Lesson video

Hi everyone, my name is Miss Koo.

I hope you enjoy the lesson today and I'm really happy you've chosen to learn with me.

There may be some easy, or hard parts of the lesson but don't worry, I am here to help.

You'll also come across some new key words and maybe some key words you've already come across before.

I do hope you'll like the lesson, so let's make a start.

In today's lesson from the unit comparing and ordering fractions and decimals with positive and negative numbers, we'll be using the identity property of multiplication and division.

By the end of the lesson, you'll be able to use the fact that 1 can be written in the form of n/n and vice versa.

Now, we're gonna look at this key word equivalent.

Two fractions are equivalent if they have the same value.

For example, a half is equal to 2/4.

2/4 is equivalent to half.

4/5 is equal to 40/50.

In other words, 40/50 is equivalent to 4/5.

A non-example would be 1/5.

1/5 is not the same value as 3 sevenths.

So, 3 sevenths is not equivalent to 1/5.

Today's lesson will be broken down into two parts.

The first part will be using bar models and number lines.

And the second part will be looking at the property of multiplication.

So, let's have a look at the first part using bar models and number lines.

Now two fractions are equivalent if they have the same value.

So, let's look at some equivalent fractions using bars to show that they are the same value.

So, for example, what fraction do you think we have here? Hopefully, you can spot it's 3/5.

Now what I'm going to do is divide each part by 2.

What do you think we have? If I divide each part by 2, you can see the fraction is now 6/10.

6/10 are still exactly the same as 3/5.

Now, with this bar, I'm going to divide each part again by 2.

What do you think we have? Well, if I divide each part by 2, I have 12/12.

12/12 is exactly the same as 6/10, is exactly the same as 3/5.

They all have the same value.

All we've done is write an equivalent fraction.

So, all of these are equivalent and there are an infinite number of equivalent fractions.

They are equivalent because we have simply subdivided each equal part.

And that's important to remember.

So, what I'm going to do is show a fraction that Aisha has shaded.

Aisha shaded 3/4 of this diagram.

So, what I want you to do is show using dividing lines to show the subdivision of how she can make these equivalent fractions.

What do you think we need to do to 3/4 to make it equivalent to 6/8? What do you think we have to do to the diagram 3/4 to make it equivalent to 9/12? See if we can subdivide using lines.

Well done.

Well remember you have to subdivide so we have equal parts.

I've chosen to subdivide my diagram to give this, so we have 6/8.

And I've chosen to subdivide my second diagram like this, so you can see we have 9/12.

But overall, you can still see we have 3/4 of our diagram shaded.

Now, let's look at some equivalent fractions using number lines and show they are the same value.

So, I'm going to start by drawing an arrow indicating where a 1/2 is.

So, hopefully you can see it's right here.

The value of a half is indicated with this arrow.

Now, what I'm going to do is draw an arrow indicating 2/4.

So same again, I'm using my number line from zero to one.

I've split my number line in 2/4 and 2/4 is right here.

It's still a half.

Now using the same number line, I'm going to identify 7/14.

So, I've split my number line into 14 equal sections, and I've identified 7/14.

You can see they are all exactly the same.

All of them represent 1/2.

Now these are equivalent because we've simply subdivided each equal part.

So, now let's have a look at a check.

What are the equivalent fractions to 1/4, and 3/4 on these number lines? See if you can identify what these equivalent fractions would be using these number lines.

So, you can give it a go and press pause if you need more time.

Great work! Well, you can see 1/4 and 3/4 has been plotted because we've broken our first number line into 4 equal sections.

Now, the second number line has broken into 8 equal sections.

So that means we have 2 eighths and 6/8, but they are the same value as 1/4 and 3/4.

The third number line splits it into 12 equal sections.

And a 1/4 is identified as 3/12, three quarters is identified as 9/12.

Well done, you got this one right.

Now, let's move on to your task.

By subdividing, I want you to create fractions which are equivalent to two thirds.

So, remember when you subdivide, ensure that you are dividing so you have equal parts.

See if you can give this one a go, and press pause if you need.

Well done.

So, let's move on to question two.

Question two shows a bar that Sam has drew.

And he's drawn this bar to show 2/9.

Now Sam then drew another bar underneath this to show 1/7.

And Sam then said, well, it shows that 2/9 is equivalent to 1/7.

Is Sam correct? Can you explain why? Well done, so let's move on to question 3.

Andeep says a half of this diagram is shaded.

Is he correct? I want you to show your working out on the diagram.

Great work.

So, let's see how you got on with these answers.

Well, for question one, there are lots of different ways which you could have subdivided to show 2/3.

So, I'm going to start with 4/6.

Well, we need to have six equal parts, and four of them will be shaded.

So that means I've used this line to represent our 4/6.

For 8/12, we need to have 12 equal parts.

So, I've decided to use these lines to subdivide so I have 12 equal parts, thus giving me 8/12 of shaded.

For 6/9, I need to have 9 equal parts.

So, I've decided to subdivide this way.

So, you can see I have 6 out of 9 equal parts.

And for 1218, I need to make 18 equal parts.

So, I've decided to subdivide like this, giving me 12 out of 18 shaded.

Very well done if you got this one right, and if you subdivide it in a different way, but you have equal parts that's absolutely fine too.

Well done.

Now for question 2 we had to identify is Sam correct and explain.

Well hopefully you can spot he's incorrect because the bar that represents the whole must be the same length in order to compare fractions in this way.

And you'll notice the bar used for two ninths is a completely different length to the bar using 1/7.

Great work if you got this one right.

For question three.

Andeep says a half of this diagram is shaded.

And we have to show working out on our diagram to identify if he's correct.

Oh, remember, splitting into equal parts really does help.

Or you may have split it into equal areas.

For here, I've split it into equal parts so I can count.

And now splitting it into equal parts, and I can see 15 out of 25 is shaded.

So that means and deep is incorrect because 15 out of 25 is not equivalent to 1/2.

Very good if you got this one right.

Great work everybody! So, let's move on to the second part of our lesson which is property of multiplication.

Now bar models and number lines are a really good visual way to see equivalent fractions, but they do take time to construct.

So, what we're going to do is look at some equivalent fractions using multiplication of 1 to show that they are the same value.

And this method is more effective and quicker because it uses the concept that we know any number multiplied by itself is always 1.

For example, we know any number multiplied by itself is always 1.

So, if we have 2/3 multiplied by 1, well, that would be 2/3.

We also know any fraction can be written as 1.

So, 2/2 is 1.

5/5 is equal to 1.

11/11 is equal to 1.

So therefore, we can combine these two facts to make an equivalent fraction.

For example, 2/3 multiplied by 1, well we know that's 2/3.

I'm going to change my 1 into 4/4.

So, if I do 2/3 multiplied by 4/4, I do know it has to be equal to 2/3, because 4/4 is 1.

Multiplying these two fractions, it's the same as 2 multiplied by 4/3 multiplied by 4, which is the same again, it's still 2/3.

So, this means 8/12 is still 2/3.

And all I've done is choose 4/4 as an equivalent fraction to 1.

And what we've done is we've made an equivalent fraction.

8/12 is the same as 2/3.

Just a reminder, we can use any fraction to be 1.

So, I'm still going to look at my 2/3 and we're still going to multiply by 1 to give me 2/3.

But I'm going to choose 1 to be 11/11.

So, I know 2/3 multiplied by 11/11 is still 2/3.

Working this out, it's the same as 2 times 11 over 3 times 11 is still 2/3.

So therefore, we know we have another pair of equivalent fractions.

22/33 is still exactly the same as 2/3.

So, what I'm going to do I'm going to do this question, and then I want you to give the second question a go.

We're going to fill in the gaps to identify the equivalent fractions.

We're looking at 4/5.

So, 4/5 is equal to 4 multiplied by what over 5 multiplied by what to equal 8/10.

For b, 3/4 is equal to 3 multiplied by what over 4 multiplied by 5 equals 15 over what.

Well, for part a, I know 4 multiplied by something must give me that 8.

So that means I know it has to be two.

Five multiplied by something has to give me the 10.

Well, I know it's two.

This works perfectly because we know 4/5 multiplied by one will give 4/5.

Thus, we have an equivalent fraction whereby 4/5 is exactly the same as 8/10.

Now let's have a look at B.

3 times what is 15? So that means 4 times 5 is what? Well, hopefully, you can spot it's got to be 5, which we understand anyway because we know 5/5 is 1, thus giving us a new denominator of 20.

So, we now identified the equivalent fraction to have 3/4 to be 15/20.

A huge well done if you spotted that.

Now I want you to do is fill in the gaps to identify the equivalent fractions.

2/7 is equal to two multiplied by what? Over seven multiplied by watt, giving us an equivalent fraction of eight over watt.

For B, 7/9 is equal to seven times watt over nine times watt is equal to something over 90.

So, you can give it a go and press pause if you need more time.

Great work! So, let's see how you got on.

Well for A, hopefully you spotted it's got to be the multiplication of 4/4.

Therefore, giving us 8/28 is the equivalent fraction to 2/7.

For B, hopefully you spotted it's got to be 10/10.

so that means our equivalent fraction to 7/9 is 70/90.

Well done if you got that one right.

Now, what we're going to do is have a look at another check question and on this check question we've identified the fraction, some working out and then the equivalent fraction.

See if you can fill in the table to show the fraction working out and the equivalent fraction where there are gaps.

Press pause if you need more time.

Great work! So, let's see how you got on.

Well, the equivalent fraction to 3/4, when we know the working out is 3/4 multiplied by 3/3, is 9/12.

What's the working out to show the fraction 2 sevenths is equivalent to 8/28? Well, it's got to be 2 multiplied by 4/7 multiplied by 4.

Next, we have the working out of 5 times 5/6 times 5.

So that means we know the original fraction was 5/6 because we know the multiplication of 1 is represented as the 5/5, thus giving us the equivalent fraction of 25/30.

Well done if you got that one right.

Now let's have a look at another check question, and I want you to match the equivalent fractions.

So, you can give it a go and press pause if you need more time.

Well done.

Let's see how you got on.

Well, 12/54 is the same as 2/9.

Did you spot we multiplied 2/9 by 6/6? So, the multiplication of 1 is shown by the 6/6.

1 third is the same as 4/12.

So, the multiplication of 1 was 4/4.

20/40 is exactly the same as 1/2 because we multiplied 1 half by 20/20.

And 2/5 is exactly the same as 10/25.

So, we multiplied 2/5 by 5/5.

Really well done if you got this one right.

Now, let's have a look at your task.

Here, I want you to fill in the gap to show the fraction working out an equivalent fraction.

You can give it a go and press pause if you need more time.

Well done.

So, let's move on to question 2.

Question 2 shows a grid and all you're asked to do is to shade the equivalent fractions to 1/3 and this will reveal a picture.

So, remember there's an infinite number of equivalent fractions so this is a tough question.

See if you can shade in all those equivalent fractions to 1/3.

See if you can give it a go and press pause because you'll need more time.

Great work! So, let's move on to question 3.

Question 3 shows a 5 by 5 multiplication grid and Jacob uses it to help write the equivalent fractions to 2/5.

He sees 2/5 is the same as 4/10, which is the same as 6/15.

Now can you use the grid to find two more equivalent fractions to 2/5? For part B, can you use the grid to find equivalent fractions to 1/4? See if you can give it a go and press pause if you need more time.

Well done.

So, let's move on to our last question.

Question 4 states that 2/3 is equivalent to 6/9.

And using number lines, bar models and the multiplication of one, can you fill in the number lines, the working out and the bar model to show that 2/3 is equal to 6/9? See if you can give it a go and press pause if you need more time.

Great work! So, let's go through these answers.

For question 1, 4/9 is equivalent to 8/18.

So, what was our working out? Well, 4/9 multiplied by 2/2 was our working out.

For B, 7/10 multiplied by 4/4, well we know it had to be the 7/10, giving us the equivalent fraction of 28/40.

For C, well, we knew our equivalent fraction, so that means our simplified fraction must be 1/3.

That means we multiply by the 1, which is represented as 8/8.

For D, we've got some missing values here, but we know the numerator of one fraction is 12, and the denominator of the equivalent fraction is 33.

So, how do we work out our answer first? Well, to identify it, you might notice we multiplied something by 3 to get 33, so it had to be 11.

We also know the 3/3 would represent the 1, so now we can figure out the original simplified fraction is 12/11 with the equivalent fraction being 36/33.

For question 2, massive well done if you discovered this smiley face as our picture.

For question 3, using the grid did you find two more equivalent fractions? Well, hopefully you spotted 8/20 and 10/25.

Remember, there are an infinite number of equivalent fractions, but we were told to use the 5 by 5 multiplication grid.

And using this 5 by 5 multiplication grid, did you find other equivalent fractions to one quarter? Well, you have one quarter, two eighths, 3/12, four sixteenths and 5/20.

Well done, you got that one right.

For question four, we needed to show using bar models, working out or number lines, that 2/3 is the same as 6/9.

So, let's start with our number line first.

Here's 2/3.

Subdividing the second number line into ninths, we have 6/9.

This shows that 2/3 is equivalent to 6/9 using our number line.

Now, let's use our bar models.

Well, there's 2/3.

Remember, subdividing, so we're dividing each third into three equal parts identifies that we have 6/9.

Now let's show a working out.

Well, the multiplication of one is illustrated by the 3/3.

So, 2/3 multiplied by three over three is our 6/9.

A huge well done today.

We went through a lot of information.

So, in summary, two fractions are equivalent if they have the same value.

Here are some examples and a non-example.

And there are different ways to show equivalent fractions.

For example, number lines, bar models and multiplying by one.

It's important to remember there's an infinite number of equivalent fractions.

And remember, the method of multiplying by one is the most effective and saves time.

A huge well done, it was great learning with you.