How to Divide Fractions with Whole Numbers

It is a fairly simple math lesson which will take hardly any time to learn. With it being an important thing that you will be using for a long time, you really need to understand it to be able to use it off the top of your head.
Children tend to get pretty scared when they see two very different types of numbers, one whole number and one fraction side-by-side. And it is fairly clear that out of the four main mathematics functions, division has to be the toughest. Put two different types of numbers together and ask a student to divide them, and the poor kid will be a mess. But never fear!

The Procedure

So now that I've promised you that dividing fractions by whole numbers is nothing to be afraid o, I'm going to have to live up to this promise. So let's get cracking right away. Get a pen and a paper and get ready to roll!

Now take a whole number and a fraction. Let's take for example, the fraction 3/4 and the whole number 5. The fraction part is the dividend (number which is to be divided) while the whole number is the divisor (the number which divides). So you will numerically represent the question thus:

3/4 ÷ 5.

So now this is the problem facing you. How would you solve it?

Step #1: Convert the whole number into a fraction. Confused? Just 5 as the numerator and one as the denominator under the 5. So you have a fraction 5/1.

Your question will now look like this.

3/4 ÷ 5/1

Step #2: The next step is to find the reciprocal of the newly converted fraction. Recipro...what? A reciprocal is a fraction turned up-side-down. So the reciprocal of 5/1 is 1/5. Now this reciprocal allows you to turn the division sign into a multiplication sign.

Your question now looks like this.

3/4 × 1/5.

Step #3: Surely you know how to multiply fractions. No? Well this is a simple one. Multiply the two numerators and the two denominators and you have your answer.

3 × 1/4 × 5.

= 3/20.

See that easy. But let's review the steps once again in case you have forgotten!
  • Whole number divide by 1
  • Reciprocal
  • Multiply
But suppose you were asked to divide whole numbers by fractions, then what would you do? Get stuck in a jam? No! You'd read on and be prepared!

How to Divide Whole Numbers by Fractions

Now then, whole number as the dividend and fraction as the divisor. Here's how you nail this one.

Let's take the same two numbers, but reverse the order.

5 ÷ 3/4

Step #1: You guessed right. Convert the whole number into a fraction. Simple as it gets.

You question now looks like this.

5/1 ÷ 3/4

Step #2: The second step? Right guess once again. Get the reciprocal of the divisor, ditch the division sign and put in the multiplication sign.

Now you have

5/1 × 4/3

Step #3: Easy as it gets. Multiply the two and you have your answer.

5 × 4/1 × 3

20/3

Dividing fractions with whole numbers and also how to divide whole numbers by fractions. I hope that helps you finish your homework. Wasn't that very, very easy?
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Last Updated: 9/20/2011
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