Multiplying and dividing algebraic fractions

When multiplying fractions we multiply the numerators and multiply the denominators: (a/b) · (c/d) = ac/(bd). In division the dividend is multiplied by the reciprocal of the divisor: (a/b) : (c/d) = (a/b) · (d/c) = ad/(bc), with c ≠ 0. A fraction is raised to a power by raising the numerator and denominator separately: (a/b)ⁿ = aⁿ/bⁿ. If we factor the numerators and denominators before multiplying and cancel common factors, the work becomes easier. The result is always written reduced. An expression can be seen as a fraction, a = a/1, so multiplying or dividing a fraction by an expression follows the same rules.