1. Wednesday, March 12 Equivalent Ratios

2. Objective: To understand how to prove fractions are equivalent.

3. Equivalent Ratios There are different ways to determine if two ratios or rates are equivalent. 1. Compare unit rates. A unit rate always has to have a denominator of what?

4. Equivalent Ratios There are different ways to determine if two ratios or rates are equivalent. 1. Compare unit rates. A unit rate always has to have a denominator of what? 1

5. Equivalent Ratios

8. ??

10. The other way to find if two ratios are equivalent is to set them equal to each other (proportion)and cross multiply. e.g. 20 miles 45 miles 5 hours = 9 hours

11. Equivalent Ratios When setting up a proportion the same units are on top and the same are on bottom. e.g. 20 miles 45 miles 5 hours = 9 hours

12. Equivalent Ratios The other way to find if two ratios are equivalent is to set them equal to each other and cross multiply. e.g. 20 45 5 = 9 5 x 45 = ?

13. Equivalent Ratios The other way to find if two ratios are equivalent is to set them equal to each other and cross multiply. e.g. 20 45 5 = 9 5 x 45 = 225

14. Equivalent Ratios The other way to find if two ratios are equivalent is to set them equal to each other and cross multiply. e.g. 20 45 5 = 9 5 x 45 = 225 20 x 9 = ?

15. Equivalent Ratios The other way to find if two ratios are equivalent is to set them equal to each other and cross multiply. e.g. 20 45 5 = 9 5 x 45 = 225 and 20 x 9 = 180

16. Equivalent Ratios The other way to find if two ratios are equivalent is to set them equal to each other and cross multiply. e.g. 20 45 5 = 9 Does 225 = 180 ?

17. Equivalent Ratios The other way to find if two ratios are equivalent is to set them equal to each other and cross multiply. e.g. 20 45 5 = 9 225 ≠ 180, they are not equivalent.

18. Equivalent Ratios Use either method.

19. Equivalent Ratios ??

23. Do this on your own.

24. Equivalent Ratios 90 x 3 = 270 and 45 x 6 = 270 270 = 270 They are equivalent.

25. Equivalent Ratios Is this a true statement? 5 2 6 = 3

26. Equivalent Ratios Is this a true statement? 5 2 6 = 3 Does 5 x 3 = 6 x 2?

27. Equivalent Ratios Is this a true statement? 5 2 6 = 3 Does 5 x 3 = 6 x 2? 15 ≠ 12 It is not a true statement.

28. Equivalent Ratios Solve the proportion. 3 6 4 = m

29. Equivalent Ratios Solve the proportion. 3 6 4 = m 3m

30. Equivalent Ratios Solve the proportion. 3 6 4 = m 3m = 24

31. Equivalent Ratios Solve the proportion. 3m 24 3 = 3 m = 8

32. Equivalent Ratios Solve the proportion. d 3 16 = 8 Do this on your own.

33. Equivalent Ratios Solve the proportion. d 3 16 = 8 8d 48 8 = 8 d = 6

34. Equivalent Ratios Solve the proportion. 34 2 x = 4 Do this on your own.

35. Equivalent Ratios Solve the proportion. 34 2 x = 4 136 2x 2 = 2 68 = x

36. Equivalent Ratios On a recent Saturday Mike rode 42 miles in 3 hours in the morning. In the afternoon he rode 56 miles in 4 hours. Are these equivalent ratios?

37. Equivalent Ratios On a recent Saturday Mike rode 42 miles in 3 hours in the morning. In the afternoon he rode 56 miles in 4 hours. Are these equivalent ratios? 42 miles 56 miles 3 hours = 4 hours Remember – When setting up a proportion, the same units must be on the top and the same units must be on the bottom.

38. Equivalent Ratios On a recent Saturday Mike rode 42 miles in 3 hours in the morning. In the afternoon he rode 56 miles in 4 hours. Are these equivalent ratios? 42 miles 56 miles 3 hours = 4 hours 3 x 56 = 42 x 4 168 = 168 They are equivalent

39. Equivalent Ratios Three out of five students in the first row made corrections on the last test. Fifteen out of 20 total students in the class made test corrections. Are these equivalent ratios? Do this on your own.

40. Equivalent Ratios Three out of five students in the first row made corrections on the last test. Fifteen out of 20 total students in the class made test corrections. Are these equivalent ratios? 3test corrections 15 test corrections 5 total = 20 total 5 x 15 = 3 x 20 75 ≠ 60 They are not equivalent.

41. Equivalent Ratios A scale model of a house has a scale of 1 inch = 2.5 feet. If the width of the house on the model is 12 inches, what is the actual width of the house? Do this on your own.

42. Equivalent Ratios A scale model of a house has a scale of 1 inch = 2.5 feet. If the width of the house on the model is 12 inches, what is the actual width of the house? 1in 12in 2.5 ft = x ft x = 12 (2.5) ft x = 30 ft

43. Equivalent Ratios On a map of Arizona, the distance between Meadview and Willow Beach is 14 inches. If the scale on the map is 2 inches = 5 miles, what is the actual distance between Meadview and Willow Beach? Do this on your own.

44. Equivalent Ratios On a map of Arizona, the distance between Meadview and Willow Beach is 14 inches. If the scale on the map is 2 inches = 5 miles, what is the actual distance between Meadview and Willow Beach? 2in 14in 5mi = x mi 2x = 70 2 2 x = 35

45. Equivalent Ratios Agenda Notes – Homework – Homework Practice 2-6 Due Thursday, March 13 You can use a calculator, but show all work!