1. 3 ? = 5. 10 20 3 6 ANSWER = 10 20 32 8 = 24 6 ? 8 6. = 24 6 ANSWER Copy and complete the statement to write an equivalent ratio.

2. Learning Target:Students will learn how to write proportions and solve proportions using cross products property.

3. Proportion: an equation that shows two ratios are equivalent. a : b = c : d

4. Cross Product Property:- The cross products of a proportion are equal.If , then a d = b c.

5. ? = EXAMPLE 1 Use cross products to decide whether the ratios form a proportion. 3 12 a. 5 18

6. Answer:3 18 = 5 1254 = 6054 does not equal 60 therefore the ratio is NOT a proportion.

7. ? = EXAMPLE 1 Use cross products to decide whether the ratios form a proportion. 8 20 b. 10 25

8. Answer:10 20 = 8 25 200 = 200200 does equals 200 therefore the ratio is a proportion.

9. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios.

10. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios. 4 12

11. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios. 4 5 4 20 = x 12

12. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios. 4 5 4 20 = x 12

13. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios. 4 5 4 20 = x 12 12 5

14. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios. 4 5 4 20 = x 12 12 5 12 5 = 60, so x = 60.

15. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios. 4 5 4 20 = x 12 12 5 12 5 = 60, so x = 60. The solution is 60. ANSWER

16. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 2 Use cross products.

17. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 2 Use cross products. 4 20 = x 12

18. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 2 Use cross products. 4 20 = x 12 4x = 240

19. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 2 Use cross products. 4 20 = x 12 4x = 240

20. EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 2 Use cross products. 4 20 = x 12 4x = 240 x = 60

21. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4

22. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION

23. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x = 3 1.4

24. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4

25. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 6.3 =1.4x

26. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x

27. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x 6.3 1.4 = x

28. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x 6.3 1.4 = x Write the related division equation.

29. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x 6.3 1.4 = x Write the related division equation. 4.5 = x

30. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x 6.3 1.4 = x Write the related division equation. 4.5 = x Divide.

31. EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x 6.3 1.4 = x Write the related division equation. 4.5 = x Divide. The solution is 4.5. ANSWER

32. GUIDED PRACTICE for Example 4 Write the related equation. Use it to solve the proportion. 22.5 30 a 50 9. 8. = = 6 60 6 y ANSWER ANSWER 1800 = 50y 135 = 6a 1800 135 y a = = 50 6 a = 22.5 y = 36

33. EXAMPLE 3 Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?

34. EXAMPLE 3 Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles? SOLUTION Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.

35. EXAMPLE 3 Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles? SOLUTION Use a proportion. Let t represent the total time, in hours, of the 20 mile trip. Write a verbal model.

36. EXAMPLE 3 Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles? SOLUTION Use a proportion. Let t represent the total time, in hours, of the 20 mile trip. Distance traveled Total distance Write a verbal model. = Time traveled Total time

37. EXAMPLE 3 Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles? SOLUTION Use a proportion. Let t represent the total time, in hours, of the 20 mile trip. Distance traveled Total distance Write a verbal model. = Time traveled Total time Substitutevalues.

38. EXAMPLE 3 Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles? SOLUTION Use a proportion. Let t represent the total time, in hours, of the 20 mile trip. Distance traveled Total distance Write a verbal model. = Time traveled Total time 20 mi 5 mi Substitutevalues. = t h 3 h

39. EXAMPLE 3 Write the cross products.

40. EXAMPLE 3 20 5 Write the cross products. = t 3

41. EXAMPLE 3 20 5 Write the cross products. = t 3 They are equal.

42. EXAMPLE 3 20 5 Write the cross products. = t 3 5t 60 = They are equal.

43. EXAMPLE 3 20 5 Write the cross products. = t 3 5t 60 = They are equal. Solve using mental math.

44. EXAMPLE 3 20 5 Write the cross products. = t 3 5t 60 = They are equal. t = 12 Solve using mental math.

45. EXAMPLE 3 20 5 Write the cross products. = t 3 5t 60 = They are equal. t = 12 Solve using mental math. It will take you 12 hours to travel 20 miles. ANSWER

46. GUIDED PRACTICE for Examples 1, 2, and 3 7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?

47. GUIDED PRACTICE for Examples 1, 2, and 3 7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles? ANSWER

48. GUIDED PRACTICE for Examples 1, 2, and 3 7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles? ANSWER 20 mi 4 mi = t h 2 h

49. GUIDED PRACTICE for Examples 1, 2, and 3 7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles? ANSWER 20 mi 4 mi = t h 2 h 20 4 = t 2

50. GUIDED PRACTICE for Examples 1, 2, and 3 7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles? ANSWER 20 mi 4 mi = t h 2 h 20 4 = t 2 4t 40 =

51. GUIDED PRACTICE for Examples 1, 2, and 3 7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles? ANSWER 20 mi 4 mi = t h 2 h 20 4 = t 2 4t 40 = t = 10h

52. Can you write proportions and solve proportions using cross products property.