Lesson video

Hello, I'm Mr. Canon.

We're going to continue learning about simplifying fractions.

Do you have a pencil and some paper? If not, pause the video, find them, and come back.

Here's some of the key words that you've been working with.

Can you remember what they mean? We're going to be using them again in this lesson.

So I'll be asking you later.

In the previous lesson, Miss Hughes left you with a couple of questions, she asked you about her puppy, Bentley.

She was wanting to know what his 45/60 of an hour.

Could you simplify it? And does using the highest common factor help.

Well, her puppy would have said, oh, that's easy, 45 minutes is 3/4 of an hour.

So that's obviously the simplest form, 3/4.

Did you find it by dividing by the highest common factor? What are the common factors? Well, there's one, three, five, and 15.

So the highest common factor was 15.

If we divide the numerator and the denominator both by 15, we get the simplest form don't we? Well done.

This here are the question that Miss Hughes left you with.

Can the fraction 6/15 be simplified? Remember, when we simplify fractions, we're trying to make the numerator and denominator the smallest possible, while keeping the proportion the same.

Where is the denominator? That's right, it's 15.

It's the number of equal parts.

Will we have a unit fraction? Oh, if we were able to simplify it to a unit fraction, then the numerator, would become one, because six divided by six is one, but we'll also need to divide the denominator by six.

Is 15 in the six times table? No 15 is not in the six times table, so we needed a different factor.

Think about your times tables.

We want to know the highest common factor of six and 15 Pause if you want some thinking time.

Have you found them? Did you get three? Three is a factor of six, because six is in the three times table.

And three is a factor of 15, because 15 is in the three times table.

To simplify 6/15, we need to divide both the numerator and denominator by three.

6/15 simplifies to 2/5 in its simplest form.

Let's see how multiplication square could help us.

You've seen an image like this in a previous lesson, I put a red circle around our denominator 15, and another ne around as numerator six.

They're both in the three times table.

So three is a factor with both six and 15.

The highlighted blue rows Show fractions that are equivalent to 6/15 along the blue rows are all the families of fractions that are equivalent.

In the first column, we see that by dividing both six and 15 by three gives us the simplest fraction, 2/5.

We can also show 6/15 on a number line between zero and one.

The whole is being divided into 15 equal parts.

So each equal parts is 1/15 is 6/15 on the number line.

We said that the highest common factor of six and 15 is three, because three is the largest number that is a factor of both six and 15.

So, if three is the highest common factor, if we mark every third interval, we've now divided the whole in a different way.

Look at the blue lines, one, two, three, four five equal parts.

Each equal parts is 1/5 of the whole 6/15 lines up with 2/5.

So 6/15 simplifies to 2/5.

Here's a generalisation that we can use.

A fraction can be simplified, when the numerator and denominator have a common factor other than one.

I'd like you to say it now.

Pause the video while you say it,.

Here's another that will help us.

To write a fraction, in its simplest form, divide both the numerator and denominator by the highest common factor.

Can you say it now, pause the video again? Where have you written the highest common factor? That's it, it's the number that we're dividing, both the numerator and denominator by.

Can you do this one? Pause the video while you write it on your paper and simplify.

Let's have a look.

There's how two children did their simplifying.

They use different methods from each other.

Simran, simplified the fraction.

She divided both the numerator and denominator by two, to get 4/6.

Then she divided the denominator and numerator by two again, and Simran has 2/3.

That's her simplified fraction.

Lastly, Simran chance that apart from one, there are no other factors of two and three that she could divide by.

So she knew that she'd found the simplest form.

Sam simplified the same fraction.

He divided both the numerator and denominator by four.

Sam also had 2/3 and it sees as his simplified fraction.

Lastly, Sam shows that apart from one, there are no other factors of two and three that he could divide by, so he also knew, that he had found the simplest form.

Well, it's the same about the two methods.

You're right, they both simplified the fraction to 2/3.

So what's different.

That's it, similar news, two steps.

Dividing both the numerator and denominator by two, twice.

Sam choose the highest common factor, so he only needed one step.

Did you chose one of these methods? Whose method was the most efficient? It was Sam's, Sam chose the highest common factor of eight and 12.

So he only needed one step.

Shall we have a look at how this looks on a number line again.

The whole is divided into 12 equal parts.

So each part is 1/12.

Is 8/12 on the number line? Now we said that the highest common factor of eight and 12 is four, because four is the largest number.

It is a factor with both eight and 12.

So four is the highest common factor.

If we mark off every fourth interval, we've divided the whole in a different way.

Look at the blue lines.

Now the whole is divided into one, two, three equal parts.

Each part is 1/3 of the whole.

8/12 lines up with one, 2/3.

So 8/12 simplifies to 2/3.

I'd like you to simplify this fraction, which times table for both 15 and 14.

What number are the both multiples on? Ask yourself this question.

What is the highest common factor of 15 and 40? There's 15/40 on the number line.

Pause the video if you think you can do it.

Carry on a bit further, if he wants a bit more help.

15 and 40 are both in the five times tables.

Five is the highest timetable that 15 and 40 are both in.

So the highest common factor of 15 and 40, is five.

We need to divide the numerator and denominator by the highest common factor, five.

40 divided by five is eight and 15 divided by five is three.

So 15/40 simplifies to 3/8.

Did you get it? Did you use the number line idea? Here on the number line, the whole is been divided into 40 equal parts.

So one part is 1/40 of the whole, the highest common factor is five.

So if we go every five intervals and mark on, with a blue line, there are now one, two, three, four, five, six, seven, eight equal parts, 15/40 lines up with 3/8.

Let's see, how multiplication square could help us again.

Put your red circle around our denominator 40 and our numerator, 15.

They're both in the five times table.

So five is a factor of both 50 and 40, The highlighted blue rows show Fractions that are equivalent to 15/40.

In the first column, we see that by dividing both 15 and 40 by five, gives us the simplest fraction, 3/8.

Which images are you finding the most helpful? So our final step, is to check whether we have the fraction in its simplest form.

Can you explain it? Oh, sure thing.

We can use this STEM sentence.

The fraction is in its simplest form because the only remaining common factor of hm and hm is hm.

You'll guess what numbers it was where I said hm.

Pause the video now to write it down or say it out loud.

Here we go then, let's say it together.

The fraction is in its simplest form, because the only remaining common factor of three and eight is one.

So this is our strategy for expressing a fraction in its simplest form efficiently.

First, identify the highest common factor of the numerator and denominator.

Then divide the numerator and denominator by the highest common factor.

Finally check that the fraction is in its simplest form because the only remaining common factor of the numerator and denominator is one.

You can come back to this slide, if you need to later.

Let's do some practise.

Ellen says that 6/18 will simplify to unit fraction.

Do we agree? If you have someone with you, discuss your ideas, and pause the video.

Hello again, do you agree with Ellen? Open the STEM sentence and write your ideas down.

Numerator six i or isn't a factor of the denominator 18.

So 6/18 will or will not simplify three unit fraction.

Pause the video while you write it down.

Did you agree with Ellen? I hope so, let's read the STEM sentence.

The numerator six is a factor of the denominator 18, So 6/18 will simplify to a unit fraction.

So 6/18 simplifies to one third because we divide the numerator and denominator both by six.

Here is another practise question.

Anna says that she has simplified 18/24 into its simplest form, do you agree? What do you think? If you have someone with you, discuss your ideas and pause the video.

Hello again.

Did you agree with Anna? Here's a STEM sentence.

Copy it out and write down your ideas.

It'll go along the lines of, Anna has or has not divided by the highest common factor.

So 9/12 is or is not the simplest form of 18/24.

Pause the video while you write it down.

Did you agree with Anna? She has simplified 18/24, but she didn't use the highest common factor.

So she Anna has not divided by the highest common factor.

So 9/12 is not the simplest form of 18/24.

So what is 18/24 expressed in its highest and its simplest form.

Can you do that? Remember to find the highest common factor first.

Pause the video, while you work out your answer.

Did you find the highest common factor is six, because six is a factor of 18 and 24? So 18/24 divides the numerator and denominator both by six, and we have three courses.

Did you get that, well done if you did.

So, the next time, I'd like you to express these fractions, in their simplest form by finding the highest common factor first.

You could rewind the video if you want to find the strategy.

And remember to check with the end, won't you? See your next time.