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 5.2 Addition and Subtraction of Decimals Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aAdd using decimal notation. bSubtract using decimal notation. cAdd and subtract negative decimals. dCombine like terms with decimal coefficients.

5.2 Addition and Subtraction of Decimals a Add using decimal notation. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Adding with decimal notation is similar to adding whole numbers. First, we line up the decimal points so that we can add corresponding place-value digits. Then we add digits from the right. For example, we add the thousandths, then the hundredths, and so on, carrying if necessary. If desired, we can write extra zeros to the right of the decimal point so that the number of places is the same in all of the addends.

EXAMPLE 5.2 Addition and Subtraction of Decimals a Add using decimal notation. 2 Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.2 Addition and Subtraction of Decimals a Add using decimal notation. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Keep in mind that any whole number has an “unwritten” decimal point at the right that can be followed by zeros.

EXAMPLE 5.2 Addition and Subtraction of Decimals a Add using decimal notation. 3 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.2 Addition and Subtraction of Decimals b Subtract using decimal notation. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Subtracting with decimal notation is similar to subtracting whole numbers.

EXAMPLE 5.2 Addition and Subtraction of Decimals b Subtract using decimal notation. 5 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.2 Addition and Subtraction of Decimals b Subtract using decimal notation. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When subtraction involves an integer, the “unwritten” decimal point can be written in. Extra zeros can then be written in to the right of the decimal point.

EXAMPLE 5.2 Addition and Subtraction of Decimals b Subtract using decimal notation. 6 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Title 5.2 Addition and Subtraction of Decimals Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To add a negative number and a positive number: a) Determine the sign of the number with the greater absolute value. b) Subtract the smaller absolute value from the larger one. c) The answer is the difference from part (b) with the sign from part (a).

EXAMPLE 5.2 Addition and Subtraction of Decimals c Add and subtract negative decimals. 7 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Title 5.2 Addition and Subtraction of Decimals Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To add two negative numbers: a) Add the absolute values. b) Make the answer negative.

5.2 Addition and Subtraction of Decimals c Add and subtract negative decimals. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To subtract, we add the opposite of the number being subtracted.

EXAMPLE 5.2 Addition and Subtraction of Decimals c Add and subtract negative decimals. 9 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.2 Addition and Subtraction of Decimals d Combine like terms with decimal coefficients. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Recall that like, or similar, terms have exactly the same variable factors. To combine like terms, we add or subtract coefficients to form an equivalent expression.

EXAMPLE 5.2 Addition and Subtraction of Decimals d Combine like terms with decimal coefficients. 11 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.2 Addition and Subtraction of Decimals d Combine like terms with decimal coefficients. Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When more than one pair of like terms is present, we can rearrange the terms and then simplify.

EXAMPLE 5.2 Addition and Subtraction of Decimals d Combine like terms with decimal coefficients. 13 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.2 Addition and Subtraction of Decimals c Add and subtract negative decimals. 8 Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.