Chapter 1 Section 5

Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Adding and Subtracting Real Numbers Add two numbers with the same sign. Add two numbers with different signs. Use the definition of subtraction. Use the rules for order of operations with real numbers. Translate words and phrases involving addition and subtraction. Use signed numbers to interpret data

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Add two numbers with the same sign. Objective 1 Slide 1.5-3

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Adding Numbers with the Same Sign To add two numbers with the same sign, add the absolute values of the numbers. The sum has the same sign as the numbers being added. Example: Add two numbers with the same sign. The sum of two negative numbers is a negative number whose distance from 0 is the sum of the distance of each number from 0. That is, the sum of two negative numbers is the negative of the sum of their absolute values. To avoid confusion, two operation symbols should not be written successively without a parenthesis between them. Slide 1.5-4

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use a number line to find each sum. Solution: 5 −7−7 Slide EXAMPLE 1 Adding Numbers on a Number Line

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Find the sum. Solution: Slide EXAMPLE 2 Adding Two Negative Numbers

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Add two numbers with different signs. Objective 2 Slide 1.5-7

Copyright © 2012, 2008, 2004 Pearson Education, Inc. For instance, to add −12 and 6, find their absolute values: and Then find the difference between these absolute values: The sum will be negative, since, so the final answer is. Adding Numbers with the Same Sign To add two numbers with different signs, find the absolute values of the numbers and subtract the lesser absolute value from the greater. Give the answer the same sign as the number having the greater absolute value. Slide Add two numbers with different signs.

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Use a number line to find the sum. 3 Slide EXAMPLE 3 Adding Numbers with Different Signs

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Find their absolute values: and Then find the difference between these absolute values: The sum will be negative, since, so the final answer is. Solution: Find the sum. Slide EXAMPLE 4 Adding Numbers with Different Signs

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Correct Check each answer. Correct Slide EXAMPLE 5 Adding Mentally

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use the definition of subtraction. Objective 3 Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. We can illustrate the subtraction of 4 from 7, written 7 − 4, with a number line. Use the definition of subtraction. The procedure to find the difference 7 − 4 is exactly the same procedure that would be used to find the sum. Slide The answer to a subtraction problem is called a difference. In the subtraction x −y, x is called the minuend and y is called the subtrahend.

Copyright © 2012, 2008, 2004 Pearson Education, Inc. The previous equation suggests that subtracting a positive number from a greater positive number is the same as adding the additive inverse of the lesser number to the greater. Definition of Subtraction For any real numbers x and y, To subtract y from x, add the additive inverse (or opposite) of y to x. That is, change the subtrahend to its opposite and add. Slide Use the definition of subtraction. (cont’d)

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Subtract. Slide EXAMPLE 6 Using the Definition of Subtraction

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Uses of the Symbol − We use the symbol − for three purposes: 1. to represent subtraction, as in 2. to represent negative numbers, such as −10, −2, and −3; 3. to represent the opposite (or negative) of a number, as in “the opposite (or negative) of 8 is −8.” We may see more than one use of − in the same expression, such as −6 − (−9), where −9 is subtracted from −6. The meaning of the symbol depends on its position in the algebraic expression. Slide Use the definition of subtraction. (cont’d)

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use the rules for order of operations with real numbers. Objective 4 Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Perform each indicated operation. Solution: Slide EXAMPLE 7 Adding and Subtracting with Grouping Symbols

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Perform each indicated operation. Solution: Slide EXAMPLE 7 Adding and Subtracting with Grouping Symbols (cont’d)

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Translate words and phrases involving addition and subtraction. Objective 5 Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Translate words and phrases involving addition and subtraction. The word sum indicates addition. The table lists other words and phrases that indicate addition in problem solving. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Write a numerical expression for the phrase and simplify the expression. 7 increased by the sum of 8 and −3 Slide EXAMPLE 8 Translating Words and Phrases (Addition)

Copyright © 2012, 2008, 2004 Pearson Education, Inc. The word difference indicates subtraction. Other words and phrases that indicate subtraction in problem solving are given in the table. In subtracting two numbers, be careful to write them in the correct order, because in general,. For example,. Think carefully before interpreting an expression involving subtraction. Slide Translate words and phrases involving addition and subtraction. (cont’d)

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Write a numerical expression for each phrase, and simplify the expression. The difference between −5 and −12 −2 subtracted from the sum of 4 and −4 Solution: Slide EXAMPLE 9 Translating Words and Phrases (Subtraction)

Copyright © 2012, 2008, 2004 Pearson Education, Inc. The highest Fahrenheit temperature ever recorded in Barrow, Alaska, was 79°F, while the lowest was −56°F. What is difference between these highest and lowest temperatures? (Source: World Almanac and Book of Facts.) Solution: Slide EXAMPLE 10 Solving a Problem Involving Subtraction

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Use signed numbers to interpret data. Objective 6 Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Refer to Figure 17 and use a signed number to represent the change in the CPI from 2002 to Slide EXAMPLE 11 Using a Signed Number to Interpret Data