There is more than one method of dividing fractions. The easiest and most commonly taught way is to “invert and multiply.”
To divide fractions take the reciprocal (invert the fraction) of the divisor and multiply the dividend.
This is the quickest technique for dividing fractions. The top and bottom are being multiplied by the same number and, since that number is the reciprocal of the bottom part, the bottom becomes one. Dividing anything by one leaves the value “anything” the same.
There is a lengthier way of dividing fractions and it could be said to be a "more correct" method. It involves the use of equivalent fractions to make the denominators of both fractions the same. This is the correct way since, strictly speaking you can’t divide apples by oranges in the same way as you can’t divide fifths by fourths.
You can explain this correct method to you child if he or she is curious. Otherwise it might be best to use just the invert and multiply method for dividing fractions.