1. Solving proportions

2. Proportions What are proportions?
- If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures.
What do we mean by similar?
- Similar describes things which have the same shape but are not the same size. 1 2 4 8 =
1:3 = 3:9

3. Solve the proportion. = t 32 7 16
ANSWER 14 = 18 24 b 12
ANSWER 9

4. What if…..
Sometimes the equivalent ratios are not simple.

5. Cross multiply

6. Cross multiply

7. Cross multiply

8. Set up and solve this proportion.
8) 5 is to 4 as 45 is to x. 5
Now cross
multiply 45
____ = ____ 4 x 5x =
180 5 5 x = 36

9. First - Set up & solve the proportion.
9) 3 is to 2 as x is to 18. 3
Now cross
multiply x
____ = ____ 2 18 2x = 54 2 2 x = 27

10. NO set up this time!!
Just solve…..
10) 6x =
144 6 6 x = 24

11. Use the cross products property
Solve the proportion = 8 x 6 15 = 8 x 6 15
Write original proportion.
8 15 = x 6
Cross products property
120 = 6x
Simplify.
20 = x
Divide each side by 6.

12. EXAMPLE 1
GUIDED PRACTICE
Solve the proportion. Check your solution. = 4 a 5 37
29.6
ANSWER

13. Solve the proportion. = 21 n 2 5
ANSWER
52.5 = 4 11 9 p
ANSWER
24.75

14. Solve the proportion. = 4 7 15 x
ANSWER
26.25 = 5 32 2 p
ANSWER
12.8

15. Solve the proportion.
It takes 30 tomatillos to make 8 ounces of enchilada
sauce. How many tomatillos does it take to make 12
ounces of enchilada sauce?
SET IT UP

16. Solve the proportion.
It takes 30 tomatillos to make 8 ounces of enchilada
sauce. How many tomatillos does it take to make 12
ounces of enchilada sauce?
SET IT UP = 30 8 x 12

17. Solve the proportion.
It takes 30 tomatillos to make 8 ounces of enchilada
sauce. How many tomatillos does it take to make 12
ounces of enchilada sauce?
ANSWER
45 tomatillos

18. Solve the proportion. a 7 9 21 =
ANSWER 3

19. Solve the proportion. 32 28 = m 14 16
ANSWER
A printer can print 12 color pages in 3 minutes. How many color pages can the printer print in 9 minutes? Write and solve a proportion to find the answer.
ANSWER 12 3 = x 9
; 36 color pages

20. How much food should the seal be fed per day? Seals
Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds.
How much food should the seal be fed per day?
Seals
SOLUTION
STEP 1
Write a proportion involving two ratios that compare the amount of food with the weight of the seal. x
280 = 8
amount of food
100
weight of seal

21. Use the scale on a map
Maps
SOLUTION
From the map’s scale, 1 centimeter represents 85 kilometers. On the map, the distance between Cleveland and Cincinnati is about 4.2 centimeters.

22. Write and solve a proportion to find the distance d between the cities.=
4.2 d 1
centimeters 85
kilometers
1 d =
Cross products property
ANSWER
The actual distance between Cleveland and Cincinnati is about 357 kilometers.
d = 357
Simplify.

23. EXAMPLE 4
Use the scale on a map
GUIDED PRACTICE
Model ships 6.
The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II.
ANSWER
about 960 ft

24. Solving Proportional Problems
So how do we use proportions and similar figures?
8 feet
4 feet
2 feet
? feet

25. Solving Proportional Problems
So how do we use proportions and similar figures?
ANSWER 4
8 feet
4 feet
2 feet
? feet

26. Try One Yourself
Set up a proportion. What is the width of the larger stick figure?
8 feet
12 feet
Knowing the two figures are similar the proportion between the two stick figures is 8 feet:12 feet.
Once written as a fraction 8/12 reduces to 2/3. So the proportion between the two stick figures is 2:3.
If the proportion is 2:3 then the student should set up this equation and solve for x:
2 / 3 = 4 / x
2 * x = 3 * 4
x = 12 / 2
x = 6 feet
4 feet
x feet

27. Solving for the Building’s Height
Here is a sample calculation for the height of a building:
x ft
3 ft =
48 ft
4 ft
x feet
48 feet
4x = 144
x = 36
yardstick
3 feet
The height of the building is 36 feet.
4 feet

28. You try it!!
11)
Now
simplify
16m = 8 16 16 m =

29. 12) Mr. Jones has taken a survey of college students and found that 40 out of 47 students are liberal arts majors. If a college has 10,827 students, what is the number of students who are liberal arts majors, rounded to the nearest whole number?
First – Set up
Your proportion! 40 x
____ = _______ 47
10,827
47x =
433,080
Now cross
multiply 47 47 x =
9214

30. 13) Geothermal energy is heat from inside the earth
13) Geothermal energy is heat from inside the earth. Underground temperatures generally increase 9°C for every 300 meters of depth. How deep would a well have to be for the temperature to reach 216°C ?
First – Set up
Your proportion! 9°
216°
____ = _____
300 m 9m =
64800 9 9 m =
7200

31. 1cm 11cm 30km x 1x = 330 x = 330 km ____ = _____
14) A map has a scale of 1 cm = 30 km. If two cities are 11 cm apart on the map, what is the actual distance between the two cities to the nearest tenth of a km?
First – Set up
Your proportion!
1cm
11cm
____ = _____
30km x 1x =
330 x =
330 km

32. Practice

33. Practice

34. Practice

35. Practice

36. Practice

37. Practice