Fractions are found in many different circumstances, and we must be able to do everything with fractions that we can do with whole numbers. We can add, subtract, multiply, and divide whole numbers, so we should be able to do the same with fractions. We know how to add, subtract, and multiply fractions, so we must now learn how to divide fractions.
To divide by a fraction, we must use two things we have already learned. The first thing is reciprocals. We must know how to find the reciprocal of fractions in order to solve division equations with fractions. We also must know how to multiply fractions. Since we already know how to do both of those things, dividing by fractions is going to be much simpler than it looks.
Look at this problem:
Since 
is what we are dividing by, that is the fraction we are going to need to change. First, find the reciprocal of 
. The reciprocal of 
is 
. Dividing by a fraction is the same as multiplying by that fraction's reciprocal. Now that we have 
, we must change the division sign to a multiplication sign. The new problem is:
We solve this problem just like any other multiplication problem with fractions. Multiply the top numbers, and then multiply the denominator.
