2. CHAPTER 3 Whole Numbers Slide 2Copyright 2011 Pearson Education, Inc. 3.1Least Common Multiples 3.2Addition and Applications 3.3Subtraction, Order, and Applications 3.4Mixed Numerals 3.5Addition and Subtraction Using Mixed Numerals; Applications 3.6Multiplication and Division Using Mixed Numerals; Applications 3.7Order of Operations; Estimation

3. OBJECTIVES 3.2 Addition and Applications Slide 3Copyright 2011 Pearson Education, Inc. aAdd using fraction notation. bSolve applied problems involving addition with fraction notation.

4. To add when denominators are the same, a) add the numerators, b) keep the denominators, and c) simplify, if possible. 3.2 Addition and Applications a Add using fraction notation. Slide 4Copyright 2011 Pearson Education, Inc.

5. EXAMPLE 1. 2. 3. Solution 1. 2. 3.2 Addition and Applications a Add using fraction notation. AAdd and simplify. (continued) Slide 5Copyright 2011 Pearson Education, Inc.

6. EXAMPLE 3.2 Addition and Applications a Add using fraction notation. ASimplify 3. Slide 6Copyright 2011 Pearson Education, Inc. 3.3. Solution

7. To add when denominators are different: a) Find the least common multiple of the denominators. That number is the least common denominator, LCD. b) Multiply by 1, using an appropriate notation, n/n, to express each number in terms of the LCD. c) Add the numerators, keeping the same denominator. d) Simplify, if possible. 3.2 Addition and Applications a Add using fraction notation. Slide 7Copyright 2011 Pearson Education, Inc.

8. EXAMPLE Solution a) The LCD is 10. 5 is a factor of 10 so the LCM of 5 and 10 is 10. b) We need to find a fraction equivalent to with a denominator of 10: c & d) We add: 3.2 Addition and Applications a Add using fraction notation. BAdd: Slide 8Copyright 2011 Pearson Education, Inc.

9. EXAMPLE Solution The LCD is 36. 12 = 2 ∙ 2 ∙ 3 18 = 2 ∙ 3 ∙ 3 LCM = 2 ∙ 2 ∙ 3 ∙ 3, or 36 Think: 12  = 36. The answer is 3, so we multiply by 1, using 3/3. Think: 18  = 36. The answer is 2, so we multiply by 1, using 2/2. 3.2 Addition and Applications a Add using fraction notation. CAdd: Slide 9Copyright 2011 Pearson Education, Inc.

10. EXAMPLE Solution 3.2 Addition and Applications a Add using fraction notation. DAdd: Slide 10Copyright 2011 Pearson Education, Inc.

11. EXAMPLE Solution Determine the LCM of 12, 9 and 21: The LCM is 2  2  3  3  7, or 252 3.2 Addition and Applications a Add using fraction notation. EAdd: (continued) Slide 11Copyright 2011 Pearson Education, Inc.

12. EXAMPLE 3.2 Addition and Applications a Add using fraction notation. EContinued (continued) Slide 12Copyright 2011 Pearson Education, Inc. In each case, we multiply by 1 to obtain the LCD. To form 1 look at the prime factorization and use the factor(s) missing from each denominator.

13. EXAMPLE 3.2 Addition and Applications a Add using fraction notation. EContinued Slide 13Copyright 2011 Pearson Education, Inc.

14. EXAMPLE Finding the Sum of Nuts Solution Familiarize. Make a drawing. We let N = the total pounds of nuts. 3.2 Addition and Applications b Solve applied problems involving addition with fraction notation. F (continued) Slide 14Copyright 2011 Pearson Education, Inc. Logan bought lb of walnuts and lb of almonds. How many pounds of nuts did Logan buy altogether?

15. EXAMPLE 3.2 Addition and Applications b Solve applied problems involving addition with fraction notation. FFinding the Sum of Nuts (continued) Slide 15Copyright 2011 Pearson Education, Inc. Translate.

16. EXAMPLE Solve. Check. Repeat the calculation. The sum should also be larger than either of the individual measurements. State. Logan bought 5/6 pounds of nuts. 3.2 Addition and Applications b Solve applied problems involving addition with fraction notation. FFinding the Sum of Nuts Slide 16Copyright 2011 Pearson Education, Inc.