Reduce the fractions, if necessary, to equivalent fractions having a common denominator; then subtract the numerator of the subtrahend from that of the minuend, and write the result over the common denominator. RULE. Multiply the integral part by the denominator of the fraction; to the product add the numerator if the sign of the fraction is plus, and subtract it if the sign is minus, and under the result write the denominator. NOTE. - By a change of the language, Examples 12-14 in Art. 87, and 11-13 in Art. 88, become examples under this case. Thus, Example 12, Art. 87, might be expressed as follows: Reduce NOTE. — It must be remembered that the sign before the dividing line belongs to the fraction as a whole. Ans. NOTE. According to the same principle an integral quantity can be reduced to a fraction having any given denominator, by multiplying the quantity by the proposed denominator, and under the product writing the denominator. 12. Reduce 4 ax to a fraction whose denominator is 90. To reduce an improper fraction to an integral or mixed quantity. As the value of a fraction is the quotient arising from dividing the numerator by the denominator (Art. 82), we perform the indicated division. Hence, RULE. Divide the numerator by the denominator; if there is any remainder, place it over the divisor, and annex the fraction so formed with its proper sign to the quotient. |