Writing Ratios as Proportions

How can you solve problems with proportions?

©Exceeding the CORE

In this lesson students will
be able to:
✓ Use Unit Rates to Solve Proportions
✓ Use Proportional Relationships to

Find Distance on a Map

How can you solve problems with proportions?

©Exceeding the CORE

A proportion is a statement that two ratios or
rates are equivalent.

1

4

2

8 are equivalent ratios.

1

4

2

8 is a proportion.

​=

​=

How can you solve problems with proportions?

©Exceeding the CORE

15

a) For every 3 text messages that Chris sends,
Andrea sends 7. How many text messages would
Chris send if Andrea sends 35 messages?

1. USE EQUIVALENT RATESTO SOLVE PROPORTIONS

𝐶ℎ𝑟𝑖𝑠
𝐴𝑛𝑑𝑟𝑒𝑎

3
7

35

𝐶ℎ𝑟𝑖𝑠
𝐴𝑛𝑑𝑟𝑒𝑎

× 5

× 5
Write a proportion.

Use common denominators
to write equivalent ratios.

Multiply the numerators and
the denominators to create an
equivalent ratio.

If Andrea sends 35 text messages, Chris sends 15 text
messages.

How can you solve problems with proportions?

©Exceeding the CORE

b) Ms. Klein is ordering pizza for the 6th
Grade dance. She plans to order 2 cheese
pizzas for every 5 pepperoni pizzas she
order. How many cheese pizzas will she
order if she orders 20 pepperoni pizzas?

1. USE EQUIVALENT RATESTO SOLVE PROPORTIONS

(PRACTICE)

𝑐ℎ𝑒𝑒𝑠𝑒

𝑝𝑒𝑝𝑝𝑒𝑟𝑜𝑛𝑖

2
5=

20

𝑐ℎ𝑒𝑒𝑠𝑒

𝑝𝑒𝑝𝑝𝑒𝑟𝑜𝑛𝑖

× 4

× 4

How can you solve problems with proportions?

©Exceeding the CORE

a) Shirley gets 6 paychecks in 2 months. How
many paychecks does she get in 9 months?

2. USE UNIT RATESTO SOLVE PROPORTIONS

6
2 =

9

1. Write a proportion.

6
2 =

27
9

× 4.5

× 4.5

𝑝𝑎𝑦𝑐ℎ𝑒𝑐𝑘𝑠

𝑚𝑜𝑛𝑡ℎ𝑠

𝑝𝑎𝑦𝑐ℎ𝑒𝑐𝑘𝑠

𝑚𝑜𝑛𝑡ℎ𝑠

9 is not of multiple of 2. So
there is no whole number
that you can multiply 6 to.

Shirley gets 27 paychecks in 9 months.

How can you solve problems with proportions?

©Exceeding the CORE

2. USE UNIT RATESTO SOLVE PROPORTIONS
b) Chad can do 45 sit-ups in 3 minutes.
At that rate, how many sit-ups can he do
in 10 minutes?

(PRACTICE)

45
3 =

10

x

x

𝑠𝑖𝑡 − 𝑢𝑝𝑠

𝑚𝑖𝑛𝑢𝑡𝑒𝑠

𝑠𝑖𝑡 − 𝑢𝑝𝑠

𝑚𝑖𝑛𝑢𝑡𝑒𝑠

How can you solve problems with proportions?

©Exceeding the CORE

A scale drawing shows a real object with accurate
sizes reduced or enlarged by a certain amount.

3. FIND DISTANCEONA MAP

 A map is a scale drawing. The measurements on a map
are in proportion to the actual distances.

 A scale describes how the dimensions in the objects
compare.

How can you solve problems with proportions?

©Exceeding the CORE

a) Janet drew a scale drawing of her house and
its lot. The scale she used was 1 inch : 5 feet.
If the actual distance between the driveway
and the front door is 15 feet, what is the
distance in the drawing?

3. FIND DISTANCEONA MAP

1 𝑖𝑛𝑐ℎ
5 𝑓𝑒𝑒𝑡 =

15 𝑓𝑒𝑒𝑡

× 3

× 3

3 inches

Write a proportion.

Write an equivalent rate to
find the missing number.

The distance in the drawing is 3 inches.

How can you solve problems with proportions?

©Exceeding the CORE

b) Seth made a scale drawing of a county park. The scale
of the drawing was 1 inch : 2.5 yards. The picnic area is 6
inches from the bathrooms in the drawing. What is the
actual distance between the picnic area and the
bathrooms?

3. FIND DISTANCEONA MAP (PRACTICE)

1 𝑖𝑛𝑐ℎ

6 𝑖𝑛𝑐ℎ𝑒𝑠

×

×

2.5 𝑦𝑎𝑟𝑑𝑠 =

Multiple Choice

Phil wants to enlarge a photo that is 6 inches wide and 8 inches tall. The enlarged photo keeps the same ratio. How tall is the enlarged photo if it is 12 inches wide?

• 18 inches tall

• 16 inches tall

• 20 inches tall

• 10 inches tall

Multiple Choice

The scale of a map is 1 inch : 3 miles.  Red Oak is 15 miles from Marsh City.  What would its distance be on the map?

• 5 inches

• 10 inches

• 15 inches

• 20 inches

Multiple Choice

Taliyah drives 120 miles in 3 hours. At the same rate, how far will she drive in 5 hours?

• 125 miles

• 150 miles

• 175 miles

• 200 miles

Multiple Choice

A fireplace burns 6 same-sized logs in 3 hours. How many logs  does the fireplace burn in 9 hours?

• 16 logs

• 18 logs

• 20 logs

• 22 logs

Multiple Choice

A warehouse uses large trucks to ship goods to stores. A fleet of 3 trucks can empty 2 storage sections in the warehouse. If 18 trucks are needed to completely empty the warehouse, how many storage sections are there in the warehouse?

• 10 storage sections

• 12 storage sections

• 14 storage sections

• 16 storage sections