Lesson video

Onto lesson three of fractions.

Today we're working on finding equivalent fractions.

As always, make sure you're prepared.

Today, you'll need a pencil and a piece of paper, or an exercise book.

Pause the video now, and get your equipment together.

In today's lesson, we're going to find the equivalent fractions.

First of all, we'll explore the relationship between the numerator and denominator.

We'll find factors and reason about simplifying fractions, before you complete your independent task to practise what you've learned, and then a quiz, to test today's learning.

Visual for you now, from the learning in yesterday's lesson, write some equivalent fractions for the fraction 8/24ths.

Pause the video while you do so.

The key here was to do same thing to both the numerator and denominator.

You may have noticed that they both have a factor of two, therefore, they could be divided by two, which would give you 4/12ths.

8/24ths is equivalent to 4/12ths because both the same thing has been done to the numerators and the denominators.

You may also have noticed that eight and 24 have a common factor of eight, so they could both have been divided by eight to give you the fraction 1/3rd.

8/24ths is equivalent to 1/3rd because the relationship between the two numerators and the two denominators is the same.

Going the other way, there were many possibilities of what you could have done.

You're multiplying the numerator and denominator by the same number, so you could have multiplied by two, which gives you 16/48ths, 8/24ths is the equivalent to 16/48ths, or multiplied by 10, to give you 80/240ths, and so on.

The key is to have the same relationship between both numerators, and both denominators.

And yesterday's lesson, we focused on the relationship of the numerator and denominator between two fractions.

So here, the numerator of the second fraction is eight times greater than the numerator of the first fraction, one multiplied by eight, is equal to eight.

In the second fraction, the denominator is also eight times greater than the denominator in the first fraction, three times eight is equal to 24.

Therefore, these fractions are equivalent.

So that's looking at the relationships between two fractions.

Now we're going to explore the relationship of the numerator and denominator within the same fraction.

So the relationship between the numerator one, and the denominator three, is that the denominator is three times greater than the numerator, one times three is equal to three.

Now, is this relationship the same within 8/24ths? Which is an equivalent fraction of 1/3rd.

I can see that 24 is three times greater than eight.

Eight times three is 24.

So the relationship between the numerator and denominator within two equivalent fractions, is also equal.

Now it's your turn.

Pause the video and explore the relationships between the numerator and denominator within the fractions.

I've done the first one for you, so you are looking to add on the annotations that I've done in purple, to the other sets of equivalent fractions.

Is the relationship always the same? Pause the video now.

So you should have noticed that the relationship between the numerator and denominator within a fraction is the same when you are looking at equivalent fractions.

Two times six is 12, Eight times six is 48.

So here is our, equivalent fractions have the same relationship between the numerator and denominator, both between fractions, that's shown in pink, and within fractions, that's shown in purple.

Now we're going to work on finding factors, which helps us to simplify fractions.

Factors are numbers that we can multiply together to get another number.

When we find the factors of two or more numbers, and then see that some of them are the same, these are called common factors.

I like to use a factor bug to help me find those common factors.

And I always make sure that I work systematically when I draw my factor bug.

So I'm going to make a factor bug for the number eight, I always start off with one and the number as the antennae, one times eight equals eight.

And then I carry on with the legs, with the other factors, two times four equals eight.

And there are no more factors for eight.

Now let me draw a factor bug for 24.

Again, I start with the antennae, one times 24 is 24.

Two times 12 is 24.

Three times eight is 24.

And four times six is 24.

Now i need to look at both factor bugs and see what factors do they have in common? Well, they both have the common factor of one.

They both have the common factor two, and four, and also eight.

So these numbers have four common factors.

But I'm interested in the highest common factor, highest common factor.

Which of these is the highest factor that they have in common? Well, the highest common factor here is the number eight.

The reason I'm interested in the highest common factor, is because I want to see what is the greatest number that both the numerator and denominator can be divided by.

That means that I'm simplifying efficiently, rather than in stages.

So they can both be divided by eight.

Eight divided by eight is one, and 24 divided by eight is three.

So 8/24ths is equivalent to 1/3rd.

Let's do another one together.

I'm looking for the highest common factor between nine and 15.

So for nine, I have one times nine is nine.

Two is not factor of nine, but three is.

Now, this is slightly different, because three times three, is the same as three squared.

So if I'm squaring, but I don't write three and the three on the arms, I write it as the stinger.

So one times nine is nine, and three squared is nine.

Let me do my factor bug for 15, one times 15 is 15, two is not a factor, but three is.

Three, and five, three times five is 15.

Now let me look at the common factors, they both have the common factor of one, and they both have the common factor of three, there's no more common factors.

So the highest common factor is three.

These can both be divided by three in order to simplify them.

Nine divided by three is three, and five divided by three is 15.

So 9/15ths is equivalent to 3/15ths.

Now it's your turn.

Pause the video and create a factor bug for the numerator and denominator.

Find the highest common factor, and use it to simplify the fraction.

So you should have done a factor bug of 10, one times 10 is 10, and two times five is 10.

And one for 14.

One times 14 is 14, and two times seven is 14.

Our common factors are one and two, so the highest common factor is two.

I know therefore, that both the numerator and denominator can be divided by two, which gives me, 10 divided by two is five, 14 divided by two is seven.

5/7ths.

Now we're going to move on to reasoning, and we'll be learning some new vocabulary here, so make sure you listen carefully, and you may want to make some notes.

A fraction is in its simplest form when one is the only common factor of the numerator and denominator.

So if I draw a factor bug for one, I knew that one times one is one, and that's it.

For three, I know that one times three is three, and that's it.

Their only common factor is one.

If I divided both of these numbers, the numerator and denominator by one, one divided by one is one, three divided by one is three, so it cannot get any simpler.

The other way I know that this fraction is in its simplest form, is because this is a unit fraction.

A unit fraction is any fraction that has a numerator of one.

So one quarter is a unit fraction.

1/24th is a unit fraction.

1/643rd is a unit fraction.

These cannot be simplified any further.

But what about non-unit fractions? A non-unit fraction is a fraction where the numerator is not one.

Can non-unit fractions be in their simplest form? Well, if I wanted to turn this fraction into a unit fraction, where the numerator was one, I would have to divide my numerator two, by two, to get one.

So I have to do the same to the denominator.

But wait, two is not a factor of seven.

And I wouldn't get a whole number as an answer.

Let me just check with a factor bug, one times two is two, and that's it.

One times seven is seven, and that's it.

Their common factor is only one, therefore, it must be in its simplest form.

So non-unit fractions can be in their simplest form.

Now it's your turn, pause the video, and explore whether these fractions are in their simplest form.

You can draw factor bugs if you think they'll help you.

So, the first fraction of three quarters, is a non-unit fraction, because the numerator is not one.

Therefore it might not be in its simplest form, but let me check.

Three and four.

I'm going to draw my factor bugs just to be sure, I don't think that they have any factors in common, other than one, but let me check.

One times three is three, and there's no more.

One times four is four, and two squared is four.

Their only common factor is one.

Therefore this is in its simplest form.

This fraction, 4/8ths, is also a non-unit fraction, because the numerator is not one, so it might not be in its simplest form.

Now, I can already see from this, that they have common factors, they both have a common factor of two, but I wonder if there's a higher common factor.

I can draw my factor bug just to be sure.

One times four is four, and two squared is four, and eight, one times eight, is eight, and two times four is eight.

Yes, they do have a higher common factor.

Their highest common factor is four, therefore to be a efficient, I can divide both numerator and denominator by four, which gives me one half.

This is now a unit fraction, so I can be sure that that is in its simplest form.

The same goes for 1/6th, this is a unit fraction, so it's definitely in its simplest form.

Now it's time for some independent learning.

Pause the video, and complete the independent task.

Come back here when you've finished so that we can go through the answers together.

For question one, you were asked to simplify the fractions as efficiently as possible.

If you're being efficient, you're looking for the highest common factor, so you do your simplifying in one step.

For 12 and 30, the highest common factor is six, so I divide both by six, and I get the answer 2/5ths.

2/5ths is equivalent to 12/30ths.

For 9/36ths, the common factor is nine.

So I divide both numerator and denominator by nine, and my equivalent fraction is 1/4, a unit fraction, so I know it's in its simplest form.

Here the common factor is seven.

Divide both numerator and denominator by seven to get 1/5ths, a unit fraction.

Finally, the common factor was two, so that is 7/13ths.

This is a non-unit fraction, but I know that it is in its simplest form, because seven and 13 only share the common factor of one.

For question two I asked all pupils in all year groups to complete a survey.

Here are the number of responses that I received for each year group.

I want that in its simplest form.

Year three, I had 25/30ths, 25 out of 30 children answered.

I know that the highest common factor here is five, I divide both by five, and I get 5/6ths.

For year four, the highest common factor of 33 and 55 is 11, divide both by 11 to get 3/5ths.

For year five, the highest common factor is 16 divided by 16, for both, and I get 2/3rds.

You might have done that in two stages, where you'd first divided by two, we looked at this one earlier on.

And finally for the last one, the highest common factor is 15.

So 45/60ths is equivalent to 3/4.

Finally, for question three, you are asked to find the value of A, B and C, where A and B are equal to 16 when added together.

Now I need to look at the relationship between two numerators that I know.

What has happened to 20 to get to five? Well it's been divided by four, therefore I have to do the same to 60, divide it by four, which gives me 15.

So I now know that A is equal to 15.

15 plus B, is equal to 16.

So 15 plus something is equal to 16.

Well, I know that that's one, so B must be equal to one.

So A is 15, B is one.

Now I need to look at the relationship here, or I could look at it this way.

I'm going to go this way.

How did I get from 20 to one, if I divided by 20? How do I get from? Oh, I must do the same thing to the denominators.

60 divided by 20, is equal to three, therefore C is equal to three.

I can check.

Five divided by five is 1, 15 divided by five is three, their definitely equivalent.

Now it's time for your final knowledge quiz.

Pause the video and complete the quiz to see what you have remembered.