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 six division two divided by five. If you switch the numerator and the denominator of two divided by five, you will have five divided by two: this is the reciprocal of two divided by five.

Thus, equation sequence six division two divided by five equals six multiplication five divided by two equals six cubed divided by one multiplication five divided by two sub one equals three divided by one multiplication five divided by one equals 15 divided by one equals 15.

So, dividing a number by two divided by five is the same as multiplying the number by five divided by two.

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.

6.4.1 Dividing Fractions with the Calculator

6.4.3 Dividing Mixed Numbers and Fractions