Chapter 8 - XYZ Custom Plus

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478<strong>Chapter</strong> 8 Real Numbers and Algebraic ExpressionsMaintaining Your SkillsWrite each of the following in symbols.109. The product of 3 and 5.110. The product of 5 and 3.111. The product of 7 and x.112. The product of 2 and y.Rewrite the following using the commutative property of multiplication.113. 3(5) 5 114. 7(x) 5Rewrite the following using the associative property of multiplication.115. 5(7 ? 8) 5 116. 4(6 ? y)Apply the distributive property to each expression and then simplify the result.117. 2(3 1 4) 118. 5(6 1 7)Extending the Concepts119. Give an example that shows that subtraction is not acommutative operation.120. Why is the expression “two negatives make a positive”not correct?121. Give an example of an everyday situation that is modeledby the subtraction problem$10 2 $12 5 2$2.122. Give an example of an everyday situation that is modeledby the subtraction problem2$10 2 $12 5 2$22.In <strong>Chapter</strong> 1 we defined an arithmetic sequence as a sequence of numbers in which each number, after the first number, isobtained from the previous number by adding the same amount each time.Find the next two numbers in each arithmetic sequence below.123. 10, 5, 0, . . .124. 8, 3, 22, . . .125. 210, 26, 22, . . .126. 24, 21, 2, . . .
Introduction . . .Multiplication with Negative NumbersSuppose you buy three shares of a certain stockon Monday, and by Friday the price per share hasdropped $5. How much money have you lost? Theanswer is $15. Because it is a loss, we can expressit as 2$15. The multiplication problem below canbe used to describe the relationship among thenumbers.3 shares each loses $5 for a total of 2$1588888n3(25) 5 215From this we conclude that it is reasonable to say that the product of a positivenumber and a negative number is a negative number.A MultiplicationIn order to generalize multiplication with negative numbers, recall that we firstdefined multiplication by whole numbers to be repeated addition. That is:3 ? 5 5 5 1 5 1 5h h hMultiplication Repeated additionThis concept is very helpful when it comes to developing the rule for multiplicationproblems that involve negative numbers. For the first example we look atwhat happens when we multiply a negative number by a positive number.Example 1Multiply: 3(25)88nm88888.4ObjectivesA Multiply positive and negativenumbers.B Apply the rule for order ofoperations to expressionscontaining positive and negativenumbers.C Solve applications involvingmultiplication with positive andnegative numbers.Examples now playing atMathTV.com/booksPractice Problems1. Multiply: 2(26)Solution Writing this product as repeated addition, we have3(25) 5 (25) 1 (25) 1 (25)5 210 1 (25)5 215The result, 215, is obtained by adding the three negative 5’s.Example 2Multiply: 23(5)2. Multiply: 22(6)SolutionIn order to write this multiplication problem in terms of repeated addition,we will have to reverse the order of the two numbers. This is easily done,because multiplication is a commutative operation.23(5) 5 5(23) Commutative property5 (23) 1 (23) 1 (23) 1 (23) 1 (23) Repeated addition5 215 AdditionThe product of 23 and 5 is 215.Example 3Multiply: 23(25)Solution It is impossible to write this product in terms of repeated addition.We will find the answer to 23(25) by solving a different problem. Look at the followingproblem:23[5 1 (25)] 5 23[0] 5 03. Multiply: 22(26)Answers1. 212 2. 2128.4 Multiplication with Negative Numbers479
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