CHAPTER 5 Decimal Notation Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 5.1Decimal Notation, Order, and Rounding 5.2Addition and Subtraction of Decimals 5.3Multiplication of Decimals 5.4Division of Decimals 5.5Using Fraction Notation with Decimal Notation 5.6Estimating 5.7Solving Equations 5.8Applications and Problem Solving

OBJECTIVES 5.4 Division of Decimals Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aDivide using decimal notation. bSimplify expressions using the rules for order of operations.

5.4 Division of Decimals a Divide using decimal notation. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The following divisions are justified by the multiplication in each check. Note that the number of decimal places in each quotient is the same as the number of decimal places in the dividend.

5.4 Division of Decimals a Divide using decimal notation. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Title 5.4 Division of Decimals Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To perform long division by a whole number: a) place the decimal point directly above the decimal point in the dividend and b) divide as though dividing whole numbers.

Title 5.4 Division of Decimals Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.4 Division of Decimals a Divide using decimal notation. 1 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.4 Division of Decimals a Divide using decimal notation. 2 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.4 Division of Decimals a Divide using decimal notation. 2 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.4 Division of Decimals a Divide using decimal notation. 2 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.4 Division of Decimals a Divide using decimal notation. 2 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.4 Division of Decimals a Divide using decimal notation. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Title 5.4 Division of Decimals Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To divide when the divisor is not a whole number: a) move the decimal point (multiply by 10, 100, and so on) to make the divisor a whole number, b) move the decimal point in the dividend the same number of places (multiply the same way), and

Title 5.4 Division of Decimals Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. c) place the decimal point for the answer directly above the new decimal point in the dividend and divide as though dividing whole numbers.

EXAMPLE 5.4 Division of Decimals a Divide using decimal notation. 5 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Note first that a negative number divided by a negative number is positive. To find the quotient, we consider

EXAMPLE 5.4 Division of Decimals a Divide using decimal notation. 5 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.4 Division of Decimals a Divide using decimal notation. 5 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.4 Division of Decimals a Divide using decimal notation. Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We move the decimal point in both the divisor and the dividend 3 places to the right. Note that the divisor is now 1.

Title 5.4 Division of Decimals Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To divide by a number like 10, 100, 1000, 0.1, 0.01, or 0.001: a) move the decimal point in the divisor until the divisor is 1 and b) move the decimal point in the dividend the same number of places and the same direction.

EXAMPLE 5.4 Division of Decimals a Divide using decimal notation. 6 Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.4 Division of Decimals a Divide using decimal notation. 9 Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.4 Division of Decimals RULES FOR ORDER OF OPERATIONS Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Do all calculations within grouping symbols first. 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.

EXAMPLE 5.4 Division of Decimals b Simplify expressions using the rules for order of operations. 12 Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.4 Division of Decimals b Simplify expressions using the rules for order of operations. 13Mountains in Peru. Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The figure shows a range of very high mountains in Peru, together with their altitudes, given both in feet and in meters. Find the average height of these mountains, in meters. Source: National Geographic, July 1968, p. 130

EXAMPLE 5.4 Division of Decimals b Simplify expressions using the rules for order of operations. 13Mountains in Peru. Slide 26Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. SOURCE: WOOD RONASVILLE HARLIN INC/NGS Image Collection

EXAMPLE 5.4 Division of Decimals b Simplify expressions using the rules for order of operations. 13Mountains in Peru. Slide 27Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The average of a set of numbers is the sum of the numbers divided by the number of addends. Thus, the average height of these mountains is m.