Lesson video

Hello, I'm Mr Coward, and welcome to today's lesson on equivalent fractions.

For today's lesson all you'll need is a pen and paper or something to write on and with.

If you could please take a moment to clear away any distractions including turning off any notifications.

And if you can try and find a quiet space to work where you won't be disturbed.

Okay, when you ready, let's begin.

Okay, so time for the try this task.

Now here we have a fraction wall.

Each row is labelled with a different fraction.

So I have a whole, halves, thirds, quarters, fifths, et cetera.

Now your task is to fill in these blanks here using the equivalent fractions of the shaded parts.

But then also to find other equivalent fractions.

So I'd like you to pause the video and have a go.

Pause in three, two, one.

Okay, welcome back.

Here are my answers.

Now, can you see how we've got a half? Well, that is the same length as three six.

So they are equal.

A third that is the same length as three ninths.

So they are equal.

Now this is tens and two, sorry, this is tens and four of them are equal to two fifths.

They are the same length, so they have the same value, so they are equal.

And we could have had lots of others.

We could have had two six, which is the same as a third.

We could have had four eights, which is the same as a half.

We could have had so many different ones.

So hopefully you found quite a few in addition to these three here.

Okay when fractions have the same value, but are written with different numerators and denominators, they are equivalent fractions.

Can you see the shape here? Can you see here the area of the shaded part? And that is equal to the area of the shaded part here and the area of the shaded part here.

It has the same value.

But this one has been split up into a different number of equal pieces.

Here t's three equal pieces.

So we have a three in the denominator.

Whereas here we have 12 equal pieces.

So we are going to have 12 in the denominator.

Okay, now we've got four pieces shed this time, not three.

So our count of number of shared pieces is four.

But these values are the same, the same area shaded.

So we said that one third and four twelves are equivalent fractions.

Now what's obviously we're not always going to get the diagram.

And one of the things to note is that when we don't get the diagram is we have this proportional relationship that the numerator, sorry, the denominator is three times bigger than the numerator.

And here we have the same proportional relationship.

The denominator is three times bigger than our numerator.

And here where we have the same proportion of the shaded.

So we're going to have the same proportion between our numerator and denominator.

And what is it? Well, it's nine equal pieces and three of them are shaded.

So three ninths.

So this proportional relationship between the numerator and the denominator is one of the things that makes them equivalent.

Okay, so I'd just like you to pause the video and have a go at filling in the blanks.

Pause in three, two, one.

Okay, welcome back.

Here are my answers.

Now for the last one there's many possible answers.

So those are just examples.

So if you didn't get the same, that's fine.

But as long as you have the same proportion, then that's okay.

Okay, so for this exercise, we're going to fill in the blanks.

Now I've already mentioned that one of the ways that we can find equivalent fractions, is using a proportional relationship between the numerator and the denominator.

But that's not of this in this question.

So another way we can do it, is by going across comparing denominator with denominator.

Now this has got four times bigger.

So our numerator must also get four times bigger.

On what this does is that keeps the same proportion.

So multiplying by the numerator and the denominator by the same thing keeps the same proportion.

So if I was to work this out, what I have to times by that would be 1.

6 recurring, as it was over here at 1.

6 recurring.

So it's kept the same proportion.

So sometimes it's easier to compare denominators and numerators as it is to compare numerator and denominator.

So I'd like you to have a go at this, okay? So I want you to compare the denominators and see if you can work out what the missing number is.

You may need to pause the video.

Okay, so this is five times bigger.

So our numerator is five times bigger.

Okay, next one.

How is this question different? Well, this time we don't know our denominator.

So what I can do is I have to work out what's the multiplicative relationship to get from 30 to 10.

And you can do divide by three, or you can think of it as times by a third.

They're the same thing it doesn't matter.

So just say, we're going with the divide by three, we divide by three and that gets us to 10.

So what must I do on here to keep the same proportion between my denominator and my numerator? I must also divide by three, okay? And you can see now you can see quite clearly here, that 30 doubled up is 60.

So the denominator is two times bigger than the numerator.

And here we can see that we've got the same thing.

The denominator is two times bigger than the numerator.

Okay, now it's probably easiest if you compared the numerators for this example, so have a go and see if you can work out the missing number.

Pause the video in three, two, one.

Okay, welcome back.

Now, going this way.

That's four times bigger.

So going backwards, going there to there we dividing by four.

So going from here to here, we are dividing by four.

16 divided by four is four.

So here is my fraction.

And you can say that this is 2.

5 times bigger.

And that if you check that that is actually 2.

5 times bigger.

So they stayed in the same proportion.

So they are equivalent.

Okay.

now this one, well, it's not easy to see how you get from 33 to nine, or at least I don't think it is.

This is easier going down that way.

We multiply by three.

So going the opposite where going upwards, we divide up by three.

Numerator is three times smaller than our denominator.

So on this one, our numerator must also be three times smaller than the denominator.

Nine divided by three, three.

Okay, so this time we've worked up and down, rather than going across.

So how about you to have a go at this? Pause the video in three, two, one.

Okay, so hopefully you saw that that is divided by two it's half the size so we divide by two here and we get the answer of 15.

Okay, really well done if you've got those correct.

Okay, so now it's time for the independent task.

So I would like you to pause the video to complete your task and resume once you've finished.

Okay, welcome back.

Here are my answers.

You may need to pause the video to mark your work.

Okay, and all that's left for today is the explore task.

So what I want you to do is I want you to use these digits here, and you're only allowed to use each one once, and you have to place them in the numerator and denominator of these two fractions, such that they are equal to each other.

And your challenge is, how many different sets of equivalent fractions can you find? So pause the video to complete your task, resume once you've finished.

Okay, ad here are some possible answers.

Now there may be more of answers than this, but these are just some of the ones that I found.

So well done if you got these, and well done if you got all those that I don't have here.

Okay, and that is all for this lesson.

Thank you very much for your hard work.

And I look forward to seeing you in the next lesson.

Thank you.