Lesson video

In the first example, we know the denominator of the simplified fraction is five.

To get from 50 to five, I need to divide by 10.

But I also want to preserve the proportional relationship between the numerator and the denominator.

So I must also divide the numerator by 10.

When I divide 20 by 10, I get two.

Let's look at the next example.

Now, the denominator is missing.

So I'm looking at the proportional relationship between the two numerators.

How do I get from 14 to two? Yes, that's correct, I need to divide by seven.

So 49 divided by seven, is seven.

In the next two examples, we already have the simplified fraction, and we will now be working the other way, so we will need to multiply.

To get from seven to 56, I need to multiply by eight.

Therefore, I also need to multiply two by eight.

Two multiplied by eight? Yes, that's correct.

It's 16.

Now let's look at the last example.

I have one, I have to multiply one by nine, to get to nine.

So I also have to multiply five by nine.

So five times nine is 45.

Did you have a go at the challenge activity? Well done if you did, and don't worry, if you didn't, we're going to look at it together now.

Did you spot what's the same about all of these fractions? Yes.

For all these fractions, the numerator is the factor of the denominator.

This means we can simply simplify them all into unit fractions.

Shall we do this together now? Let's say this out loud.

Three is a factor of 18, three divided by three is one, 18 divided by three is six, the unit fraction is 1/6.

Next one.

Five is a factor of 20, five divided by five is one, 20 divided by five is four, the unit fraction is 1/4.

Next one.

Four is a factor of eight, four divided by four is one, and eight divided by four is two.

The unit fraction is 1/2.

Next one.

Two is a factor of 18, two divided by two is one, 18 divided by two is nine, the unit fraction is 1/9.

And the final two to go.

Four is a factor of 12, four divided by four is one, 12 divided by four is three, the unit fraction is 1/3.

And finally, 6/60.

Six is a factor of 60, six divided by six is one, 60 divided by six is 10, and the final unit fraction is 1/10.

I like this task because it shows us one reason why we go to the trouble of simplifying fractions.

Now these fractions are unit fractions, so we can compare them easily.

So remember, when we compare unit fractions, the greater the denominator, the smaller the fraction.

Can you see which ones would go first on the number line, and which one would go last? That's right.

1/10 is the smallest.

Imagine if we'd had to simplify 6/60.

That would have been very tricky to divide the number line into 60 intervals.

Here are the fractions in order from smallest to largest on the number line.

Were you right? Yes, so it confirms that 1/10 is the smallest, 1/9.

Can you predict which one would come next? Well done.

Yes, it is 1/6.

1/4, 1/3 and finally 1/2.

Well done.

I find that generalisation is really helpful.

So, sometimes simplifying fractions is useful because it helps us to make comparisons.

Another context in which we need to be able to express fractions in their simplest form is when we are calculating with fractions.

Let's first think about adding fractions.

You probably remember how to do this from year three or four but let's have a recap.

It was a while ago.

The first problem we're going to solve is about an apple.

I divide the apple into eight equal parts.

What fraction of the whole Apple, is one part? That's right, each part is 1/8 of the whole apple.

I eat 3/8 of the apple, my sister eats 2/8 of the apple.

I want to know how much of the apple we have eaten all together.

What can we draw to help us solve this? Perhaps we could draw a diagram like this.

What does the blue part represent? That's right, it's three 1/8 of the apple, which I ate.

What about the yellow part? Shall we say it together? The yellow part represents the two 1/8 of the apple which my sister ate.

So now we can see how much of the apple we have eaten all together.

Three 1/8, and two, 1/8 equals five 1/8.

Could we say it in a different way? We could say 3/8, and 2/8 equals 5/8.

Another way we could show this would be on a number line.

My number line is divided into eight equal parts, so each interval represents 1/8.

Here we have the three 1/8 I ate.

And then I need to add on the two 1/8 my sister ate.

We can see how much of the Apple has been eaten.

Five 1/8 which we can also say, as 5/8.

What equation or number sentence could you write to represent the story of the apple? Pause the video now and have a go at writing one down? Did you write an equation to represent the story about the apple? Is it the same as mine? What does the 3/8 represent? Let's say it together.

The 3/8 represents how much of the apple I ate.

What does the 2/8 represent? The 2/8 represents how much of the apple my sister ate.

What does the 5/8 represent? The 5/8 represents how much of the apple we ate all together.

What do you notice about the numbers in my equation? What stays the same? What changes? Yes, you're right.

The denominator stays the same.

It is always eight.

But the numerator is different for each of the fractions.

Why is this? Have a think.

What does the denominator represent? Remember, the denominator is the number of equal parts in a whole.

Here the denominator is always eight, because I divided the apple into eight equal parts.

That doesn't change.

I didn't cut it up into any more pieces, and I didn't stick any parts all together.

The number line may help you to visualise the calculation.

The numerator does change.

Can you say Why? The numerator is different because I didn't eat the same number of parts of the whole apple as my sister.

And all together we ate more parts than either one of us alone.

How could we put all of this together into one sentence to help us remember what to do when adding fractions? We could say when adding fractions with the same denominators, just add the numerators.

Shall we say all together? When adding fractions with the same denominators, just add the numerators.

Let's look at another problem.

A team of children are taking part in a relay race.

The team must complete all of the races legs within 60 minutes.

Anushka takes seven minutes to complete her leg.

Joel takes eight minutes to complete his leg.

What fraction of the available time have Anushka and Joel used up? What is the unit we are working in, for this question? We are working in 60ths.

So what is the calculation we need to do? Pause the video, and jot down an equation to represent the story.

7/60 plus 8/60 equals? Did you write down the same equation as me? Shall we say which each add end represents.

7/60 represents the time Anushka took run her leg.

8/60 represents the time Joel took to run his leg.

Now we need to find out how much time Anushka and Joel took all together.

How would we work this out? Can you remember our generalisation? When adding fractions with the same denominator, just add the numerators.

So the sum is 15/60.

What does that mean in this context? It means that Anushka and Joel have used up 15 of the 60 minutes available to their team.

Why do you think their team was given 60 minutes? Yes, well done.

60 minutes is one hour.

Sometimes we talk about 15 minutes, but I don't think we usually talk about 15/60, of an hour.

So sometimes we have to simplify a fraction, so that it makes more sense in its context.

I can see here that the numerator is a factor of the denominator.

If I divide both the numerator and the denominator by 15, I get the unit fraction.

Yes, 1/4.

It makes much more sense in the context of this story, to say that Anushka and Joel have taken 1/4 of an hour to complete their legs of the relay race.

Let's recap.

Sometimes it's useful to express fractions in their simplest form, because we're comparing them.

Sometimes we're calculating with fractions, so we express the fraction in its simplest form.

Because that makes most sense in that context.

At other times, we might be asked to do abstract calculations, ones that don't have a context.

When we are doing these kinds of calculations, we might be asked to give our answer in the simplest form.

For example, 3/10 plus 3/10.

Pause the video and have a go.

What did you do first? First, I remembered our generalisation and just added the numerators.

Did you get 6/10 as well? But did you remember to give the answer in its simplest form? If so, what did you do next? I am looking for the highest common factor of six and 10.

Yes, it's two.

I'm going to divide both the numerator and the denominator by two.

And that will give me 3/5 in my simplest form.

Are you ready to have a go on your own? First you'll need to solve these addition calculations.

You might like to draw a number line, or you might just use the generalisation to help you.

After solving the calculations, you need to check that the answer is in its simplest form.

If it's not, you will need to simplify using the method that we have been practising.

Pause the video now.

Did you have a go by yourself? I hope so.

Let's see how you got on.

Do you agree? We can simplify the sums of the first two equations, but 4/13 is already in its simplest form.

Here are some more equations for you to try at home.

The last one is a subtraction.

Perhaps you can write a generalisation for what we do when we are subtracting fractions.