Dividing By Fractions

Dividing by fractions using a pencil and paper? Here are a few sample problems that show you how to do it.

Dividing fractions is just like multiplying fractions, but with a twist (literally). All you need to do is twist around the numbers in the second fraction in your equation and then treat it like you would a multiplication problem.

Here's an explanation of how to do it.

First you need to know a couple of terms. The top number in a fraction is the numerator. The bottom number in a fraction is the denominator. So in the fraction 3/4, 3 is the numerator and 4 is the denominator. In the fraction 1/2, 1 is the numerator and 2 is the denominator.

So let's try those fractions in a problem. You want to divide 3/4 by 1/2. The first thing you do is take the second fraction and flip-flop the numerator and denominator (this flip-flopping is commonly known as "reciprocating"). So for 1/2, make the 2 the numerator and 1 the denominator. You then multiply 3/4 x 2/1. You multiply the two numerators to get the numerator of your answer, then multiply the two denominators to get the denominator of your answer. So 3 x 2 = 6 and 4 x 1 = 1. Your answer is 6/4. Of course, you can simplify that by dividing 6 by 4, which, of course, is 1-1/2. So in the end, 3/4 divided by 1/2 = 1-1/2. Again, just flip the numerator and



denominator in the second fraction, then multiply the two fractions to get your answer, then simplify your answer if necessary.

Let's use whole numbers now. What is 3-1/4 divided by 1-1/8? First you need to get rid of the whole numbers and make them complete fractions. You do that by multiplying the whole number by the denominator, then adding the

numerator. The answer you get is your numerator, and that goes over the denominator. So in 3-1/4, it's the whole number (3) times the denominator (4) plus the numerator. So 3 x 4 = 12. 12 + 1 = 13. The denominator is 4. So 3-1/4 = 13/4. In the second number (1-1/8), it's (1 x 8) + 1. The denominator is 8. So 1-1/8 = 9/8. So when you

ask what 3-1/4 divided by 1-1/8 is, it's the same as asking what 13/4 divided by 9/8 is. We now flip-flop the 9/8, making it 8/9, then multiply. So now our equation is now 13/4 x 8/9. 13 x 8 = 104. 4 x 9 = 36. So our answer is 104/36. To simplify that, what is the highest number that will divide evenly into both the numerator and

denominator? The answer is 4. So if we dived 104 by 4, we get 26. If we divide 36 by 4, we get 9. So 104/36 = 26/9. To simplify further, 26 divided by 9 = 2, with a remainder of 8. So 26/9 = 2-8/9. This means that the answer to our original question...what is 3-1/4 divided by 1-1/8.....is 2-8/9.

This may all seem very complicated, but once you do a few problems and check your work with a calculator, you will gain the confidence you need to do it without a calculator. Just remember to flip-flop (or reciprocate) the second fraction, then multiply your two fractions. Then simplify your answer, and you're done.

© High Speed Ventures 2011