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Welcome to our final lesson in this fractions unit.

Today we'll be solving fraction problems involving all four operations.

You'll only need a pencil and a piece of paper.

So pause the video and get your things together.

In today's lesson, we'll be solving problems involving all four operations.

So after your initial knowledge quiz, we'll do some revision of adding and subtracting fractions then we'll look at how to approach word problems and then you'll do some final independent work and no quiz for today.

So let's start with your initial knowledge quiz, pause the video and complete the quiz and click restart once you've finished.

Great job.

So let's get straight to our revision of adding fractions.

So when we're looking at adding two fractions with the same denominator, you're simply adding the numerators and that gives you your answer.

So we know that 2/7 plus 4/7 is equal to 6/7.

When you're approaching adding fractions with different denominators, we have to convert them so that they have the same denominator and we use the multiple least.

So I've written out my multiples of four and then multiples of six.

And I found that the lowest common multiple is 24.

So I need to convert 3/4 and 5/6 into fractions with a denominator of 24.

Now, remember that whatever we do to the denominator, we must do to the numerator so that the relationship stays the same.

So to get from four to 24, we've multiplied by six.

So we have to do the same to the three, 3 times 6 is 18.

So 3/4 is equivalent to 18/24 and six has been multiplied by four.

So I must do the same to the numerator.

5 times 4 is 20.

So 5/6 is equivalent to 20/24.

Then I can add them together, which gives me 38/24, and then I can convert to a mixed number, 1 14/24, which in this case simplifies to 1 7/12 So quick revision, now it's your turn.

Pause the video and practise adding the fractions.

So you will have converted these to have the same denominator.

In this case, the lowest common denominator was 15.

So converting these to fifteenths, we would have 5/15 plus 6/15 is equal to 11/15 and that's in its simplest form.

These ones with the same denominator it's very straightforward.

4 plus 2 is 6 and the denominator remains the same, and that simplifies to 2/3.

For c, your common denominator was 24, and you have 20/24 and 18/24 which equals to 38/24 which simplifies to 1 7/12.

Your final common denominator was 21.

So you had 12/21 and 14/21 which gives you 26/21 and converts to 1 5/21.

Now, let's look at what we do when we're adding mixed numbers.

When the fractions have the same denominator, all we do is add the integers, 1 add 3 is 4, and then add the fractions, 1 plus 3 is 4.

And the denominator stays the same, so that's 4 4/5.

But when we have a mixed number with where the fractions have different denominators, we're going to convert these to improper fractions and then convert them to have the same denominator.

So 1 4/5 is equal to 9/5, 2 1/3 is equal to 7/3, and then we need to convert them to have the same denominator.

The common denominator is 15, we multiplied 5 by 3 so we do the same to the nine, so it's 27/15.

We multiplied 3 by 5 so we do the same to seven.

So it's 35/15 added together that equals to 62/15 which converts to a mixed number of 4 2/15.

So convert to an improper fraction given the same denominator and then solve.

Pause the video and practise adding these mixed numbers.

So for your first one, the fractions had the same denominator so you just add the integers, 2 plus 4 is 6, add the fractions, 1/4 plus 3/4 is 4/4.

We know that 4/4 is equal to one whole.

So this one is seven.

The second one, you convert it to an improper fraction, 13/9 plus 7/3.

And we know that they need to have the same denominator.

13/9 can stay the same, 7/3 will become 21/9.

And if we add 13/9 and 21/9, we get 34/9 which converts to 3 7/9.

Your third one part c, we convert them to 31/8 and 5/4.

The common denominator is eight.

So this one can stay the same, and this one to turn to eight so we multiply numerator and denominator by two so that's 10/8.

So that will be equal to 41/8, and we know that 5/8 are in 41 with 1/8 remaining.

Then your last one, this is 41/9 and 11/6.

Both of these will need converting, the common denominator here is 18.

So nine was multiplied by two, so this is 82/18 and 6 was multiplied by 3 so that's 33/18.

Added that together is 115/18, and then converted to a mixed number, we know there are 6/18 in 115 with 7/18 remaining.

Now let's revise subtracting fractions.

When we have two fractions with the same denominator, we simply subtract the numerators.

So 4/7 subtract 2/7 gives us the difference of 2/7, 4 takeaway 2 is equal to 2.

And when we have fractions with different denominators, we just need to find the common multiple the same as with adding, we can see that the common multiple here is eight.

So 6/8 can stay the same, 1/4 multiplied by 2 is 2/8.

So 6/8 subtract 2/8 is equal to 4/8 and that simplifies to 1/2.

So have a go now at practising subtracting these fractions.

For your first one, your common denominator was 21.

So you multiplied 3 by 3 so you do the same to five.

So you've got 15/21 and then you multiply 3 by 7, so you do the same to 1 subtract 7/21, and that is equal to 8/21 which is in its simplest form.

B, we needed to convert only the second one because the common denominator is four.

You multiply 2 by 2 to give us 4, so multiply 1 by 2 to give us 2, 3/4 takeaway 2/4 is equal to 1/4.

Here, we have the same denominator.

So we simply subtract numerators, 4/9.

And here our common denominator is 15ths.

You multiplied 5 by 3, so you do the same to the four.

You multiply 3 by 5, so you do the same to the one.

12 subtract 5 is 7/15.

Now, we're going to apply this knowledge of fractions to solve problems. And this is involving all four operations.

We need to figure out what is the question asking us to do.

In year six 3/4 of the children get driven to school in a car.

Of these children only 1/8 get driven home as well.

So what fraction of the class gets driven both to and from school? What we're being asked here is to find an 1/8 of 3/4.

So we know that the whole year is 3/4 that get driven to school and only 1/8 of these get driven home from school as well.

Now, remember we know that 1/8 of 3/4 is the same as multiplying 1/8 by 3/4, which is equal to 3/32.

That's like our next question.

A jug contains 3/4 of litre of orange juice.

After you pour 5/8 of a litre into a glass, how much is left in the jug? So if I'm pouring juice out of the jug, I'm taking it away from the jug.

So my question is a subtraction question.

So I started with 3/4 of a litre and I poured out 5/8 of a litre.

So I'm doing 3/4 subtract 5/8, and then this is really straightforward subtraction, I need a common denominator of eight.

6/8 takeaway 5/8 means that 1/8 of a litre is left in the jug.

Now here's a third question.

Think about what we're being asked to do here.

Youcef walks 7/8 of a mile to school.

Hassan walks 1/2 of a mile to school.

How much further does Youcef walk than Hassan? So here we're being asked to find the difference between the distances that they walk to school.

So if we're finding the difference, we're subtracting.

We know that Youcef walks further, so his is going to be the greatest fraction of a mile here.

So we're doing 7/8 of a mile subtract 1/2 where we need the common denominator of eight and 1/2 is equal to 4/8.

So that is 3/8 of a mile.

So Youcef walks 3/8 of a mile further than Hassan.

And just an interesting fact, 3/8 of a mile is equal to 600 metres.

So here's the final question that we'll look at together.

Fatma has 3/4 of a pizza left.

She wants to share it between herself and her two friends, Tasnia and Matila.

So she's got the 3/4 of a pizza and she's going to share it equally between herself and her two friends.

So that means that she is going to share it into three equal groups.

So she is dividing 3/4 by 3.

So she's dividing it by three.

She's going to be finding 1/3.

So we know that she's finding 1/3 of 3/4 which is the same as 3/4 times by 1/3.

And that is equal to 3/12 which simplifies to 1/4.

So they'll each get 1/4 of the pizza.

Now you're going to do some independent questions.

The most important thing is to annotate your questions so that you understand what you are being asked to do and which of the four operations you need to apply.

So pause the video and complete the task and then click restart once you've finished.

So for your first question, you had a pyramid where each block is the product of the two blocks below and you were asked to complete the pyramid.

So your first one, you were looking at 1/2 times 1/3 and that gives you 1/6.

For your second one, 1/3 multiplied by 3/4 which is equal to 3/12 or 1/4.

And then for your final one, so I look at the simplified version, 1/6 times 1/4 is 1/24.

For question two, Harriet has 8 3/4 metres of fabric, and she uses 5/6 of the fabric to make a dress.

So we're looking at how much fabric she uses.

So what you're being asked to find is 5/6 of 8 3/4.

And we know that that is the same as 5/6 times 8 3/4, which can be converted to an improper fraction and then multiply so that's 175/24 which simplifies to 7 7/24 of a metre.

That's how much fabric she used.

Question three.

Sally is serving squash to her friends.

She fills a jug to 4/5 of its capacity.

So it's 4/5 full, but unfortunately she spills 1/10 of the volume of squash before serving.

Then she serves the remaining squash equally between six friends.

What fraction of the capacity of the jug does each person receive? Now, this is a two-step problem.

The first thing was to find out how much was left after she spelt 1/10.

So you were looking at 4/5 subtract 1/10 which you converted 4/5 to 8/10.

So there's 7/10 of the jug left.

Then she divided that 7/10 of the jug between six friends.

So 7/10 divided by 6 which is the same as finding 1/6 of 7/10 which is the same as 1/6 multiplied by 7/10 which is equal to 7/60.

And that's is the fraction of the capacity of the jug that each person received.

Question four.

In year seven, the children take part in one enrichment activity on a Wednesday afternoon.

They can choose between cookery, basketball and film club.

So they have three choices.

3/8 of the children take a cookery, 1/6 of the children take basketball, and you were asked for the fraction that take film club.

So what you needed to look at here was first of all, what fraction take cookery and basketball? So you're looking at adding 3/8 and 1/6, converting them to fractions with the same denominators meant that 13/24 took either cookery or basketball.

And then you needed to find the difference between 13/24 and the whole to find the remaining fraction that took film club.

So the hole was 24/24 subtract the 13/24 means that 11/24 of the year seven took film club.

And your final question, you were looking at how much I run.

So I'm training for a 10k run.

Last week, I ran 1 7/8 of a kilometre each day.

So how many kilometres did I run together? So you had to use your knowledge of calendar maths to know that that would be seven days.

So we're looking at multiplying 1 7/8 by 7, which converts to 15/8.

15/8 multiplied by 7, and I've converted that to a fraction over one is equal to 105/8, that's 13 1/8.

So last week I ran 13 1/8 of a kilometre.

Well done, you've worked really hard today.

Those weren't easy questions, but you can see how you apply your knowledge of fractions to word problems now.

Now, in our next lesson, we'll be starting a new topic called decimals and measures and we'll be learning how to generate and describe linear number sequences.

I'm looking forward to seeing you then.