Lesson video

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This is our third lesson in our fractions topic.

Today, we'll be dividing a proper fraction by an integer.

It's just a pencil and piece of paper lesson.

So pause the video now and get your things if you haven't done so already.

In today's lesson, we'll start with a quiz to test your knowledge from the previous lesson.

Then we'll be looking at the connection between fractions and division before deepening our understanding of dividing a fraction by an integer then you'll complete some independent work and a final quiz.

So let's start with your initial knowledge quiz.

Pause the video now and complete the quiz and click restart once you're finished.

Good job.

Now we're starting by looking today at the connection between fractions and division.

So we've got a word problem here, 12 bars of chocolate are shared equally between four people, how much chocolate does each person get? So we're going to look at how to represent this pictorially.

So we've got 12 bars of chocolate, shared between four people.

So here are our four groups.

And we can see from this representation that each of those four people will receive three bars of chocolate.

Or we know that sharing 12 wholes into four equal groups gives us three, so four equal groups of three, and that's the same as 12 divided by four.

But we also can remember from our previous lesson that if we're dividing by four, we're finding a quarter of something.

And if we're finding a quarter of something, that is the same as multiplying by one quarter.

So finding a quarter of 12 is the same as doing one quarter multiplied by 12.

So we're linking here division and multiplication of fractions.

Let's have a look at another one.

So here, the question is we have six bars of chocolate and they're shared equally between two people, how much chocolate does each person get? So I wouldn't need to pause the video and create your own pictorial representation of this problem.

And you can always go back to our previous slide to see how that might look, pause the video now.

So you had your six bars of chocolate, so you may have drawn a bar model divided into six equal parts, and you're sharing them between two people so you're sharing them into two groups and you can see that each of two groups will get three bars of chocolate.

So you're sharing six wholes into two equal groups of three, which is the same as six divided by two.

And then if we link it back to our multiplication from yesterday, if we're dividing something by two, we're finding a half and finding a half of six is the same as doing a half multiplied by six.

And if you remember back to yesterday, we could turn this integer into a fraction over one, one multiplied by six is six, two multiplied by one is two and if I convert that back to in fact, it turns into an integer because there are three groups of two in six.

How're we going to deepen our understanding of this by applying this two division questions.

So these are the sorts of questions that you may have seen before.

So we've got three quarters divided by five.

What we're doing here is we're dividing three quarters, which is the whole here into five equal groups.

So we're dividing three quarters into fifths.

If we divide something by five, we are finding fifths.

What we're actually doing here is we're finding a fifth of three quarters.

And that is the same as three quarters times a fifth or a fifth times three quarters.

So remember that we multiply numerators, which is three and denominators, which is 20.

So three quarters divided by five is equal to 3/20, is the same if we're dividing by five, it's the same as finding one fifth.

Let's look at another one.

Omar has one third of a bottle of juice left.

So the whole is a third.

He shares the juice equally between five people.

And we want to know what fraction of the juice does each person get.

So what we're actually being asked here to do is take our whole here which is a third and divide it by five.

So let's look at it pictorially.

We've got a third and we've divided it into five equal parts.

So we're dividing it into fifths, okay? We're trying to find a fifth of a third.

So this is how we can represent it, we can represent it how we did up here, a third divided by five, or we can think about it as a fifth of a group of one third, which is the same as a third times a fifth, one times one is one and three times five is 1/15, So a third divided by five is equal to 1/15.

Now you're going to look at one independently I'll read it out to you first.

So Novie has three fifths of a pack of stickers left, So that's the whole, she wants to share the remaining stickers equally with her friend Elizabeth.

Now, what we're saying here is that she wants to share them between herself and Elizabeth, so think about what you're dividing your fraction by.

and I would like you to represent this pictorially and then if you think back to our previous one, I'll just pop back.

If you think about representing it in these three different ways, pause the video now and represent the problem.

So you knew that the whole was three fifths and it was being divided into two equal parts between Novie herself and Elizabeth.

So if you're dividing something by two, you're finding a half, and the ways that you could have represented that was by thinking about finding three fifths divided by two, which is the same as finding a half of three fifths, which is the same as a half multiplied by three fifths.

One times three is equal to three and two times five is equal to 10.

So you're going to complete some independent work.

Now, the main thing that you need to think of doing is converting your division question into a multiplication question by thinking about what am I actually being asked to do here.

And as always, it's very helpful to draw yourself a picture to make that connection.

So pause the video now and complete the task, then click restart once you're finished and we'll work through those solutions together.

So for the first question, you were asked to find 9/10 divided by three.

Remember that if we're dividing something by three, we're finding a third.

So you were doing a third of 9/10, which is the same as 9 /10 times one third, which is equal to 9/30, which simplifies to 3/10.

And we're looking at the same procedure here.

So we're looking at dividing 10/12, sorry by five, which is the same as finding a fifth of 10/12, which is the same as 10/12 multiplied by one fifth, 10 times one is 10, 12 times five is 60 and that simplifies to one sixth.

If we're dividing by four, we're finding a quarter.

So if finding a quarter of 8/11, which is the same as 8/11 times one quarter, which is equal to 8/44, which simplifies to 2/11 by dividing by four, then you'll find a one.

If we're dividing by two, we're finding a half.

So we're doing seven eighths multiplied by one half, which is equal to 7/16.

In question two, we had a word problem.

Sally has forgotten to take her phone charger away for the weekend.

And she has four fifths of her battery life remaining.

She has to make it last for three days.

So how much of the battery can she use each day, if she wants to use an equal amount each day? So you are being asked to divide four-fifths by three, which is the same as four fifths multiplied by one third, because you're finding four fifths or third or four fifths.

And I've also got a representation here, pictorially to think of it in a different way.

So we know that Sally has four fifths of her battery left and over three days that can be divided into 15 parts of battery life.

So she has 12 parts left because she's already used 3/15.

So she's got 12/15, which is coloured in and split equally over those three equal days means that she has 4/15 to use each day for 15 days.

So for question three, dividing by two is the same as finding a half of something.

So I'm thinking what multiply by one half is equal to 3/8, I know the three times on is three and four times two is eight.

So three quarters times a half is three eighth so a half of three quarters is three eighths.

For the next one, we're dividing something by three to find one ninth.

I know that dividing by three, it's the same as finding one third of something.

So I know that one times one is one and three times three is nine.

So a third of a third is a ninth.

Question four, this is a multi step problem.

So the field is two thirds of a kilometres long by one ninth of a kilometre wide.

Hopefully you drew yourself an image there so the area of the field is split into three equal parts.

And you have to find the area as a fraction of each section.

So I gave you a hint to find the area first We know the area is length times width, so the area was 2/27 of a kilometre squared and then I'll just put my units in there.

And then the field was divided into three equal sections.

So we know that the whole area is 2/27 and we needed to divide that by three.

So 2/27 divided by three is the same as finding a third of 2/27, which is the same as 2/27 times one third, which is equal to 2/81 kilometres squared So each section had an area of 2/81 of a kilometre squared.

And question five, you were asked to find the value of the calculation when A equals three and B equals nine So you just needed to substitute those numbers in.

So A is three, then it's three fifths divided by B is nine so divided by nine so you're dividing by nine.

You're finding a ninth of three fifths, three fifths times one ninth is equal to 3/45, which can be divided by three and simplified to 1/15.

Now it's time for your final quiz, so pause the video and complete the quiz and click restart once you're finished.

Great work today in our next lesson, we'll be looking at both multiplying and dividing proper fractions, I'll see you then.