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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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