In this question we find a and y common to both terms; and, they being cancelled, the result is bx dmm® In performing this question, we first find the greatest common measure of the two terms of the fraction, which is x+b; we then divide both terms by it. Thus, CASE III. 118. To reduce a mixed quantity to the form of a fraction. RULE. Multiply the integral part by the denominator of the fractional part; to this product annex the numerator of the fraction, prefixing to it the sign of the fraction; under the whole write the denominator of the fraction. a2-5n3 10. Change 11m-4n+3m-2n2 to the form of a fraction. 33m2-22mn2-12mn+3n3+a2 Ans. 3m-2n2 119. To represent a fraction in the form of a whole or mixed quantity. RULE. Divide the numerator by the denominator for the integral part, and write the remainder, if any, over the denominator for the fractional part; annex this to the integral part, and it will represent the quantity required. 120. To reduce a complex fraction to a simple one. RULE. If the numerator or denominator, or both, be whole or mixed quantities, reduce them to improper fractions. Then multiply the denominator of the lower fraction into the numerator of the upper for a new numerator and the denominator of the upper fraction into the numerator of the lower for a new denominator; or, invert the denominator of the complex fraction when reduced, and place it in a line with the numerator; then multiply the two numerators together for a new numerator, and the two denominators together for a new denominator. All fractions in this proposition must be reduced to this form, before they can be solved by the above rule. Now, every fraction denotes a division of the numerator by the denominator, and its value is equal to the quotient obtained by such a division. Hence, by the nature of division, we have, |