1. Notes for January 13 Proportions!!!

2. Word of the Day Inane stupid; dumb; pathetic

3.  IWBAT solve algebraic proportions.

4. Write each fraction in lowest terms (simplify). 14 16 1. 9 72 3. 24 64 2. 45 120 4. 7878 3838 1818 3838

5. 7:5 28:20

6. Find two ratios that are equivalent to each given ratio. B. 18 54 1313 128 48 A. = 9 27 = 9 2 27 2 = 9 ÷ 9 27 ÷ 9 9 27 = Two ratios equivalent to are and. 9 27 18 54 1313 Two ratios equivalent to are and. 64 24 128 48 8383 = 64 2 24 2 64 24 = Multiply or divide the numerator and denominator by the same nonzero number. 8383 = 64 ÷ 8 24 ÷ 8 64 24 =

7. Ratios that are equivalent are said to be proportional, or in proportion. Equivalent ratios are identical when they are written in simplest form.

8. 12 15 B. and 27 36 3 27 A. and 2 18 Since, the ratios are in proportion. 1919 = 1919 1919 = 3 ÷ 3 27 ÷ 3 3 27 = 1919 = 2 ÷ 2 18 ÷ 2 2 18 = 4545 = 12 ÷ 3 15 ÷ 3 12 15 = 3434 = 27 ÷ 9 36 ÷ 9 27 36 = Since, the ratios are not in proportion. 4545  3434

9. 14 49 B. and 16 36 Since, the ratios are in proportion. 1515 = 1515 1515 = 3 ÷ 3 15 ÷ 3 3 15 = 1515 = 9 ÷ 9 45 ÷ 9 9 45 = 2727 = 14 ÷ 7 49 ÷ 7 14 49 = 4949 = 16 ÷ 4 36 ÷ 4 16 36 = Since, the ratios are not in proportion. 2727  4949 3 15 A. and 9 45

10. We can also use cross products to figure out whether two ratios are in proportion.

11. 4 10 6 15 Since the cross products are equal, the ratios are proportional. 60 = ? 60 = 60 Find cross products. 60 4 10 6 15

12.  Algebraic proportions are the same as regular proportions.  The cross-products must equal each other!

13.  To solve algebraic proportions, follow these steps: 1.)Cross-multiply 2.)Set the products equal to each other 3.)Solve for x 4.)Box your answer

14.  The most important thing to remember is to:

15.  Solve for x in the following proportion:

16.  Cross-multiply 2(12) = 24 4(x) = 4x

17. Set the products equal to each other 4 x = 24 What am I called?

18.  Solve for x

19.  Solve for x in the following proportion:

20.  Cross-multiply 5(-6) = -30 x(15) = 15x

21. Set the products equal to each other 15 x = -30 What am I called?

22.  Solve for x

25. Notes for January 14th Proportions!!!

26. Let’s not make it too hard to begin with. Let’s start by just throwing a coefficient in front of the x.

27.  What happens when you see one of these?

28.  Cross-multiply 2 x (10) = 20 x 8(5) = 40

29. Set the products equal to each other 20 x = 40 What am I called?

30.  Solve for x

31.  Solve the following proportion

32.  Cross-multiply 20(3 x ) = 60 x 12(5) = 60

33. Set the products equal to each other 60 x = 60 What am I called?

34.  Solve for x

36. As a kicker, I have much expertise in this manner … LET’S KICK IT UP!!!

37.  What happens when you see a proportion?

38.  When solving proportions like that, you must remember that each numerator and denominator are together – like a couple. You cannot separate them.

39. 1.) Cross-Multiply 2.) Set the products equal to each other 3.) Use the Distributive Property 4.) Solve for x 5.) Box your answer

40.  Cross-multiply 2( x – 2) = 2( x – 2) -4(5) = -20

41.  Set the products each to each other 2( x – 2) = -20

42.  Use the Distributive Property and solve for x

43.  Solve the following proportion:

44.  Cross-multiply -2( x + 6) = -2( x + 6) 3( x - 5) = 3( x – 5)

45.  Set the products each to each other -2( x + 6) = 3( x – 5)

46.  Use the Distributive Property and solve for x

48. It’ll be a Party in Ms. Ryan’s Room!

51. Exit Ticket 1. Are these two ratios in proportion? j A. Yes B. No C. Not sure 2. Solve for k : j A. k = 40 B. k = 4 C. k = 5 D. k = 8 3. Solve for x (simplify your answer): j A. x = 12 B. x = 4/7 C. x = -21 D. x = 12/21 4. Solve for b: j A. b = 1.5 B. b = 8.5 C. b = -1.5 D. B = -8.5