form.

​

There are 7 apples

There are 4 oranges

4

Your Turn

Question #3 – Find the missing piece in the following ratio (what is the value of x?).

Multiplying by 2

=

x

4

Your Turn

Question #4 – Find the missing piece in the following ratio (what is the value of x?).

Multiplying by 3

=

x

8

Ratios

Example 2 – Michael has 6 action video games compared to 10 sports video games. Jessie has 8 action games compared to 16 sports video games. Who has the higher ratio of action to sports video games?

6 action

10 sports

10

Michael

0.60

8 action

16 sports

16

Jessie

0.50

Michael has the higher ratio of action to sports video games.

Your Turn

Question #5 – There are 24 girls compared to 30 boys in 6^th grade. There are 30 girls compared to 40 boys in 8^th grade. Which grade level has the higher ratio of girls to boys?

24 girls

30 boys

30

6^th Grade

0.80

30 girls

40 boys

40

7^th Grade

0.75

6^th grade has the higher ratio of girls to boys.

Rate

• Rate is a specific type of ratio that compares two different types of measurement

Examples

• distance and time (“miles per hour”)

• money and weight (“dollars per pound”)

Rate

Examples

• 150 miles in 2 hours
• $10 for 2 pounds
• 210 words in 3 minutes

Unit Rate

A rate that is simplified so that it has a denominator of 1 is a unit rate.

Example 2 – Larry can type 240 words in 4 minutes. Find out how many words he can type in one minute.

÷ 4

÷ 4

=

words

minute

Larry can type 60 words in one minute.

60

Your Turn

Question #6 – A 12-ounce can of Diet Coke costs 60 cents. Find the cost of 1 ounce. (Submit the unit rate as a fraction to CPS)

÷ 12

÷ 12

=

cents

ounce

5

Each ounce of Diet Coke costs 5 cents ($0.05).

Your Turn

Question #7 – Steven drives 280 miles in 4 hours. How far does Steven drive in one hour? (Submit the unit rate as a fraction to CPS)

​

÷ 4

÷ 4

=

miles

hour

70

Steven drives 70 miles in one hour.

Your Turn

Question #8 – Audrey buys 3 tickets to a concert for $90. Find the cost of each ticket. (Submit the unit rate as a fraction to CPS)

​

Each ticket costs $30.

÷ 3

÷ 3

=

dollars

ticket

30

Average Rate

• Average rate is the average speed (how fast something is happening).

average rate =

distance

time

d =

rt

Your Turn

Question #9 – Jean finishes a 4-mile race in 0.5 hour. Find Jean’s average rate in miles per hour.

average rate =

distance

time

4 miles

0.5 hour

=

8

miles per hour

Jean’s average speed in the race is 8 miles per hour.

Sunshine State Standards�(http://www.floridastandards.org/Standards/FLStandardSearch.aspx

• MA.6.A.2.2 – Interpret and compare ratios and rates.