How Do You Divide Mixed Numbers?

Divide mixed fractions by converting them to improper fractions, then multiplying the dividend with the reciprocal of the divisor. If possible, simplify the answer by dividing the numerator and denominator with the greatest common factor.

  1. Convert mixed fractions to improper fractions

    Multiply the whole number with the denominator. Add the result to the numerator, then place the final number over the denominator to convert the mixed fraction to an improper fraction.

  2. Find the reciprocal of the divisor

    Flip the divisor so that the numerator is on the bottom and the denominator is on top. This is the reciprocal. Inverting the divisor allows you to find the answer as a whole number.

  3. Multiply the dividend and the reciprocal

    Multiply the numerators together, then multiply the denominators together to get the answer.

  4. Simplify and check the result

    Determine if the resulting numerator and denominator have a common factor. If so, find the greatest common factor to simplify the answer. Check your answer by multiplying the final result with the original divisor. The answer is correct if it is the same as the original dividend. To divide 2/3 by 4/5, multiply 2/3 by 5/4 to get 10/12, or 5/6 when simplified. To check the answer, multiply 5/6 with 4/5 to get 20/30, or 2/3.