How do you divide mixed numbers with like denominators?

Answer 1

Written as improper fractions, divide the numerators (converting any resulting improper fraction to a mixed number if required).

However, I would rather not remember this short cut as it could result in being used inappropriately (when the denominators are different), but instead stick to using the standard method, writing out the calculation in full and cancelling down before doing the actual multiplications.

The same way as mixed numbers without like denominators:

1. Convert the mixed numbers into improper (top heavy) fractions.
2. Invert (turn upside down) the divisor.
3. Multiply the fractions together (by multiplying the numerators together and the denominators together).

However, with the same denominators, in inverting the divisor it will mean that its numerator is the same as the denominator of the [original] dividend and so will cancel, leaving the result as the numerator of the first improper fraction over the numerator of the second - dividing the improper fractions' numerators.