Learning Target:

I can…Set up and solve proportions

Proportion:

An equation that shows two ratios are equivalent

To check to see if it is a proportion:

= Cross multiply and see if you get the

same number or find the unit rate

=

Is the following a proportion? (a = yes, b = no)

1. 3 = 2_ 25 15

2. 6 = 4_24 16

Solving Proportions

To solve proportions, cross multiply – then divide!

Example:

y_ = 10_15 25y ∙ 25 = 15 ∙ 10y ∙ 25 = 150y = 6

Use a proportion to fill in a table or find missing points.1) Cindy took two trips. There is a proportional relationship between the number of miles she travels and the gallons of gas her car uses. Fill in the blank.

Trip 1 Trip 2Miles Traveled

200 160

Gallons Used 4600

2) Amaya types as the same speed for all of her essays so there is a proportional relationship between the number words she types and the minutes it takes her. Fill in the blank.

Essay 1 Essay 2

Words 3120

Minutes 30 12

3) James is making muffins. As he makes more servings, there is a proportional relationship between the cups of sugar he uses and the cups of flour. Fill in the blanks.

Serving 1

Serving 2

Serving 3

Serving 4

Serving 5

Sugar 1

Flour 2 3

Knowing Missing Points

4) Line k show a proportional relationship between x and y. If (2,5) is a point on this line, then fill in the missing coordinates below:

a. (4, ______) d. (_______, 15)

b. (1, ______) e. (_______, 7.5)

c. (7, ______) f. (_______, 0)

Knowing Missing Points

5) Line k show a proportional relationship between x and y. If (4,6) is a point on this line, then fill in the missing coordinates below:

a. (8, ______) d. (_______, 15)

b. (1, ______) e. (_______, 7.5)

c. (7, ______) f. (_______, 0)

Proportions and Percent:Write a proportion to solve the following, always putting the percent over _____________.

1) Lila wants to score at an 86% on her test. If her test has 50 points, how many points must she earn on the test to reach her goal?

2) Reynaldo wants to score at an 90% on his test. If his test has 70 points, how many points must she earn on the test to reach his goal?

Ratio and Proportions

1) A local Humane Society houses 200 animals. The ratio of dogs to all animals is 13:20. a. Write a proportion that gives the number of dogs d.

b. How many dogs are in the Human Society?

Ratio and Proportions

2) The ratio of boys to all students in a school is 1:3. There are 600 students in a school.a. Write a proportion that gives the number of boys b..

b. How many boys are in the school?

c. How many girls are in the school?

Ratio and Proportions

3) Mona counted a total of 56 ducks on the pond in Town Park. The ratio of female ducks to male ducks that Mona counted was 5:3. What was the total number of female ducks Mona counted on the pond?

The female to male ratio at General Sherman is 1:2. If there are 720 students at General Sherman, how many are girls?

A. 360B. 1440C. 240D. 300

Review

The ratio of male to female horses is 2:5. How many male horses are there if there are a total of 21 horses?

A. 15B. 6C. 10D. 4

Exit

The ratio of male to female students is 2:3. How many male students are there if there are a total of 300 students?

Learning Target:

I can…Solve word problems using a proportion

To solve proportions, ____________________________ – then ______________!

Word Problems – MAKE SURE YOU SHOW THE PROPORTION WITH _________!!!

Cross Multiply 3 ∙ 10 = 4 ∙ x

30 = 4x

Divide by 4 x =$7.50

Quick Check!

Quick Check!

Proportions Review

Erica gets 24 miles per gallon of gas when driving on the open highway. How many gallons of gas will her car use traveling a distance of 384 miles?

The scale on Myra’s atlas reads 1 inch equals 40 miles. How many inches on the map represent 125 miles?

CPS Quick Check!

1. How much would 4 pounds of oranges cost if 2 pounds cost $3?

2 pounds = 4 pounds $3 $6

Shadow Proportion Problems

2) A 5-ft tall student casts a 12-ft shadow. A tree casts a 27-ft shadow. How tall is the tree?

a. 11.25 ftb. 64.8 ftc. 297 ftd. 34 ft

SCALES

Chan is designing a new swimming pool that will have a length of 34 feet. He plans to make a scale drawing of the pool. In his drawing inches represents 1 foot. What should be the length, in inches, of Chan’s scale drawing of the pool?

Using a Map Scale

If the distance from the swimming pool to the horse corral is 4cm, how many meters away is it?

Using a Map Scale

If the from the lodge to the horse corral is 3cm in the picture, how many meters away is it in real life?

Using a Map Scale

If the distance from the mess hall to the swimming pool is 350m in real life, how many centimeters away is it in the drawing?

Similar Figures

1. Shape but different size2. They are proportional• Symbol ~

Similar Figures

Determine the length of the unknown side.

12

9

15

4

3

?

Determine the length of the unknown side.

4

2

24

?

Find the value of x

K

L

H G

J

4

6

x

15

What is the perimeter of ABC?

12

9

15

4

3

?A

B

C

Two Step Proportions

Lisa’s father is an architect. He builds a cardboard model of each building he designs. The scale of his model to the actual building is 1 inch = 8 feet.

How tall will the actual building be when the model is 3 feet tall?

On a scale drawing of a house a rectangular bedroom has a length of 4 inches and a perimeter of 20 inches. The scale is 1 inches = 2 foot. What is the actual width of the bedroom?

On a scale drawing of a house a rectangular bedroom has a length of 5 inches and a perimeter of 26 inches. The scale is 1 inches = 2 foot. What is the actual width of the bedroom?

2 step proportions

What is the perimeter of triangle DEF?15

2025

60

80

Learning Target:

I can…Solve ALL types of proportion problems

Below is a scale drawing of a house. If the kitchen actually has a length of 12 feet, what is the scale of the drawing to the actual house?

Learning Target:

I can…Find the missing side of similar figures

Similar Figures

• Have the same _______________ and _______________ sides.

• To find a missing side of similar figures, set up a ________________________ and solve.

1.

2. Solve for x

• Shapes within shapes are also ________________________.

• To find the missing side, ____________ the shapes and set up a proportion.

Find the value of x

K

L

H G

J

4

6

x

15

How tall is the tree?

Find the value of x

To find the perimeter of shapes, ___________________________.

The two rectangles are similar. What is the PERIMETER of rectangle EFGH?

To find two missing sides:

1. )

2)

X

Y Z

J

K

A.(1, 1)B.(4, 5)C.(6, -3)D.(4, -3)

Exit – Solve for x

Learning Target:

I can…Master ratio and proportions

Shadow problems 1,

2.

3. A landscape architect uses scale drawings to design layouts for his clients. The plan he is working on now is for a yard that is 150 feet long and 120 feet wide. When making a scale drawing he uses a ratio of 12:1, actual number of feet in the yard that he is working on to number of inches on the drawing. What are the dimensions of the scale drawing?

4.

Find the actual dimensions (length and width) of the kitchen. *Hint: you will need to use two proportions!

5. On a scale drawing of a house a rectangular bedroom has a length of 5 inches and a perimeter of 26inches. The scale is 1 inch = 2 foot. What is the actual width of the bedroom?

6. An architect builds a cardboard model of each building he designs. The scale of his model to the building is 1 in = 3 ft. How tall will the actual building be when the model is 3ft tall?

• Find the perimeter of each triangle.

Learning Target:

I can…Show what I know on my ratio and proportions

quiz

Ratio Review

Write the ratio of roses to flowers if Big Bob’s flowers has 13 tulips and 5 roses.

Ratio - Exit

In the local coed softball league, the female to male ratio is 4:6. If there are 160 players in the league, how many are female?

EXIT

An architect builds a cardboard model of each building he designs. The scale of his model to the building is 1 in = 4 ft. How tall will the actual building be when the model is 2 ft tall?

Challenge1.

2. On a scale drawing of a house a rectangular bedroom has a length of 5 inches and a perimeter of 26inches. The scale is 1 inch = 2 foot. What is the actual width of the bedroom?

3. An architect builds a cardboard model of each building he designs. The scale of his model to the building is 1 in = 3 ft. How tall will the actual building be when the model is 3ft tall?

Proportion Review!

3.125 inches

$3.25