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 3.7 Order of Operations; Estimation Slide 3Copyright 2011 Pearson Education, Inc. aSimplify expressions using the rules for order of operations. bEstimate with fraction notation and mixed numerals.

1. Do all calculations within parentheses before operations outside. 2. Evaluate all exponential expressions. 3. Do all multiplications and divisions in order from left to right. 4. Do all additions and subtractions in order from left to right. Rules for Order of Operations 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. Slide 4Copyright 2011 Pearson Education, Inc.

EXAMPLE Doing the division first by multiplying by the reciprocal. Doing the multiplications in order from left to right. Removing a factor of 1. Solution 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. ASimplify: (continued) Slide 5Copyright 2011 Pearson Education, Inc.

EXAMPLE 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. ASimplify: Slide 6Copyright 2011 Pearson Education, Inc. Adding. Simplifying.

EXAMPLE Order of Operations; Estimation Divide first (multiply by the reciprocal). Simplifying. Solution 3.7 a Simplify expressions using the rules for order of operations. BSimplify: (continued) Slide 7Copyright 2011 Pearson Education, Inc.

EXAMPLE 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. BSimplify: Slide 8Copyright 2011 Pearson Education, Inc. Subtracting. Simplifying.

EXAMPLE Tanner measured the lengths of three of his friends feet. They measured 13 ½ inches, 11 5/8 inches, and 13 ¼ inches. What was the average length of the three friends feet? 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. CFind the Average Foot Length (continued) Slide 9Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution To compute an average, we add the values and then divide the sum by the number of values. We let f = the average length of the feet. 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. CFind the Average Foot Length (continued) Slide 10Copyright 2011 Pearson Education, Inc.

EXAMPLE We first add: 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. CFind the Average Foot Length (continued) Slide 11Copyright 2011 Pearson Education, Inc.

EXAMPLE Then we divide: The average length of the friends feet were 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. CFind the Average Foot Length Slide 12Copyright 2011 Pearson Education, Inc.

EXAMPLE Carrying out the operations inside parentheses first, multiplying by the 1 to obtain the LCD. Solution 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. DSimplify: (continued) Slide 13Copyright 2011 Pearson Education, Inc.

EXAMPLE 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. DSimplify: Slide 14Copyright 2011 Pearson Education, Inc. Completing the operations within parentheses.

EXAMPLE 3.7 Order of Operations; Estimation a Simplify expressions using the rules for order of operations. DSimplify: Slide 15Copyright 2011 Pearson Education, Inc. Common denominator Adding Doing the multiplication

EXAMPLE a.b. c. Solution a. A fraction is close to 0 when the numerator is small in comparison to the denominator. Thus, 0 is an estimate because 3 is small in comparison to Order of Operations; Estimation b Estimate with fraction notation and mixed numerals. EEstimate each of the following as 0, ½, or 1. (continued) Slide 16Copyright 2011 Pearson Education, Inc.

EXAMPLE b. b. A fraction is close to ½ when the denominator is about twice the numerator. Thus ½ is an estimate because 2 ∙ 15 = 30 and 30 is close to 33. Estimate with fraction notation and mixed numerals. 3.7 Order of Operations; Estimation b E (continued) Slide 17Copyright 2011 Pearson Education, Inc. Estimate each of the following as 0, ½, or 1.

EXAMPLE c. c. A fraction is close to 1 when the numerator is nearly equal to the denominator. Thus 1 is an estimate because 41 is nearly equal to Order of Operations; Estimation b Estimate with fraction notation and mixed numerals. E Slide 18Copyright 2011 Pearson Education, Inc. Estimate each of the following as 0, ½, or 1.

EXAMPLE Find a number for the box so that is close to but less than 1. Solution If the number in the box were 7, we would have 1, so we increase 7 to 8. An answer is 8, is close to Order of Operations; Estimation b Estimate with fraction notation and mixed numerals. F Slide 19Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution Since 75 is large, any small number such as 1, 2, or 3 will make the fraction close to 0. is close to Order of Operations; Estimation b Estimate with fraction notation and mixed numerals. GFind a number for the box so that is close to but greater than 0. Slide 20Copyright 2011 Pearson Education, Inc.

EXAMPLE Solution We estimate each fraction as 0, ½, or 1. Then we calculate. Estimate as a whole number or as a mixed numeral where the fractional part is ½. 3.7 Order of Operations; Estimation b Estimate with fraction notation and mixed numerals. H Slide 21Copyright 2011 Pearson Education, Inc.