1. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 1 Real Numbers and Introduction to Algebra

2. 22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: Quiz on Sections 1.2 and 1.3

3. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 1.5 Subtracting Real Numbers

4. 44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Objectives:  Subtract real numbers  Solve problems with subtraction  Evaluate algebraic expressions  Find complementary and supplementary angles

5. 55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If a and b are real numbers, then a – b = a + (– b) Subtracting Real Numbers

6. 66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Subtract. a. 4 ‒ 7 = ‒ 3 b. ‒ 8 ‒ ( ‒ 9) = 1 c. (–5) – 6 – (–3) = ‒ 8

7. 77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Subtract. a. 4 ‒ 7 = ‒ 3 b. ‒ 8 ‒ ( ‒ 9) = 1 c. (–5) – 6 – (–3) = ‒ 8

8. 88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Subtract. a. 4 ‒ 7 = ‒ 3 b. ‒ 8 ‒ ( ‒ 9) = 1 c. (–5) – 6 – (–3) = ‒ 8

9. 99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Subtract. a. 4 ‒ 7 = ‒ 3 b. ‒ 8 ‒ ( ‒ 9) = 1 c. (–5) – 6 – (–3) = ‒ 8

10. 10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Subtract. a. 6.9 ‒ ( ‒ 1.8) = 6.9 + 1.8 = 8.7 b. Example 2

11. 11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Subtract. a. 6.9 ‒ ( ‒ 1.8) = 6.9 + 1.8 = 8.7 b. Example 2

12. 12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Subtract. a. 6.9 ‒ ( ‒ 1.8) = 6.9 + 1.8 = 8.7 b. Example 2

13. 13 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Subtract. a. 6.9 ‒ ( ‒ 1.8) = 6.9 + 1.8 = 8.7 b. Example 2

14. 14 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Subtract. a. 6.9 ‒ ( ‒ 1.8) = 6.9 + 1.8 = 8.7 b. Example 2

15. 15 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ 9 – 5 + 11 – ( ‒ 7) = ‒ 9 + (–5) + 11 + 7 = 4 b. Example 3

16. 16 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ 9 – 5 + 11 – ( ‒ 7) = ‒ 9 + (–5) + 11 + 7 = 4 b. Example 3

17. 17 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ 9 – 5 + 11 – ( ‒ 7) = ‒ 9 + (–5) + 11 + 7 = 4 b. Example 3

18. 18 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ 9 – 5 + 11 – ( ‒ 7) = ‒ 9 + (–5) + 11 + 7 = 4 b. Example 3

19. 19 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ 9 – 5 + 11 – ( ‒ 7) = ‒ 9 + (–5) + 11 + 7 = 4 b. Example 3

20. 20 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ 9 – 5 + 11 – ( ‒ 7) = ‒ 9 + (–5) + 11 + 7 = 4 b. Example 3

21. 21 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ 9 – 5 + 11 – ( ‒ 7) = ‒ 9 + (–5) + 11 + 7 = 4 b. Example 3

22. 22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ 9 – 5 + 11 – ( ‒ 7) = ‒ 9 + (–5) + 11 + 7 = 4 b. Example 3

23. 23 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the value of the expression when x = 4 and y = ‒ 3. Example 4

24. 24 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the value of the expression when x = 4 and y = ‒ 3. Example 4 Plug it in!

25. 25 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the value of the expression when x = 4 and y = ‒ 3. Example 4 Plug it in!

26. 26 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the value of the expression when x = 4 and y = ‒ 3. Example 4 Plug it in!

27. 27 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the value of the expression when x = 4 and y = ‒ 3. Example 4 Plug it in!

28. 28 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the value of the expression when x = 4 and y = ‒ 3. Example 4 Plug it in! Simplify.

29. 29 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the value of the expression when x = 4 and y = ‒ 3. Example 4 Plug it in! Simplify.

30. 30 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the value of the expression when x = 4 and y = ‒ 3. Example 4 Plug it in! Simplify.

31. 31 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the value of the expression when x = 4 and y = ‒ 3. Example 4 Plug it in! Simplify.

32. 32 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 6 is a solution of x – 9 = 15. Example 5 x – 9 = 15 ‒ 6 – 9 ? 15 –15 ≠ 15 Thus, ‒ 6 is not a solution of x – 9 = 15.

33. 33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 6 is a solution of x – 9 = 15. Example 5 x – 9 = 15 ‒ 6 – 9 ? 15 –15 ≠ 15 Thus, ‒ 6 is not a solution of x – 9 = 15.

34. 34 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 6 is a solution of x – 9 = 15. Example 5 x – 9 = 15 ‒ 6 – 9 ? 15 –15 ≠ 15 Thus, ‒ 6 is not a solution of x – 9 = 15. Plug it in!

35. 35 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 6 is a solution of x – 9 = 15. Example 5 x – 9 = 15 ‒ 6 – 9 ? 15 –15 ≠ 15 Thus, ‒ 6 is not a solution of x – 9 = 15. Plug it in!

36. 36 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 6 is a solution of x – 9 = 15. Example 5 x – 9 = 15 ‒ 6 – 9 ? 15 –15 ≠ 15 Thus, ‒ 6 is not a solution of x – 9 = 15. Plug it in!

37. 37 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 6 is a solution of x – 9 = 15. Example 5 x – 9 = 15 ‒ 6 – 9 ? 15 –15 ≠ 15 Thus, ‒ 6 is not a solution of x – 9 = 15. Plug it in! Simplify.

38. 38 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 6 is a solution of x – 9 = 15. Example 5 x – 9 = 15 ‒ 6 – 9 ? 15 –15 ≠ 15 Thus, ‒ 6 is not a solution of x – 9 = 15. Plug it in! Simplify.

39. 39 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 6 is a solution of x – 9 = 15. Example 5 x – 9 = 15 ‒ 6 – 9 ? 15 –15 ≠ 15 Thus, ‒ 6 is not a solution of x – 9 = 15. Plug it in! Simplify.

40. 40 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. At 6:00 PM, the temperature at the Winter Olympics was 14°; by morning the temperature dropped to -23°. Find the overall change in temperature. Example 6

41. 41 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. At 6:00 PM, the temperature at the Winter Olympics was 14°; by morning the temperature dropped to -23°. Find the overall change in temperature. Example 6 What are we looking for?

42. 42 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. At 6:00 PM, the temperature at the Winter Olympics was 14°; by morning the temperature dropped to -23°. Find the overall change in temperature. Example 6 What are we looking for?

43. 43 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. At 6:00 PM, the temperature at the Winter Olympics was 14°; by morning the temperature dropped to -23°. Find the overall change in temperature. Example 6 What are we looking for? What do we need to find it?

44. 44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. At 6:00 PM, the temperature at the Winter Olympics was 14°; by morning the temperature dropped to -23°. Find the overall change in temperature. Example 6 What are we looking for? What do we need to find it?

45. 45 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. At 6:00 PM, the temperature at the Winter Olympics was 14°; by morning the temperature dropped to -23°. Find the overall change in temperature. Example 6 What are we looking for? What do we need to find it?

46. 46 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. At 6:00 PM, the temperature at the Winter Olympics was 14°; by morning the temperature dropped to -23°. Find the overall change in temperature. Example 6 What are we looking for? What do we need to find it? For the overall change, we take the end temp and subtract the beginning temp.

47. 47 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. At 6:00 PM, the temperature at the Winter Olympics was 14°; by morning the temperature dropped to -23°. Find the overall change in temperature. Example 6 What are we looking for? What do we need to find it? For the overall change, we take the end temp and subtract the beginning temp. -23° - 14°

48. 48 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. At 6:00 PM, the temperature at the Winter Olympics was 14°; by morning the temperature dropped to -23°. Find the overall change in temperature. Example 6 What are we looking for? What do we need to find it? For the overall change, we take the end temp and subtract the beginning temp. -23° - 14° = -37°

49. 49 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. At 6:00 PM, the temperature at the Winter Olympics was 14°; by morning the temperature dropped to -23°. Find the overall change in temperature. Example 6 What are we looking for? What do we need to find it? For the overall change, we take the end temp and subtract the beginning temp. -23° - 14° = -37°

50. 50 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Complementary angles are two angles whose sum is 90 o. Find the measure of the following complementary angles. x 37° Complementary Angles Example:

51. 51 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Complementary angles are two angles whose sum is 90 o. Find the measure of the following complementary angles. x 37° Complementary Angles Example:

52. 52 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Complementary angles are two angles whose sum is 90 o. Find the measure of the following complementary angles. x 37° Complementary Angles Example:

53. 53 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Complementary angles are two angles whose sum is 90 o. Find the measure of the following complementary angles. x 37° Complementary Angles Example:

54. 54 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Complementary angles are two angles whose sum is 90 o. Find the measure of the following complementary angles. x 37° Complementary Angles Example:

55. 55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Complementary angles are two angles whose sum is 90 o. Find the measure of the following complementary angles. x 37° Complementary Angles Example:

56. 56 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Supplementary angles are two angles whose sum is 180 o. Find the measure of the following supplementary angles. x123° Supplementary Angles Example:

57. 57 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Supplementary angles are two angles whose sum is 180 o. Find the measure of the following supplementary angles. x123° Supplementary Angles Example:

58. 58 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Supplementary angles are two angles whose sum is 180 o. Find the measure of the following supplementary angles. x123° Supplementary Angles Example:

59. 59 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Supplementary angles are two angles whose sum is 180 o. Find the measure of the following supplementary angles. x123° Supplementary Angles Example:

60. 60 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Supplementary angles are two angles whose sum is 180 o. Find the measure of the following supplementary angles. x123° Supplementary Angles Example:

61. 61 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Supplementary angles are two angles whose sum is 180 o. Find the measure of the following supplementary angles. x123° Supplementary Angles Example:

62. 62 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Closure:  Verbally review objectives with students.