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38 Rh CHAPTER V.

Division.

53. When a quantity a is divided by the quantity b, the quotient is defined to be that which when multiplied by b produces a. The operation is denoted by a 6, {a }{b } or a/b; in each of these modes of expression a is called the dividend, and b the divisor.

Division is thus the inverse of multiplication, and (a b)xb=a

54. The Rule of Signs holds for division.

Thus

ab \div a= {ab}{a} = {a \times b}{a} = b -ab \div a= {-ab}{a} = {a \times(- b)}{a} =- b ab \div (-a)= {ab}{-a} = {(-a )\times (-b)}{-a} = -b -ab \div (-a)= {-ab}{-a} = {(-a) \times b}{-a} = b

Hence in division as well as multiplication

like signs produce +, unlike signs produce —.

55. Since Division is the inverse of Multiplication, it follows that the Laws of Commutation, Association, and Distribution, which have been established for Multiplication, hold for Division.