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Hello everybody, my name is Mr. Kelsall, and welcome to today's lesson about adding and subtracting fractions with a common denominator, looking at improper fractions.

Now before we start you will need a pen and a piece of paper.

Also, please try and find a quiet place, somewhere that you won't get disturbed, and don't forget to move any sort of distractions.

For example, putting your mobile phone on silent or move it away completely.

Pause the video, and then when you're ready, let's begin.

Today's lesson is about adding and subtracting fractions with a common denominator, where there are improper fractions or mixed number fractions.

We're going to start by looking how we add above one whole one.

We're going to look at mixed number fractions, and then we're going to look at multi step questions.

And at the end as always, it's quiz time.

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

Now our star words are fraction, denominator, numerator, and vinculum.

We'll be talking about proper fractions, improper fractions, and mixed number fractions.

We'll be looking at equivalent fractions and how to simplify fractions.

And for all of this you'll need to identify a common denominator.

In order to access this lesson you'll need to understand a fraction is part of a whole.

The denominator is the number of parts the whole is split into, and the numerator is the number of parts of the whole.

The vinculum is the line between the numerator and the denominator.

A proper fraction: the numerator is less than the denominator.

In an improper fraction, the numerator is greater than the denominator.

A mixed number fraction is a combination of a fraction and a whole.

For equivalent fractions, it's a fraction which represents the same number.

And the process of simplifying is to reduce the numerator and the denominator.

We know that when they have the same denominator we can add the fractions by adding the numerators.

If we've got different denominators, we need to find an equivalent fraction and a common denominator and then add the numerators.

So bit of revision, draw these as improper fractions and as mixed number fractions.

How would you convert from improper fractions to mixed number fractions, and can you do this mentally, without drawing? Pause the video, and when you're ready press play.

So, I know one and one quarter means one whole and one quarter.

So if I've got my one whole one, and within my one whole one I've got four quarters, and then my other one I've got one quarter.

So in total I have five quarters.

I can do this mentally by thinking one times four, one lot of four quarters is one, and add on one, gives me five.

Let's do the same process with this.

I've got two whole ones, and there are three thirds in whole one.

So six thirds in two whole ones, and I've got two extra thirds which gives me eight thirds.

Let's look how that would be represented.

So I've got three thirds, six thirds, seven thirds, eight thirds.

And my last one, three and a half, I'm going to do mentally, I'm going to say three lots of two halves is six halves, add the one gives me seven halves.

You should be able to do this mentally.

You should be able to convert between improper fractions and mixed number fractions and vice versa quite confidently.

So for our new learning, let's learn to convert fractions and then add and subtract.

Have a look at these questions.

Can you use a number line to draw them? Can you draw this as a bar model? The question is one and one quarter add one eighth.

So I'm thinking this one I'm just going to sit to one side and come back to later.

And I'm just going to think about 1/4 add 1/8.

If I'm drawing that on a number line I can start with my quarters, but actually I need to find the common denominator.

So this one quarter I know is the same as two eighths, so let's write that as two eighths.

Now I got one and two eighths, add on one eighth.

Instead of using my quarter number line, I'm going to use my eighths number line.

So I'm going to start my two eighths, and add one eighth.

So I've done this part and this part to get three eighths.

However, I started with one whole one to begin with, so I need to add that as well.

So I know that one quarter add one eighth can be written as one and two eighths add on one eighth which gives me one and three eighths.

Okay, pause the video, have a go at the questions on the screen.

Press play when you are ready.

Okay, this time I'm starting with two and two thirds.

So again I'm just going to think about the two whole ones later.

I'm going to start at two thirds, which is there, and I need to take away one sixth.

So I've got different denominators, I need to find a common denominator.

My common denominator is sixes, so I'll convert my two thirds to sixths.

So I've got two whole ones, two thirds becomes four sixths, and taking away one sixth.

So I the start of four sixths, and I take away one sixth, and left with three sixths.

So I've still got my two whole ones, and four sixths take one sixths is three sixths.

And if you remember, that's the same three sixths is equal then to, one half.

So I can write this as two and one half.

The second question is a little bit easier.

It's three and one half take away one half.

Well I'm going to start at my half, and just take away one half.

So three and one half, take away one half, just gives me three on its own.

Which brings us to our develop learning for today.

We're looking at converting fractions to add and subtract.

And we'll look at crossing barriers, so crossing whole numbers.

Have a look at these questions, and think how you would add and subtract these fractions.

Think, would you need to use a number line or a bar model, and would this help? I'll do the first one, and then I'll pause the video and let you have a go at the others.

So, I'm going to draw it with a bar model first.

I've got one whole one, which is split into quarters, and I've got four of these quarters.

I've got my next whole one, which is split into quarters, and I've got three of these quarters.

So I've got one whole one, and three quarters.

And I need to add on five eighths.

Now the problem is that I'm majored on quarters rather than eights, so I need to convert these to eighths.

So if I draw a line here, I now know that that is six eighths.

So I can convert this from one whole one and three quarters to one whole one and six eighths.

And then adding on my five eighths.

Well, let's see if we can draw these.

I've got one eighth, two eighths, I then need to go into another whole one.

And I've got three eighths, four eighths, five eighths.

So in total I've got two whole ones and three eighths.

That's as a mixed number fraction, I can write it as an improper fraction.

I've got eight whole ones, 16 whole ones, 17, 18, 19, whole ones so I've got 19 eighths.

I can repeat the same process, but this time I can use a number line.

So I've got one, two, three, and I'm going to start by marking on my one and three quarters, which is here.

However, because I need to convert it to eighths, I'll need to split to eighths.

Now this dot's at one and three quarters, and I'm adding on five eighths.

Let's just mark the eighths on the second number line.

So one and three quarters, one eighth, two eighths, three eighths, four eighths, five eighths.

So that brings me to two and three eighths.

If I wanted to count in eighths I've got, eight eighths, 16 eighths, 17, 18, 19 eighths.

And finally, I could do this with numbers alone.

So I could say, three quarters is the same as six eighths.

And I'm going to add on five eighths, six eighths and five eighths gives me 11 eighths.

So I've got one and 11 eighths.

Now if you remember, we don't want fractions like this because we've got a mixed number fraction and an improper fraction together.

So, I'm going to convert this 11 eighths to a whole number.

So eleven eighths is the same as one and three eighths, But I've got another one in there, so this is two and three eighths.

Okay, pause the video, have a go at the other two questions.

You'll notice these are takeaways.

This time, you'll have to count back.

Think which is going to be best, a number line, mentally? You decide.

Pause the video, and when you're ready, press play to continue.

Okay, I'm just going to do this with numbers.

Two and two thirds, taking away sixths, five sixths, I'm going to go revert the thirds into sixths, two thirds is the same as four sixths, I'm taking away five sixths.

I could draw a number line, but actually I can count in fractions already, so I'm going to use that skill because it's a mental skill.

I'm going to count to two and four sixths, two and three sixths, two sixths, one sixths, zero sixths, and now onto one and five sixths.

So I know that two and four sixths, takeaway five sixths leaves me with one and five sixths.

I could do the same skill using improper fractions.

Two and four sixths, if I convert to an improper fraction, it goes six sixths, 12 sixths, 13, 14, 15, 16 sixths, and I'm taking away five sixths, which leaves me with eleven sixths.

If I wanted to convert that back to a mixed number fraction, I know that six sixths is one whole one, and there's five sixths left over.

My final one's a little bit easier, because I don't have to convert any fractions, but I do have to count back in fractions.

I'm starting at three and one half, and I'm going to take away a half, which gives me three.

And then I'm going to take away one, which leaves me with two.

Nice and easy, I can do this mentally.

Let's look at the same style of questions, in context, in a real life problem.

On the first day training, Ameena ran one and a half kilometres.

On the second day of training, she ran one and three quarters a kilometre.

How far did she run in total? Pause your video, press play when you're ready to continue.

I'm doing one and one half, add on one and three quarters.

I need to convert these to a common denominator, so one and one half is the same as one and two quarters, add on one and three quarters.

There's a range of ways I can do this, but I'm going to do one add one gives me two.

Two quarters and three quarters gives me five quarters.

But I also know that five quarters is one whole one and a quarter left over.

So I want to add the whole one to my two, which gives me three whole ones and one quarter of a kilometre.

Represent the same question with a bar model, and I could do my one and one half add on one and three quarters.

This time I've added the whole numbers together first, so there's my one whole one and my other one whole one, gives me two whole ones.

I'm adding a half and three quarters.

I still get the same answer, I can convert them.

One and three quarters, if I convert them to improper fraction, one and three quarters is seven quarters.

One and one half, I'll step underneath to think that's one and two quarters.

And I need to convert to improper fractions, that's six quarters.

Six quarters add seven quarters gives me 13 quarters.

If I convert back to a mixed number fraction, four quarters, eight quarters, 12 quarters, is three whole ones and one quarter is left.

Now it's time for your independent task.

Add or subtract these fractions.

You'll notice that there are three fractions together, with an addition and subtraction, and sometimes there's a missing number fraction.

Think about the inverse.

Pause the video, and when you're ready, press play for the answers.

Okay, question one is you convert to eighths, you've got one and two eighths add five eighths add four eighths gives you two and three eighths which is the same as 19 eighths.

Question two, I'm going to convert to sixths.

Three and three sixths, take away four sixths, add one sixth gives me three.

Question three, I'm going to convert to quarters, and I'm going to find the inverse, so two and three quarters, Question three, I'm going to convert to quarters, and I'm going to find the inverse, so four and two quarters, take away two and three quarters, gives me one and three quarters, which is the same as seven quarters.

And question four I'm going to convert to eighths, four and two eighths, take away three and three eighths, leaves me with seven eighths.

Congratulations on completing your task, if you'd like to, please ask your parent or carer, to share your work on Twitter, tagging @OakNational and also #LearnwithOak.

And before we go, please complete the quiz.

So that brings us to the end of today's lesson on adding and subtracting fractions with common denominators and looking at improper fractions.

A really big well done for all the fantastic learning that you've achieved today.

Now, before we finish, perhaps quickly review your notes, and try to identify the most important part of your learning from today.

Well, all that's left for me to say is, thank you, take care, and enjoy the rest of your learning for today.