Lesson video

Hi everyone, my name is Ms. Ku.

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 keywords and maybe some keywords 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.

And 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 keyword equivalent.

Two fractions are equivalent if they have the same value.

For example, 1/2 is equal to 2/4.

2/4 is equivalent to 1/2.

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 3/7.

So 3/7 is not equivalent to 1/5.

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

The first part, we'll be using bar models and number lines.

And the second part, we'll 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 is 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 12/20.

12/20 is exactly the same 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 an infinite number of equivalent fractions.

They're 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 would you 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 1/2 is.

So hopefully you can see it's right here.

The value of 1/2 is indicated with this arrow.

Now what I'm gonna do is draw an arrow indicating 2/4.

So same again, I'm using my number line from 0 to 1.

I've split my number line in 2/4 and 2/4 is right here, it's still 1/2.

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 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 four equal sections.

Now the second number line has broken into eight equal sections.

So that means we have 2/8 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 1/4 is identified as 3/12.

3/4 is identified as 9/12.

Well done if 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 2/3.

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 2.

Question 2 shows a bar that Sam has drawn 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 and can you explain why? Well done, so let's move on to Question 3.

Andeep says 1/2 of this diagram is shaded.

Is he correct? And 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 1, 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 are shaded.

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

So I've decided to subdivide this way.

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

And for 12/18, 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've got this one right.

And if you subdivided 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 2/9 is a completely different length to the bar using 1/7.

Great work if you got this one right.

For Question 3, Andeep says 1/2 of this diagram is shaded and we have to show a working out on our diagram to identify if he's correct.

Well, 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 part, and I can see 15 out of 25 is shaded.

So that means Andeep 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 over 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 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 over 3 multiplied by 4, which same again, is 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 gonna look at my 2/3 and we're still gonna 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 gonna 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 2.

5 multiplied by something has to give me the 10.

Well, I know it's 2.

This works perfectly because we know 4/5 multiplied by 1 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 a 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 2 multiplied by what? Over 7 multiplied by what? Giving us an equivalent fraction of 8 over what? For B, 7/9 is equal to 7 times what? Over 9 times what? Is equal to something over 90.

See if 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 gotta be 10/10.

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

Well done if you've 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 2/7 is equivalent to 8/28? Well it's got to be 2 multiplied by 4 over 7 multiplied by 4.

Next, we have the working out of 5 times 5 over 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.

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

Well done, so 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.

1/3 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 1/2 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.

See if 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? And 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 1, can you fill in the number line, 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 multiplied 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, you might notice we multiplied something by 3 to give 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 1/4? Well, you have 1/4, 2/8, 3/12, 4/16, and 5/20.

Well done if you got that one right.

For Question 4, 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 our working out.

Well, the multiplication of 1 is illustrated by the 3/3.

So 2/3 multiplied by 3/3 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, or multiplying by 1.

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

And remember the method of multiplying by 1 is the most effective and saves time.

A huge well done.

It was great learning with you.