6.4.2 Dividing Fractions
From the calculator exercises on the previous page, you can see that to divide by a fraction, you convert the second fraction (the one you are dividing by) into its reciprocal, then multiply by that fraction instead. If you’re interested in finding out why this works, it will be covered later in a section titled “Division or multiplication? That is the question.”
Just once more, let’s consider . If you switch the numerator and the denominator of , you will have : this is the reciprocal of .
So, dividing a number by is the same as multiplying the number by .
This process of finding the reciprocal of the fraction that appears after the division sign, and then multiplying by that value, can be used in any division problem. If you’re interested in finding out why this works, it is covered in Unit 7.