Lesson video

Hello, everybody.

My name is Mr. Kelsall and welcome to today's lesson on equivalent fractions.

Now, before we start, you're going to need a pen and a piece of paper.

Also, please try and find a quiet place somewhere that you won't 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.

Now pause the video, and when you're ready, let's begin.

Today's lesson is all about equivalent fractions.

We are going to by reminding ourselves about what a fraction is, we are then going to look at equivalent fractions, we're then going to look all the skills that you will need within converting between equivalent fractions.

And after that it's quiz time.

I've mentioned already, 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 a proper fraction, an improper fraction, and a mixed number fraction.

We'll start using the words equivalent fraction and simplify a fraction.

Reminder, a fraction is part of a whole.

The denominator is the number of parts that 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.

If I have 3/4, I could start by drawing the vinculum, I know that I've got three parts out of four parts selected.

So the fraction is the part of a whole, the denominator is four, it has been split into four parts, the numerator is three, there are three parts selected.

So have a look at these two shapes.

How can we show that these are equal parts? Pause the video and when you're ready, press play to continue.

So with the first one it looks a bit like the letter H, if I just go over some of the lines and emphasise the lines.

Now at this point, I split this fraction into eight equal parts.

I know that my first part has two parts shaded, my next part also has two parts shaded, the part at the top also two parts shaded, and the part at the bottom also has two parts shaded.

So I've shown that each of this part of the shape, there are two parts for each one.

And this proves that the shape has equal parts.

Now, for shape number two, imagine this is a piece of squared paper, and if you want to get a piece of squared paper, you can do, and I'm going to fold it exactly in half.

I know my top half and my bottom half are equal sizes.

Now my top half, I'm going to split into half again, so I know that this part is 1/4, and I know this part is 1/4 I'm then going to look at my bottom half and instead of folding it horizontally, I'm going to fold it diagonally, but I've still folded in it exactly in half.

And you can prove this, if you have a piece of squared paper, fold it once, fold this this diagonal shape, rip it into two parts and put the triangles next to each other and you'll find that they're the same size.

So this triangle is half of a half and this triangle is half of a half, so these are both quarters.

So I've got 1/4, 1/4, 1/4, 1/4.

So I know that this shape has been split into four equal parts.

Coming back to those keywords again, and say these with me, if you can.

I know that a fraction is a part of the hole, I know the denominator is the number of parts the whole is split into.

And the numerator is the number of parts of the whole.

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

And I've got three things I need to remind myself of, a proper fraction is where the numerator is less than the denominator, an improper fraction is where the numerator is greater than the denominator and a mixed number fraction is where you've got a whole and a fraction together.

So now we look at these new terms, an equivalent fraction, and it's just a fraction that represents the same number and simplifying a fraction, which is to reduce the numerator and the denominator.

Let's look at some examples.

If I draw myself a shape, I split the shape into two parts.

I know I have halves at the moment and I'm going to select one of these two parts.

So I know my shape is 1/2.

However, if I decide I want to split my shape again, I'd now split my shape into four parts and two of these parts have been selected.

Therefore, I can say that 1/2 is an equivalent fraction to 2/4.

In the same way I can talk about simplifying a fraction, so let's take another shape.

Let's say I have this shape have been split into thirds and then half it, so I've got sixths, So I know this shape is sixths.

I'm going to shade four of the six parts, so I have 4/6.

I want to know what this is equivalent to and I'm going to reduce the numerator and the denominator.

Let's imagine that the middle line doesn't exist and I just have my shape and now it's split into three parts and I've got one part shaded and another part shaded.

So I've got two parts out of three parts shaded.

So I can say that 4/6 is equivalent to 2/3 and I've just simplified 4/6 to give me 2/3 I've reduced the numerator and the denominator.

Take a moment to have a look at these fractions.

How many equal parts are there? Can you represent these as a fraction? And how many different equivalent fractions can you write? Pause the video and when you're ready, press play to continue.

I know that my first fraction has been split into four parts and one of these four parts has been selected, I know my second fraction has been split into eight parts and two of these parts have been selected.

I know my final fraction has been split into four, eight, 12, 16 parts, and four of these parts have been selected.

I can say that 1/4 is equivalent to 2/8 and that is equivalent to 4/16.

I could also say that I want to reduce 4/16 to give me 2/8 and I want to reduce or simplify 2/8 to give me 1/4.

I can also say that 1/4 is equivalent to 4/16 and I can say, I want to simplify 4/16 to give me 1/4.

Again, take a moment to pause the video, have a look at the shape, ask yourself a question.

How many equal parts are there? And then can you represent this as a fraction? And then once you've done that ask yourself, how many equivalent fractions can you write? So I'll start you off, I'm going to say I would like this part shading.

Okay.

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

Okay.

So first of all, if I look at this shape and I make it into equal parts, I know that I have four equal parts and I've got one of those four parts shaded.

However, I could make it into a different equivalent fraction by splitting it along these lines.

I now have four, eight, 12, 16.

I have 16 parts in total and I have four of these parts shaded.

If I count them further and I split them again, I want to split all of the squares into triangles, and that involves splitting them into two.

I now have 32 parts and I have eight of those 32 parts shaded.

So I can say 1/4 is equivalent to 4/16 is equivalent to 8/32.

I could also say, I'm going to simplify 4/16 to give me 1/4 or I could simplify 8/32 to give me 1/4.

And this brings us onto our new learning for today.

In front of you, you have a series of cards.

What I would like you to do is group these fractions look for fractions which are equivalent, some you'll spot straight away, some you'll have to think about, pause the video and when you're ready, press play to continue.

And here are the answers.

Okay.

Moving on to our develop learning for today.

Look at these equivalent fractions.

How many equal parts are there? Can you represent these as a fraction? And can you simplify this? Pause the video and press play when you're ready.

The answers are on the screen, and I can see that all of these fractions are equivalent to 1/4.

I can simplify all of them apart from the circles, which is already 1/4, so I can't simplify it further.

Okay.

We're going to look at five different skills that you may need when you are finding equivalent fractions.

The first one is when you have a missing numerator.

Now, if I have the fraction of 2/3 and I say that is equivalent to something ninths, I need to find out what the missing numerator is here.

Now, I need to eventually be able to do this mentally.

But for the moment, I can just draw this out as a picture.

So I've got 1/3, 2/3, I can then split that into ninths and I can say I've got one, two, three, four, five, six ninths.

Now that's if you do draw the picture, if you start thinking, how can I do it mentally? How do I get from three to nine? Well, I can multiply it by three.

How do I go from two to six? I multiply it by three.

This is where I want to find a missing numerator.

Pause the video and have a go at the questions which are on the screen.

Okay.

I know that if I multiply 4 by 2, it gives me 8.

So 3 multiply by 2 gives me 6.

So 3/4 is equivalent to 6/8.

I know that to get from two to 10, I multiply by five.

So 1 multiplied by 5 gives me 5.

So I know that 1/2 is equivalent to 10.

Second skill is to find a missing denominator, so if I start with let's do 3/4 is equivalent to nine over something.

This time I'm going to use my mental method first to see if that helps me and I'll check it with a picture.

I know to get from three to nine, I multiply by three.

So 4 times 3 gives me 12.

I think that 3/4 is equivalent to 9/12, lets draw the opposite picture and see if it makes sense.

So I'm going to take my shape, I'll split it into four equal parts and I've got one part, two part, three parts shaded.

I'm then going to split this by three and ask myself, how many do I have now? I've got one, two, three, four, five, six, seven, eight, nine parts out of 12.

So this is correct.

Okay.

There are few questions on the screen for you to have a go at, pause the video and when you're ready, press play to continue.

And your answers are on the screen.

I know that 3/5 is equivalent to 9/15 and 4/7 is equal to 8/14.

The skill number three is to find a missing numerator and a missing denominator.

Before I present an example here, I can see 3/7 is equivalent to six somethings and something twenty-eighths, pause the video, have a go, when you're ready, press play to continue.

So I know to get from three to six, I multiply by two.

So to get from seven, I multiply by two to get 14.

I'm then going one step further because I'm now going to 14 to 28, which I know is multiplied by two.

So 6 multiplied by 2 it gives me 12.

I've used basically the same procedure, but I've used it now to find the missing denominator and then the missing numerator.

There are two questions on the screen, have a look, have a go, pause the video and when you're ready for the answers, press play to continue.

I know 2/3 is equivalent to 6/9 because I'm multiplying by three and 6/9 is equivalent to 12/18 cause I'm multiplying by two, 1/5 is equivalent to 4/20 because I'm multiplying by four, and 4/20 is equivalent to 20/100 because I'm multiplying by five.

Skill number four is simplifying a fraction.

So I need to take these fractions and I need to make them simpler than what they are.

So my first fraction is 18/20, I know that 18 and 20 are both in my two-times tables.

So I could divide these by two, so 18 divided by 2 is 9, 20 divided by 2 is 10.

So I've simplified 18/20 to become 9/10.

For my next question, 12/15 isn't in our two-times tables, 12 is but 15 isn't, so what times-tables are both of these in? I can spot they are in my three times table, so if I divide 12 by 3, it gives me 4.

15 by 3, gives me 5.

So 12/15, I can simplify to give me 4/5.

Your last one is 20/100.

Have a think, see if you can simplify this.

So I know that 20 and 100 in my 10 times tables, if I divide by 10, I get 2/10 and actually I've also noticed two and 10 are in my two times table, so I can divide again by two, which gives me 1/5.

There are three questions on the screen, pause the video, have a go, and when you're ready, press play to continue.

Sorry, 3/9 is equivalent to 1/3, 8/12 is equivalent to 2/3 and 30/100 is equivalent to 3/10.

Well, our final skill is when we've got two steps that we need to make.

Now in this question, I've set 6/9 and I need to convert that into twelfths.

My problem is that 12 isn't in my nine times tables, so I have a bit of a problem.

So I'm thinking, how do I get from 6/9 to something twelfths? It means I need to take two steps, I need to recognise that 6/9 is actually the same as 2/3, and once I've recognised that, I can make the jump from third to twelfths and I can multiply it by four.

So 3 multiplied by 4 is 12, 2 multiply by 4 is 8.

So I can say 6/9 is equivalent to 2/3, and 2/3 is equivalent to 8/12, so 6/9 equivalent to 8/12.

Close the video, have a go at the next question and when you're ready, press play to continue.

Okay.

I know 4/10, I can simplify it to give me 2/5, and once I'm in fifths, I can recognise that five to 15, I multiply by three.

So 2 times 3 gives me 6.

So I know 2/5 is equal to 6/15.

So these are the five skills that you are looking at when you're looking at equivalent fractions, a missing numerator, a missing denominator, a question where both are missing, some way you have to simplify it and some way you have to do more than one step.

Now it's the time for your independent task for today.

Have a look at this fraction wall, what equivalent fractions can you find? Try and set yourself some questions, try and find equivalent fractions.

When you're ready, close the video, press play to continue.

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.

Now before we go, please complete the quiz.

That brings us to the end of today's lesson on equivalent fractions.

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

Now, before you finish, perhaps quickly, just look back at your notes and try to identify the most important parts of your learning from today.

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

Take care and enjoy the rest of your learning today.