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

OBJECTIVES 3.6 Multiplication and Division Using Mixed Numerals; Applications Slide 3Copyright 2011 Pearson Education, Inc. aMultiply using mixed numerals. bDivide using mixed numerals. cSolve applied problems involving multiplication and division with mixed numerals.

To multiply using mixed numerals, first convert to fraction notation and multiply. Then convert the answer to a mixed numeral, if appropriate. 3.6 Multiplication and Division Using Mixed Numerals; Applications Multiplication using Mixed Numerals Slide 4Copyright 2011 Pearson Education, Inc.

EXAMPLE Note that fraction notation is needed to carry out the multiplication Solution 3.6 Multiplication and Division Using Mixed Numerals; Applications a Multiply using mixed numerals. AMultiply: Slide 5Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution 3.6 Multiplication and Division Using Mixed Numerals; Applications a Multiply using mixed numerals. BMultiply: Slide 6Copyright 2011 Pearson Education, Inc.

To divide using mixed numerals, first write fraction notation and divide. Then convert the answer to a mixed numeral, if appropriate. 3.6 Multiplication and Division Using Mixed Numerals; Applications Division using Mixed Numerals Slide 7Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution 3.6 Multiplication and Division Using Mixed Numerals; Applications b Divide using mixed numerals. CDivide: Slide 8Copyright 2011 Pearson Education, Inc.

EXAMPLE Divide using mixed numerals. Remember to multiply by the reciprocal of the divisor. Solution 3.6 Multiplication and Division Using Mixed Numerals; Applications b DDivide: Slide 9Copyright 2011 Pearson Education, Inc.

EXAMPLE A backpack requires 2 ¼ yards of material. How many backpacks can be made from 36 ¾ yards of material? Solution Familiarize. Draw a picture to help us visualize the situation. 2 ¼ yards 36 ¾ yards of material 3.6 Multiplication and Division Using Mixed Numerals; Applications c Solve applied problems involving multiplication and division with mixed numerals. ENumber of Backpacks Made from Material (continued) Slide 10Copyright 2011 Pearson Education, Inc.

EXAMPLE Since each backpack takes 2 ¼ yards, the question can be regarded as how many 2 ¼ are in 36 ¾? Let b represent the number of backpacks. Translate. 3.6 Multiplication and Division Using Mixed Numerals; Applications c Solve applied problems involving multiplication and division with mixed numerals. ENumber of Backpacks Made from Material (continued) Slide 11Copyright 2011 Pearson Education, Inc.

EXAMPLE Solve. 3.6 Multiplication and Division Using Mixed Numerals; Applications c Solve applied problems involving multiplication and division with mixed numerals. E (continued) Slide 12Copyright 2011 Pearson Education, Inc. Number of Backpacks Made from Material

EXAMPLE Check. Check by estimating. 36 ∙ 2 = 18 which is close to our answer State. The number of backpacks that could be made is However, only 16 complete backpacks could be made. 3.6 Multiplication and Division Using Mixed Numerals; Applications c Solve applied problems involving multiplication and division with mixed numerals. E Slide 13Copyright 2011 Pearson Education, Inc. Number of Backpacks Made from Material

EXAMPLE 12 ½ ft 14 ½ ft 6 ft 10 ½ ft 3.6 Multiplication and Division Using Mixed Numerals; Applications c Solve applied problems involving multiplication and division with mixed numerals. FWhat is the area of the shaded region? (continued) Slide 14Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution Familiarize. We need to determine what the area of the shaded region is. Recall the area of a rectangle is base times height. To determine the shaded part we subtract the smaller rectangle from the larger rectangle. 3.6 Multiplication and Division Using Mixed Numerals; Applications c Solve applied problems involving multiplication and division with mixed numerals. FArea of Shaded Region (continued) Slide 15Copyright 2011 Pearson Education, Inc.

EXAMPLE 3.6 Multiplication and Division Using Mixed Numerals; Applications c Solve applied problems involving multiplication and division with mixed numerals. FArea of Shaded Region (continued) Slide 16Copyright 2011 Pearson Education, Inc. Translate. Solve. We first multiply then subtract:

EXAMPLE Solve (continued). 3.6 Multiplication and Division Using Mixed Numerals; Applications c Solve applied problems involving multiplication and division with mixed numerals. FArea of Shaded Region (continued) Slide 17Copyright 2011 Pearson Education, Inc.

EXAMPLE Check. We could repeat our calculation or estimate our answer. (14 ∙ 12) ∙ (10 ∙ 6) = 108 Which is close to our answer. State. The area of the shaded region is 3.6 Multiplication and Division Using Mixed Numerals; Applications c Solve applied problems involving multiplication and division with mixed numerals. FArea of Shaded Region Slide 18Copyright 2011 Pearson Education, Inc.