1. 7.1 OBJ: Use ratios and proportions.
EQ: How do we use ratios to set up proportions?

2. VOCABULARY
Ratio: a comparison of a number a and a nonzero number b using division.
All ratios must be in reduced form.

3. 60 cm : 200 cm can be written as the fraction . 60 cm 200 cm
Example 1
Simplify Ratios
Simplify the ratio. a.
60 cm : 200 cm b.
3 ft
18 in.
SOLUTION a.
60 cm : 200 cm can be written as the fraction
60 cm
200 cm =
60 cm
200 cm
60 ÷ 20
200 ÷ 20 3 10
Simplify.
is read as “3 to 10.” = 3

4. Example 1 3 ft 3 · 12 in. b. = 18 in. 36 ÷ 18 = 18 ÷ 18 =
Simplify Ratios =
3 · 12 in.
18 in.
3 ft b. =
36 ÷ 18
18 ÷ 18 2 1 = 4

5. In the diagram, AB : BC is 4 : 1 and AC = 30. Find AB and BC.
Example 2
Use Ratios
In the diagram, AB : BC is 4 : 1 and AC = 30. Find AB and BC.
SOLUTION
Let x = BC. Because the ratio of AB to BC is 4 to 1, you know that AB = 4x.
AB + BC = AC
Segment Addition Postulate
4x + x = 30
Substitute 4x for AB, x for BC, and 30 for AC.
5x = 30
Add like terms.
x = 6
Divide each side by 5. 5

6. To find AB and BC, substitute 6 for x.
Example 2
Use Ratios
To find AB and BC, substitute 6 for x.
AB = 4x = 4 · 6 = 24
BC = x = 6
ANSWER
So, AB = 24 and BC = 6. 6

7. Example 3
Use Ratios
The perimeter of a rectangle is 80 feet. The ratio of the length to the width is 7 : 3. Find the length and the width of the rectangle.
SOLUTION
The ratio of length to width is 7 to 3. You can let the length l = 7x and the width w = 3x.
2l + 2w = P
Formula for the perimeter of a rectangle
2(7x) + 2(3x) = 80
Substitute 7x for l, 3x for w, and 80 for P.
14x + 6x = 80
Multiply.
20x = 80
Add like terms.
x = 4
Divide each side by 20. 7

9. To find the length and width of the rectangle, substitute 4 for x.
Example 3
Use Ratios
To find the length and width of the rectangle, substitute 4 for x.
l = 7x = 7 · 4 = 28
w = 3x = 3 · 4 = 12
ANSWER
The length is 28 feet, and the width is 12 feet. 9

10. In the diagram, EF : FG is 2 : 1 and EG = 24. Find EF and FG.
Checkpoint
Use Ratios 1.
In the diagram, EF : FG is 2 : 1 and EG = 24. Find EF and FG.

11. In the diagram, EF : FG is 2 : 1 and EG = 24. Find EF and FG.
Checkpoint
Use Ratios 1.
In the diagram, EF : FG is 2 : 1 and EG = 24. Find EF and FG.
ANSWER
EF = 16; FG = 8 2.
The perimeter of a rectangle is 84 feet. The ratio of the length to the width is 4 : 3. Find the length and the width of the rectangle.
ANSWER
length, 24 ft; width, 18 ft

13. VOCABULARY
Ratio: a comparison of a number a and a nonzero number b using division.
Proportion: an equation that states that two ratios are equal.

15. Cross Product Property
In a proportion, the product of the extremes is equal to the product of the means.

16. Ex: Solve the Proportion.
x = 1

17. Example 4 Solve the proportion . = y + 2 6 5 3 SOLUTION = y + 2 6 5 3
Solve a Proportion
Solve the proportion =
y + 2 6 5 3
SOLUTION
Write original proportion. =
y + 2 6 5 3
5 · 6 = 3(y + 2)
Cross product property
30 = 3y + 6
Multiply and use distributive property.
30 – 6 = 3y + 6 – 6
Subtract 6 from each side.
24 = 3y
Simplify.
Divide each side by 3. = 3y 3 24
8 = y
Simplify. 17

18. Solve the proportion. We do….
Checkpoint
Solve a Proportion
Solve the proportion. We do…. 1. = 6 8 3 x
ANSWER 4 2. = 15 y 5 3
ANSWER 9 3. =
m + 2 5 14 10
ANSWER 5

19. From the scale on the map, you know that 1 inch represents 180 miles.
Example 5
Write and Solve a Proportion
Use the map of Texas to estimate the distance between Dallas and Houston.
SOLUTION
From the scale on the map, you know that 1 inch represents 180 miles. 19

20. On the map, the distance between Dallas and Houston
Example 5
Write and Solve a Proportion
On the map, the distance between Dallas and Houston
is 1 inches, which can be written as 1.25 inches. 1 4
Let x represent the actual distance between Dallas and Houston. You can write the following proportion.
Write a proportion. =
1.25 in.
x mi
1 in.
180 mi.
1 · x = 180 · 1.25
Cross product property
x = 225
Simplify.
ANSWER
The distance between Dallas and Houston is about 225 miles. 20

21. Homework
Worksheet 7.1A