306APPENDIX BREVIEW OF ARITHMETIC AND ALGEBRAYou also need to remember that when multiplying negative numbers, a negative number multiplied by a negative number equals a positive number. Thus, () () = ab (�) (�) = +20DivisionJust as subtraction is the opposite of addition, division is the opposite or inverse of multiplication. Division can be viewed as a shortcut to subtraction. When you divide 20 by 4, you are actually determining the number of times that 4 can be subtracted from 20. In general, however, the number of times one number can be divided by another may not be an exact integer value because there could be a remainder. For example, if you divide 21 by 4, the answer is 5 with a remainder of 1, or 51�. As in the case of subtraction, neither the commutative nor associative law of addition and multiplication holds for division. aba 93�9 6 (3 2) = 4 (6 3) 2 = 1 The distributive law holds only when the numbers to be added are contained in the numerator, not the denominator. Thus, a+b a b = + c c c For example, 1 1 = 2+3 5 but 1 2+3 1 1 + 2 3 but a b+c a a + b cThe last important property of division states that if the numerator and the denominator are multiplied or divided by the same number, the resulting quotient is not affected. Therefore, 80 =2 40 then 5(80) 400 = =2 5( 40) 200
