Lesson video

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Hello, I'm Mr. Langton and in this lesson we're going to review adding and subtracting fractions.

You're going to need something to write with and something to write on.

Then I want you to find a quiet space with no distractions and when you're ready, we'll start.

We'll begin with the try this activity.

Use the number cards to try and complete the addition frame in as many ways as you can.

If you're feeling really confident, then see if you can do this without using the same card more than once.

I'm going to pause the video and let you have a go.

When you're ready, unpause it and we'll go through it.

You can start in three, two, one.

So how did you get on? I've come up with a few answers that we can go through now.

Firstly, if both the denominators are 12, there's quite a few options that you can go with.

I went with five twelfths and two twelfths, that makes seven twelfths.

Now instead of five and two, I could've had six and one, or I could've had one and six, I could've had two and five, or I could've had three and four and four and three, so quite a few options there.

Now in both cases, I've got the same denominator so it's a good answer, but it's not the best one that I could find.

Now I did come up with one for different denominators if I work with thirds and quarters, I found that one third add one quarter will be seven twelfths and the reason for that, if I turn my thirds into twelfths.

One third is equivalent to four twelfths and one quarter is equivalent to three twelfths so when I add those together I get seven twelfths.

I was quite proud of myself but once again, this time my numerators are the same so I've not used four different cards.

I then started thinking, if I compared what I'd got here, and I thought hang on a minute, two twelfths is the same as one sixth, isn't it? And so I can have five twelfths add one sixth.

That gives me seven twelfths and I've used four different cards, really pleased with myself there.

I've just got to thinking, could I do something similar with this last one? Is there anything here that I could do? So I started thinking and said well, one third is the same as two sixths and I hadn't used two or six in the other one, so I can keep that as a quarter.

Two sixths add a quarter, that'll work.

There are other ones as well, maybe you got them, but there's some answers you can go with.

I want to review adding and subtracting fractions now just to make sure that you're okay with it.

I know you've done it before, but it's always good to do a review.

Looking at the first question, seven eighths add three quarters.

If we're going to add or subtract fractions, we always need to make sure we start off with a common denominator.

So I'm looking at my eight and my four and the lowest common denominator would be eight so I'm going to rewrite both fractions so that they're eighths.

Now seven eighths is already in eighths, that's useful, I don't need to change that one.

Three quarters, if I want to change quarters into eighths, I need to multiply the denominator and the numerator by two which gives me six eighths.

Now if I add those together now, seven eighths and six eighths is 13 eighths.

And there we go, I've added them together.

Now we don't always like having top heavy fractions so sometimes it's nice to change them into mixed numbers.

The way that I like to do that is treat it as a division, fractions are divisions.

We're going to do 13 divided by eight.

How many times does eight go into 13? It goes in once with a remainder of five so 13 over eight is one whole one with five left over and because we're dividing by eight, we're working in eighths, it'll be one and five eighths.

Let's look at the second one.

Seven eighths take away three fifths.

We going to need a common denominator and it's got to be a number that's in the eight times table and the five times table.

And the lowest common multiple of eight and five, the lowest number in both those times tables is going to be 40.

Now to turn eighths into fortieths, I need to multiply by five so I need to do the same to my numerator which is going to give me 35 over 40.

To turn my fifths into fortieths I need to multiply by eight.

Multiply that one by eight, three eighths, and 24.

And now I can subtract them.

35 take away 24 is 11 over 40.

I can't simplify it anymore, there's no number that goes into 11 and 40 so I'm done.

Now let's look at the last one.

Starting with a mixed number can be tricky.

Sometimes you can ignore it and just work out the fractions separately and then put them into number in the end, but it doesn't always work out, you need to be quite careful when you do that.

So I like to start off by making my mixed number into an improper fraction.

So two and one third, I've got two whole ones and a third.

Now if I'm working in thirds, let's draw a diagram over here, if I work in thirds, that's one whole one isn't it? So if I've got two whole ones.

That's six thirds.

And of course I've got two and a third so altogether two and a third is seven thirds and I'm adding on two fifths.

So now I need a common denominator.

The lowest common multiple of three and five, so the smallest number that's in both those times tables is going to be 15.

So let's change each of these fractions into fifteenths.

So 15 goes into three five times, I need to multiply my numerator and my denominator by five which give me 35 over 15.

And to get from five to 15, going in three times, I need to multiply by three, it gives me six fifteenths, which altogether, if I add them together, is 41 fifteenths.

And once again, let's change it back into a mixed number.

So I'm going to do my division.

41 divided by 15.

How many does 41, sorry, how many times does 15 go into 41? 15, 30, it's going to go twice which is 30 with 11 left over, so two remainder 11.

So that's going to be two whole ones and 11 fifteenths leftover, don't forget we're working in fifteenths.

Okay, it's your turn to have a go now.

Pause the video and have a go at the questions.

When you're done, unpause it and we'll go through the answers together.

Good luck.

So how did you get on? Here are the answers, have a look and compare them with yours.

Some of my fractions are simplified so you might have got slightly different answers so do just check that they're equivalent and of course I've made them into mixed numbers where you might have left them top heavy.

The magic square was a little bit sneaky because I didn't think to add up the three fractions first, I was presumed that they were going to add up to make a whole one and so I started subtracting from one and that didn't work out for me so I had to have another look.

Finally, we've got the explore activity.

Use the number cards to complete the addition and subtraction frames in as many ways as you can.

If you're feeling really confident, see if you can do it without using the same number more than once.

I'm going to be honest with you, it's really hard and if you're going to be able to manage that, you might want to put on your thinking cap first.

Pause it and have a go.

Three, two, one.

Okay, let's discuss a couple of ideas.

I'm going to keep my thinking hat on, it's quite tough.

If we use the same denominators, I'm sure you can find lots of numbers that'll add up to make 13 so we can make it out of 12 for each one and let's just see, just for example, what if we make that one three and let's make that one four, that makes seven so we need another six don't we, so that works.

Three twelfths add four twelfths add six twelfths.

That's going to make 13 twelfths so we've got an answer that we can use, that's great.

Over here to make one twelfth, so let's make them twelfths again.

And some numbers we're going to subtract to make one twelfth so we could have, well four take away three can't we? So that works.

And with my thinking hat on, I was wondering, is there a way to do it without? So I was having a look and I thought, well actually, four twelfths is a third.

I'll write that in a different colour, that's one third.

Now we've used the three already there but can we change three twelfths? Three twelfths would be a quarter, rub that out let's go for blue this time, one quarter, so I'm almost there but I've used one twice so I need to think of something different there.

One third is the same as two sixths so that's no good.

I've got it, I've got it, are you ready? Let's, so it's going to be, let's change that quarter to two eighths.

One quarter is the same as two eighths.

Sorry, I need my pen.

Two eighths and there we have it, six completely different digits.

There's the three fractions that add up to make 13 over 12.

Finally, can we do the same thing over here on the right? We've used 12 in both of them, can one of them simplify? We could make, I don't think that's going to work is it but I do know that that's the same as a third and that's the same as a quarter so I'm not there yet but I know that a quarter is the same as two eighths and that is a possible solution, yep.

So once again, we got there.

How did you get on? Did you manage to get any of these?.