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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.

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're not going to be disturbed.

And don't forget to remove any sorts of distractions.

For example, put 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.

We're going to start by looking at equivalent fractions.

We'll then extend this to common denominators, and then we'll then look at fractions and subtracting fractions in a different context.

After that it's quiz time.

I mentioned already that you'll need a pen and a piece of paper.

And our star words for today are fraction, denominator, numerator, and vinculum.

We'll be talking about proper fraction, an improper fraction and then mixed number fraction.

We'll be looking at equivalent fractions and simplifying a fraction.

In order to access this lesson, you'll need to know that 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, which have been selected.

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

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

Improper fraction is where the numerator is greater than the denominator.

A mixed number fraction is a fraction and a whole together.

An equivalent fraction is a fraction that represents the same number.

And to simplify a fraction, you reduce the numerator and the denominator.

We're going to be looking at adding and subtracting fractions of the same denominator and a common denominator.

So, have a look at these shapes.

How many fractions can you represent by folding the piece of paper or by drawing lines on the shapes? Pause the video, then when you're ready, press play to continue.

I've drawn a few on the screen for you.

More revision about equivalent fractions.

Match the fractions with the pictures and have a think.

What could the missing fraction or fractions be? Pause the video, when you're ready, press play to continue.

So the first one represents four thirty-twoths, which is the same as one eighth.

The second one represents three twelfths, which is the same as one quarter.

The third one represents 12 twentieths, and that can also be seen as three fifths, or it could be seen as six tenths.

Okay, so when I'm counting these, I know that the orange rod takes up 10 squares, and the white rod takes up one square.

So I could say that the white square is one tenth of the orange rod.

And if the white square is one tenth, then the red one is two white squares, so that must be two tenths of the orange rod.

The green one is three tenths.

Purple is four tenths, black is five, six, seven tenths, and the burgundy is eight tenths.

Now, I'd just like to point your attention to a few of these.

I know that two tenths has an equivalent fraction in fifths.

Can you remember what it is? Well done, I know that two tenths is the same as one fifth.

When I look at my purple rod, I've got four tenths.

And again, I can find the equivalent fraction in fifths.

It's two fifths, I've got six tenths, which isn't there.

And that's three fifths.

And then I've got the burgundy one, which is eight tenths.

And that is four fifths.

I mentioned these because it's worth looking at all these equivalent fractions throughout this lesson.

If we can find equivalent fractions, we can help ourselves find common multiples.

So let's continue with this new learning.

Let's remind ourselves, the orange rod is worth one, and I can see the purple rod takes up four out of 10 squares.

And I know that's four tenths.

And I also know it's two fifths.

The green rod takes up three tenths.

But I want to add together two fifths, add on three tenths.

How am I going to do this? Have a look, what does the calculation on the page show you? How would you represent this on a number line? And which is the correct answer, and why? Pause the video and when you're ready, press play to continue.

Calculation number one, two tenths, sorry.

Two fifths out of three tenths gives me five fifteenths.

Well, I know that's incorrect, because I'm not measuring in fifteenths.

I know that I can see things are in tenths.

And what's happened here is this common mistake.

The person has added two and three to give five, and the value of five and 10 to give 15.

That does not represent the calculation that we see.

Example number two, we've got two fifths.

Add on three tenths, and it gives us a total of five tenths.

Well, let's have a think about this.

Two fifths, how many tenths is that? That's the same as four tenths.

So four tenths and three tenths, well, it doesn't give us five tenths.

We're expecting to see seven tenths, so that answer is also incorrect.

And two thirds, sorry, two fifths add on three tenths.

We've somehow got the answer of five fifths, that is wrong.

When I look at this, none of these answers are correct.

When I look at this, I can see that two fifths is the same as four tenths, and four tenths, add on three tenths, gives me seven tenths.

I can also represent this on a number line.

I know I have my two fifths, I'm going to add on three tenths.

It's worth paying attention to how I converted that two fifths previously.

I know that two fifths is the same as four tenths, because for every one fifth, I have two tenths.

So I know two fifths is equivalent to four tenths.

So four tenths add on three tenths gives me a total of seven tenths.

So I'm beginning to think about common multiples and how I can use these to add two fractions, which have got a common denominator.

So, I'm going to look at using a number line to solve this problem.

I'm looking at my first question, which is three eighths add on one quarter.

So if I got one, two, three eighths, I then need to add on one quarter.

I can see that one quarter is the same as two eights, or I could try and convert this mentally.

But one quarter is two eighths, so I need to add on two eighths.

Three eighths and two eighths is five eighths, so three eighths add one quarter is five eighths.

I can repeat this process for question two.

I'll start off with one sixth, and I'm adding two thirds.

And I can see that two thirds is the same as four sixes.

If I needed to convert thirds to sixes, I'd be thinking two thirds equals something sixes.

So I'm converting my 10 to my two, times my two, so it's four sixes.

So let's add on four sixes, one, two, three, four sixes.

So I had a one six and four sixes is five six, so one six out of two thirds is five sixes.

And again, with one half and five eighths, I need to find a common denominator.

So I'm thinking eighths.

So one half is how many eighths multiplied by four, multiplied by four.

So I know one half is four eighths, so that's my one half.

I need to add on a further five eighths.

One, two, thee, four, and five, you'll notice that I go beyond one.

So the final answer will be one and one eighth, or I could write it as nine eighths.

For our develop learning today, we're looking at common multiples.

So have a look at these fractions and where possible, try and sketch us a bar model, try and draw a number line, and try and write the fact families for these questions.

I'll do the first one for you.

To one quarter add one half.

Well, I'm thinking I'm converting my half into quarters.

So one half is the same as two quarters.

So I'm thinking one quarter add two quarters gives me three quarters.

I can draw this on a bar model if I wish, I can take a whole one and I can split it into quarters.

And I can think I'm adding two quarters, which is the same as one half.

And I'm adding a further quarter.

So in total I've got three quarters.

If I wanted to write this as a fact family, I could say two quarters, add one quarter gives me three quarters.

I could say three quarters, take one quarter gives me two quarters.

I could say three quarters, take two quarters, gives me one quarter.

Okay, pause the video, try the rest of the questions, and press play when you're ready.

So two quarters add one eighth is the same as four eighths and one eighth which gives me five eighths.

Three sixths add one third is the same as three sixths add two sixths, which gives me five sixes.

Repeat the process with these questions, pause the video.

And when you're ready, press play.

For four-fifths and two tenths, is the same as eight tenths and two tenths, which is 10 tenths, which is one whole one.

Three quarters subtract one eighth is the same as six eighths.

Take one eighth, which gives me five eighths.

That brings us to our independent task.

Use the grid to describe the fraction of the flag that is in each colour.

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

Okay, as I superimpose the grid onto the flag, I can see that I've got four parts, which are green.

And I've got a total of four, eight, 12, 16, 20, 24.

So my green part is four out of 24.

And that was four out of 24, so I can simplify it to get me two twelfths.

And I can simplify it further to give me one sixth.

Now my white is exactly the same.

I've got one, two, three, four parts, but I've got two more here.

So I've got six parts out of the total of 24.

So I can simplify this, it becomes three out of 12.

I can simplify again, becomes one quarter.

My orange is the same as white, I have one, two, three, four, five, six.

So our orange will also be one quarter.

And finally I have blue, which is eight parts out of 24.

I can simplify that.

I could simplify it straight away by recognising that both eight and 24 are in my eight times tables.

So if I divide by eight, it gives me one third.

So to summarise, the green part of the flag is one sixth, the white part and the orange part are a quarter each.

And the blue part is one third.

Congratulations on completing your task.

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

Now before we go, please complete the quiz.

And so that brings us the end of today's lesson on adding and subtracting fractions with a common denominator, a really big well done for all the learning that you have achieved today.

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

Well, all that's left for me to say is thank you very much.

Take care, and enjoy your learning for the rest of today.