How To Multiply Proper Fractions By A Proper Fraction

Hi, I'm Rebecca. And in this film we're going to look at how to multiply a proper fraction by a proper fraction. Now, children can find it really hard to visualize what happens when you multiply fractions. So here's an example that may help them. Here I have a calculation. 1/2 times 2/5. Now, what this is actually asking is what is 1/2 of 2/5? So I have a circle here divided into 5 equal parts with 2/5 shaded, and I'm going to start by finding a half of it. So I'm going to split each part into two. Then I need to find a half of the shaded part, so I'm going to shade in two parts. So here you can see I have two parts shaded, and that's our numerator. But I don't have fifths anymore because I've halved them. I've now got tenths, so I can get 2/10. So let's see what that would look like on a bar model. Here I have my bar, and again, I have two fifths shaded. I want to find a half of each part and then I want to find a half of the shaded part. And as you can see, it gives the Same answer of 2/10. So, looking at the written method, actually, all we've done here is we've multiplied the numerator together to give us 2, and then the denominators, 2 times 5 is 10. And at this point, and at every point, you'd want to be challenging your pupils to see that they can actually simplify their 2/10 by halving the numerator and the denominator to give you one fifth. And that's how you multiply proper fractions.