An algebraic fraction is an expression of the form a/b. The principles that govern numerical fractions in arithmetic apply equally to algebraic fractions. In this chapter, we focus on reducing fractions to their lowest terms and performing basic operations like multiplication and division.
To reduce a fraction to its lowest terms, we must factor both the numerator and the denominator completely and then cancel out the factors that are common to both. This is only possible when terms are multiplied; you cannot cancel terms that are added or subtracted without factoring first.
A fraction has three signs associated with it: the sign of the numerator, the sign of the denominator, and the sign before the fraction itself. You can change any two of these signs without changing the value of the fraction.
To multiply algebraic fractions, multiply the numerators together and the denominators together. However, it is much more efficient to factor all expressions first and cancel common factors before performing the multiplication.
To divide by a fraction, invert the divisor (the second fraction) and multiply. This is often remembered as "Copy, Dot, Flop" or "Multiply by the Reciprocal."