230 CHAPTER 5 Number Theory and the Real Number System Next, we discuss the four possible cases for division of integers, which are similar to those for multiplication. CASE 1: ÷ POSITIVE INTEGER POSITIVE INTEGER A positive integer divided by a positive integer is positive. 6 2 3, since 3(2) 6 = = CASE 2: ÷ POSITIVE INTEGER NEGATIVE INTEGER A positive integer divided by a negative integer is negative. 6 2 3, since ( 3)( 2) 6 − = − − − = CASE 3: ÷ NEGATIVE INTEGER POSITIVE INTEGER A negative integer divided by a positive integer is negative. 6 2 3, since ( 3)(2) 6 − = − − = − CASE 4: ÷ NEGATIVE INTEGER NEGATIVE INTEGER A negative integer divided by a negative integer is positive. 6 2 3, since 3( 2) 6 − − = − = − The examples were restricted to integers. The rules for division, however, can be used for any numbers. You should realize that division of integers does not always result in an integer. The rules for division are summarized as follows. Rules for Division 1. The quotient of two numbers with like signs ( ÷ positive positive or ÷ negative negative) is a positive number. 2. The quotient of two numbers with unlike signs ( ÷ positive negative or ÷ negative positive) is a negative number. Solution a) = 63 9 7 b) 63 9 7 − = − c) − = − 63 9 7 d) 63 9 7 − − = 7 Example 8 Dividing Integers Evaluate. a) 63 9 b) 63 9 − c) − 63 9 d) 63 9 − − Now try Exercise 35 Exponents An understanding of exponents is important in mathematics. In the expression 5 ,2 the 2 is referred to as the exponent and the 5 is referred to as the base. We read 52 as 5 to the second power, or 5 squared, which means = ⋅ 5 5 5 2 2 factors of5
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