Dividing fractions
Dividing fractions is very similar to multiplying fractions. If you know how to multiply fractions and what reciprocals are, to divide fractions, simply take the reciprocal of the fraction you are dividing by, and then multiply the two fractions.
We can divide fractions using the following steps:
- When dividing two fractions, first determine which fraction is the dividend (the number being divided), and which fraction is the divisor (number the dividend is divided by)
- Switch the positions of the numerator and denominator of the divisor; this is called taking the reciprocal
- Multiply the numerators of the dividend and the reciprocated divisor
- Multiply the denominators of the dividend and the reciprocated divisor
- Simplify the resulting fraction if necessary
Example
Solve:
First we identify 
as the dividend, and 
as the divisor.
Next we take the reciprocal of the divisor, :
Then we multiply the fractions:
Finally, since the numbers 10 and 88 share a factor of 2, we simplify the fraction by factoring out the 2:
Dividing fractions and whole numbers
Dividing fractions by whole numbers works in the same way described above; the only difference is that the whole number needs to be expressed as a fraction. To express a whole number as a fraction, all we need to do is write the whole number over 1, since any number divided by 1 is itself.
Example
Solve:
Write 4 as a fraction, then take the reciprocal and multiply:
3 and 16 don't share any factors so the fraction is already in simplest form.