106 Chapter 2 Integers and Algebraic Expressions Section 2.4 Multiplication and Division of Integers Answer 1. 5 152 152 152 1. Multiplication of Integers We know from our knowledge of arithmetic that the product of two positive numbers is a positive number. This can be shown by using repeated addition. For example: 3142 4 4 4 12 Now consider a product of numbers with different signs. For example: 3142 4 142 142 12 13 times 42 This example suggests that the product of a positive number and a negative number is negative. Now what if we have a product of two negative numbers? To determine the sign, consider the following pattern of products. 3 4 12 2 4 8 1 4 4 0 4 0 1 4 4 2 4 8 3 4 12 The pattern increases by 4 with each row. The product of two negative numbers is positive. From the first four rows, we see that the product increases by 4 for each row. For the pattern to continue, it follows that the product of two negative numbers must be positive. Multipliying Signed Numbers 1. The product of two numbers with the same sign is positive. Examples: 152 162 30 152 162 30 2. The product of two numbers with different signs is negative. Examples: 41102 40 41102 40 3. The product of any number and zero is zero. Examples: 3102 0 0162 0 Concepts 1. Multiplication of Integers 2. Multiplying Many Factors 3. Exponential Expressions 4. Division of Integers Concept Connections 1. Write 4152 as repeated addition. Avoiding Mistakes Try not to confuse the rule for multiplying two negative numbers with the rule for adding two negative numbers. • The product of two negative numbers is positive. • The sum of two negative numbers is negative.
miller_prealgebra_2e_ch1_3
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