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

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Presentation on theme: "Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 1 Real Numbers and Introduction to Algebra."— Presentation transcript:

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: 1. -14 + (-3) +11 2. [-2 + (-7)] + [-11 + 22] 3. |43 + (-73)| + |-20| 4. 6 – 2 × 2 +2 5

3 33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. -14 + (-3) +11 -6 2. [-2 + (-7)] + [-11 + 22] 3. |43 + (-73)| + |-20| 4. 6 – 2 × 2 +2 5

4 44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. -14 + (-3) +11 -6 2. [-2 + (-7)] + [-11 + 22] 2 3. |43 + (-73)| + |-20| 4. 6 – 2 × 2 +2 5

5 55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. -14 + (-3) +11 -6 2. [-2 + (-7)] + [-11 + 22] 2 3. |43 + (-73)| + |-20| 50 4. 6 – 2 × 2 +2 5

6 66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. -14 + (-3) +11 -6 2. [-2 + (-7)] + [-11 + 22] 2 3. |43 + (-73)| + |-20| 50 4. 6 – 2 × 2 +2 5 34

7 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 1.4 Adding Real Numbers

8 88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Objectives:  Add real numbers  Solve problems with addition  Find additive inverses

9 99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Adding Real Numbers Adding real numbers can be visualized on a number line. A positive number can be represented on the number line by an arrow of appropriate length pointing to the right, and a negative number by an arrow of appropriate length pointing to the left.

10 10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Add: ‒ 5 + 2 2– 201345– 1– 3– 4– 5 Start End ‒5‒5 2 ‒ 5 + 2 = ‒ 3

11 11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Add: ‒ 5 + 2 2– 201345– 1– 3– 4– 5 Start End ‒5‒5 2 ‒ 5 + 2 = ‒ 3

12 12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 1 Add: ‒ 5 + 2 2– 201345– 1– 3– 4– 5 Start End ‒5‒5 2 ‒ 5 + 2 = ‒ 3

13 13 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Adding Real Numbers To add two real numbers 1. with the same sign, add their absolute values. Use their common sign as the sign of the answer. 2. with different signs, subtract their absolute values. Give the answer the same sign as the number with the larger absolute value.

14 14 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Add without using a number line: a. ( ‒ 8) + ( ‒ 3) = ‒ 11 Same sign b. ( ‒ 7) + 1 = ‒ 6 Different signs c.Different signs d. ( ‒ 12.6) + ( ‒ 1.7) = ‒ 14.3Same signs

15 15 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Add without using a number line: a. ( ‒ 8) + ( ‒ 3) = ‒ 11 Same sign b. ( ‒ 7) + 1 = ‒ 6 Different signs c.Different signs d. ( ‒ 12.6) + ( ‒ 1.7) = ‒ 14.3Same signs

16 16 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Add without using a number line: a. ( ‒ 8) + ( ‒ 3) = ‒ 11 Same sign b. ( ‒ 7) + 1 = ‒ 6 Different signs c.Different signs d. ( ‒ 12.6) + ( ‒ 1.7) = ‒ 14.3Same signs

17 17 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Add without using a number line: a. ( ‒ 8) + ( ‒ 3) = ‒ 11 Same sign b. ( ‒ 7) + 1 = ‒ 6 Different signs c.Different signs d. ( ‒ 12.6) + ( ‒ 1.7) = ‒ 14.3Same signs

18 18 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Add without using a number line: a. ( ‒ 8) + ( ‒ 3) = ‒ 11 Same sign b. ( ‒ 7) + 1 = ‒ 6 Different signs c.Different signs d. ( ‒ 12.6) + ( ‒ 1.7) = ‒ 14.3Same signs

19 19 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Add without using a number line: a. ( ‒ 8) + ( ‒ 3) = ‒ 11 Same sign b. ( ‒ 7) + 1 = ‒ 6 Different signs c.Different signs d. ( ‒ 12.6) + ( ‒ 1.7) = ‒ 14.3Same signs

20 20 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Add without using a number line: a. ( ‒ 8) + ( ‒ 3) = ‒ 11 Same sign b. ( ‒ 7) + 1 = ‒ 6 Different signs c.Different signs d. ( ‒ 12.6) + ( ‒ 1.7) = ‒ 14.3Same signs

21 21 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Add without using a number line: a. ( ‒ 8) + ( ‒ 3) = ‒ 11 Same sign b. ( ‒ 7) + 1 = ‒ 6 Different signs c.Different signs d. ( ‒ 12.6) + ( ‒ 1.7) = ‒ 14.3Same signs

22 22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example 2 Add without using a number line: a. ( ‒ 8) + ( ‒ 3) = ‒ 11 Same sign b. ( ‒ 7) + 1 = ‒ 6 Different signs c.Different signs d. ( ‒ 12.6) + ( ‒ 1.7) = ‒ 14.3Same signs

23 23 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Opposites or Additive Inverses Two numbers the same distance from 0 on the number line, but lie on opposite sides of 0 are called opposites or additive inverses of each other. The opposite of 8 is ‒ 8. The opposite of ‒ 2.9 is 2.9. Additive Inverses

24 24 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Opposites or Additive Inverses Two numbers the same distance from 0 on the number line, but lie on opposite sides of 0 are called opposites or additive inverses of each other. The opposite of 8 is ‒ 8. The opposite of ‒ 2.9 is 2.9. Additive Inverses

25 25 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Opposites or Additive Inverses Two numbers the same distance from 0 on the number line, but lie on opposite sides of 0 are called opposites or additive inverses of each other. The opposite of 8 is ‒ 8. The opposite of ‒ 2.9 is 2.9. Additive Inverses

26 26 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the opposite of each number. a. ‒ 16 The opposite is 16. b. 5 The opposite is ‒ 5. Example 3

27 27 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the opposite of each number. a. ‒ 16 The opposite is 16. b. 5 The opposite is ‒ 5. Example 3

28 28 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the opposite of each number. a. ‒ 16 The opposite is 16. b. 5 The opposite is ‒ 5. Example 3

29 29 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If a is a number, then –(–a) = a. The sum of a number a and its opposite ‒ a is 0. meaning: a + ( ‒ a) = 0 Also, ‒ a + a = 0. General Rules

30 30 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ ( ‒ 16) = 16 b. ‒ ( ‒ 5x) = 5x c. ‒ |9| = ‒ 9 d. ‒ | ‒ 2| = ‒ 2 Example 4

31 31 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ ( ‒ 16) = 16 b. ‒ ( ‒ 5x) = 5x c. ‒ |9| = ‒ 9 d. ‒ | ‒ 2| = ‒ 2 Example 4

32 32 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ ( ‒ 16) = 16 b. ‒ ( ‒ 5x) = 5x c. ‒ |9| = ‒ 9 d. ‒ | ‒ 2| = ‒ 2 Example 4

33 33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ ( ‒ 16) = 16 b. ‒ ( ‒ 5x) = 5x c. ‒ |9| = ‒ 9 d. ‒ | ‒ 2| = ‒ 2 Example 4

34 34 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplify each expression. a. ‒ ( ‒ 16) = 16 b. ‒ ( ‒ 5x) = 5x c. ‒ |9| = ‒ 9 d. ‒ | ‒ 2| = ‒ 2 Example 4

35 35 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate 5x + y when x = 4 and y = ‒ 2. Example 5 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18

36 36 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate 5x + y when x = 4 and y = ‒ 2. Example 5 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18 Plug it in! 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18

37 37 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate 5x + y when x = 4 and y = ‒ 2. Example 5 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18 Plug it in! 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18

38 38 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate 5x + y when x = 4 and y = ‒ 2. Example 5 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18 Plug it in! 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18

39 39 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate 5x + y when x = 4 and y = ‒ 2. Example 5 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18 Plug it in! Simplify. 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18

40 40 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate 5x + y when x = 4 and y = ‒ 2. Example 5 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18 Plug it in! Simplify. 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18

41 41 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate 5x + y when x = 4 and y = ‒ 2. Example 5 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18 Plug it in! Simplify. 5x + y = 5·4 + ( ‒ 2) = 20 + ( ‒ 2) = 18

42 42 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. During a four day period, a share of Walmart stock recorded the following gains and losses: Find the overall gain or loss for the stock for the four days. Example 6 TuesdayWednesday a loss of $2a loss of $1 ThursdayFriday a gain of $3

43 43 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. During a four day period, a share of Walmart stock recorded the following gains and losses: Find the overall gain or loss for the stock for the four days. original price – 2 – 1 + 3 + 3 = + 3 Example 6 TuesdayWednesday a loss of $2a loss of $1 ThursdayFriday a gain of $3

44 44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. During a four day period, a share of Walmart stock recorded the following gains and losses: Find the overall gain or loss for the stock for the four days. original price – 2 – 1 + 3 + 3 = + 3 Example 6 TuesdayWednesday a loss of $2a loss of $1 ThursdayFriday a gain of $3

45 45 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. During a four day period, a share of Walmart stock recorded the following gains and losses: Find the overall gain or loss for the stock for the four days. original price – 2 – 1 + 3 + 3 = + 3 Example 6 TuesdayWednesday a loss of $2a loss of $1 ThursdayFriday a gain of $3

46 46 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. During a four day period, a share of Walmart stock recorded the following gains and losses: Find the overall gain or loss for the stock for the four days. original price – 2 – 1 + 3 + 3 = + 3 Example 6 TuesdayWednesday a loss of $2a loss of $1 ThursdayFriday a gain of $3

47 47 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. During a four day period, a share of Walmart stock recorded the following gains and losses: Find the overall gain or loss for the stock for the four days. original price – 2 – 1 + 3 + 3 = + 3 Example 6 TuesdayWednesday a loss of $2a loss of $1 ThursdayFriday a gain of $3

48 48 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. During a four day period, a share of Walmart stock recorded the following gains and losses: Find the overall gain or loss for the stock for the four days. original price – 2 – 1 + 3 + 3 = + 3 Example 6 TuesdayWednesday a loss of $2a loss of $1 ThursdayFriday a gain of $3

49 49 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Closure:  How do you add two numbers using a number line?  What is the rule for adding numbers based on their signs?  What is the additive inverse? Give an example.

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