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5.6

## National STEM Learning Centre

Skip to 0 minutes and 7 seconds SPEAKER 1: So let’s have a look now at how we divide one fraction by another. We’re going to have a look at 2/5 divided by 2/3.

Skip to 0 minutes and 15 seconds SPEAKER 2: So I’ve come across a method for doing this, and I’ve heard it being called the KFC method. So K means that you keep this one the same. F, we’re going to flip the second one, and then C, we’re going to change this from a division to a multiplication. And that seems to work every time.

Skip to 0 minutes and 33 seconds SPEAKER 1: OK, so you’re saying we’re going to keep this the same, so 2/5. We’re going to change to a multiplication and flip this one to be 3/2.

Skip to 0 minutes and 45 seconds SPEAKER 2: And I can do multiplication, so 2 times 3 gives us 6 on the top. 5 times 2 is 10, so it’s going to be 6/10.

Skip to 0 minutes and 53 seconds SPEAKER 1: OK, which we can simplify to be 3/5. OK, and do you know why that works? Where does it come from?

Skip to 1 minute and 2 seconds SPEAKER 1: So maths, it’s quite poor practise if we don’t understand the reason behind some things. So let’s have a look into that. So if we have 2/5 divided by 2/3– so you put 2/5. And we could write this quite crudely as 2/5 divided by 2/3.

Skip to 1 minute and 17 seconds SPEAKER 2: So the fraction and then another fraction underneath?

Skip to 1 minute and 20 seconds SPEAKER 1: Yes, it isn’t ideal, but just to show the reasoning where it comes from. Now, we know if we want to get rid of a denominator, if we multiply by the reciprocal, that would equal 1. So you would have 3/2. Because these are fractions and equivalent, do the same thing top and bottom, so 3/2.

Skip to 1 minute and 43 seconds SPEAKER 2: So this thing that you’re multiplying by on the right-hand side is 3/2 over 3/2. So that’s just 1, so it’s not going to change the value?

Skip to 1 minute and 51 seconds SPEAKER 1: Absolutely, perfect, good, and the reason we’re doing this is to have our reciprocal to get rid of our denominator. So with that in mind, our denominator now becomes 1. Our numerator becomes 2/5 times 3/2. So we have our 2/5 multiplied by 3/2. So can we see now that’s where our reasoning comes from?

Skip to 2 minutes and 15 seconds SPEAKER 2: Ah, because that’s 1, we can almost ignore it. And then we just do the multiplication?

Skip to 2 minutes and 20 seconds SPEAKER 1: Exactly, yes, that’s exactly where it comes from. So we have our 2 multiplied by 3. As we solved earlier, it’s our 6. 5 multiplied by 2, product 10. So finally, same answer but with the more reasoning, it’s 3/5.

# Dividing fractions

How would you explain what happens when we divide one fraction by another? Before you watch the video, have a go at this task:

## Describe

In the comments below, before you watch the video or continue, just have a go at writing out an explanation of what happens when you divide one fraction by another.

Explaining the exact meaning of what is meant when we divide one fraction by another, for example dividing two fifths by three halves, might be difficult as it is not easy to represent this using manipulatives. In these cases, we might decide to show pictorially that we are attempting to find how many three halves go into two fifths. However, this too can be very confusing especially, when students know that three halves is a bigger fraction than two fifths.

This may explain why students are often taught ‘how’ to divide fractions by using a simple algorithm. We can, however, if we understand the properties of reciprocals, explain quite simply why the algorithm for dividing fractions works.

Watch the video in which Paula and Michael explain. How would you amend your description?

## Problem worksheet

Complete questions 7 and 8 from this week’s worksheet.

## Teaching resource

This teaching resource directly addresses one of the common misconceptions to do with dividing whole numbers by fractions: Dividing whole numbers by fractions.