Learning Target:

1. Learning Target: I can… Set up and solve proportions

2. Proportion: An equation that shows two ratios are equivalent

3. To check to see if it is a proportion:  =  Cross multiply and see if you get the same number or find the unit rate  = 

4. Is the following a proportion? (a = yes, b = no) 1. 3 = 2_ 25 15 2. 6 = 4_ 24 16

5. Solving Proportions To solve proportions, cross multiply – then divide! Example: y_ = 10_ 15 25 y ∙ 25 = 15 ∙ 10 y ∙ 25 = 150 y = 6

8. 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.

9. 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.

10. 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.

11. 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)

12. 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)

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

14. 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?

15. Ratio and Proportions 1) A local Humane Society houses 200 animals. The ratio of dogs to all animals is 13:20. Write a proportion that gives the number of dogs d. How many dogs are in the Human Society?

16. Ratio and Proportions 2) The ratio of boys to all students in a school is 1:3. There are 600 students in a school. Write a proportion that gives the number of boys b.. How many boys are in the school? How many girls are in the school?

17. 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?

18. The female to male ratio at General Sherman is 1:2. If there are 720 students at General Sherman, how many are girls? • 360 • 1440 • 240 • 300

19. 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? • 15 • 6 • 10 • 4

20. 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?

21. Learning Target: I can… Solve word problems using a proportion

22. To solve proportions, ____________________________ – then ______________! Word Problems – MAKE SURE YOU SHOW THE PROPORTION WITH _________!!!

23. Cross Multiply 3 ∙ 10 = 4 ∙ x 30 = 4x Divide by 4 x =$7.50

24. Quick Check!

25. Quick Check!

26. Proportions Review

27. 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?

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

29. CPS Quick Check! • How much would 4 pounds of oranges cost if 2 pounds cost $3? 2 pounds = 4 pounds $3 $6

30. Shadow Proportion Problems

31. 2) A 5-ft tall student casts a 12-ft shadow. A tree casts a 27-ft shadow. How tall is the tree? • 11.25 ft • 64.8 ft • 297 ft • 34 ft

34. SCALES

35. 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?

36. Using a Map Scale If the distance from the swimming pool to the horse corral is 4cm, how many meters away is it?

37. 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?

38. 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?

39. Similar Figures • Shape but different size • They are proportional • Symbol ~

40. Similar Figures

41. Determine the length of the unknown side. 15 12 ? 4 3 9

42. Determine the length of the unknown side. ? 2 24 4

45. Find the value of x

46. What is the perimeter of ABC? 15 12 B ? 4 A C 3 9

47. Two Step Proportions

48. 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?

49. 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?