A fraction is a rational number expressed as the ratio of two integers. The top number of the ratio is referred to as the numerator, and bottom number is the denominator. Like other rational numbers, fractions can be added, subtracted, multiplied and divided. Unlike adding and subtracting fractions, the multiplication and division of two fractions can be performed regardless of the value of the denominators. Therefore, the process for finding the quotient of two fractions with different denominators is very straightforward and is applicable for all division problems.

Determine the identity of the two fractions that require division. For instance, suppose you're given the problem (2/7) / (1/2) = x.

Find the reciprocal, or inverse of either of the two fractions. The inverse is found by reversing the position of the number and denominator. The reciprocal of (1/2) is (2/1).

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Multiply the reciprocal by the other fraction. The product of two fractions is obtained by multiplying the numerators and denominators respectively: (2/7) * (2/1) = (4/7).

Reduce the quotient if it is not in lowest terms. In the example, the fraction, 4/7, is already in lowest terms; therefore, it is the final answer.