Divide Fractions and Mixed Numbers

Divide Fractions and Mixed Numbers

To divide fractions, invert the divisor and multiply.

Reciprocals are used to rewrite division problems as related multiplication problems. This is mathematically legal because the product of a fraction and its reciprocal equals one. To find that reciprocal, invert the fraction. That means you flip the numerator and denominator.  For instance, the reciprocal of   is

To find the reciprocal of a whole number, first write the whole number as a fraction with a denominator of 1; then find the reciprocal of the fraction.


Find the reciprocal of 3.

Think 3 = . The reciprocal of  is .


Find .

Rewrite the division as a a multiplication by the reciprocal.  Then simplify where needed

We can check our work by working backwards:

We got back to the first number in the problem, 12.  Therefore, 30 is the correct answer.

Dividing Mixed Numbers

When one or more of the numbers in a quotient is a mixed number, write the mixed number as an improper fraction before dividing.