129. Following then this rule for the division of by, we shall have the quotient; the division of by will produce or, and that of by & will give 10 or . 130. Hence also is derived the more usual rule that is given for the division of fractions. Invert the divisor, and proceed as in multiplication, and the product will be the quotient sought. Thus divided by is the same as multiplied by or 2, viz. or; also & divided by is the same as multiplied by 3, viz. 1, &c. 131. In general then it appears that to divide by the fraction is only to multiply by or 2; to divide by is to multiply by, or 3, &c. &c. Thus the number 100 divided by is 200, and 1000 divided by is 3000, &c. 1 divided by T gives 1000, and 1 divided by To 100000. So also gives From this it may be easily understood that 1 divided by 0 must give a quotient infinitely great; since the division of 1 by the small fraction To produces the very great number of 1000000000. 133. Since every number divided by itself is equal to unity, it will be easily seen that a fraction divided by itself must likewise give 1 for the quotient. And this is evident from the rule laid down for the division of fractions; for divided by is the same as multiplied by, viz. 1=1, and generally ab a by is the same as multiplied by viz. 134. We have yet to explain an expression frequently used. It is asked for example what is the half of? This means that is to be multiplied by. Again, if it were asked what of, we should multiply by, the product is the value of of which will be or. Thus also of of is the pro duct duct of all these fractions multiplied into each other, viz. into,, and that into, *%== These are usually termed compound fractions. 32 135. We have finally to observe with respect to the signs + and, that the same principles are applicable to fractions, as have been already established with respect to whole numbers. Thus, 5 x 8x Ex. 1. Reduce and to fractions having a common b C denominator. 5cx 8bx. ANSW.- and bc bc 5 1018 Ex. 2. Reduce and to fractions having a common 1 x 4' 2' |