Lesson video

Hi everyone.

My name is Ms. Coop.

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 checking and securing, converting mixed numbers to improper fractions, and by the end of the lesson you'll have awareness that fractions of the form A over B, where A is greater than B, are greater than one and so can convert from a mixed number to an improper fraction.

Let's have a look at some key words.

Well, a proper fraction is a fraction where the numerator is less than the denominator.

For example, two over three, two-thirds.

You'll notice the numerator is two and the denominator is three.

The numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

For example, seven fifths.

You'll notice the numerator is seven, and that's greater than the five, which is the denominator.

A mixed number is an improper fraction written as an integer part, plus the fractional part, where the fractional part is a proper fraction.

For example, three and a half.

We have the integer three, and the proper fraction one half.

In today's lesson, it'll be broken into three parts.

The first part will be on integers as improper fractions.

The second part will be mixed numbers to improper fractions.

And the third part will be comparing mixed numbers and improper fractions.

Let's make a start on integers as improper fractions.

Remember, an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Here we have two examples.

A non-example would be three quarters.

As you can see, the numerator is less than the denominator.

I just wanna emphasise the example: five over five.

Remember, we also know that the numerator is equal to the denominator.

Now when we have five over five, this is equal to one.

I want you to have a look at this diagram.

Can you explain the improper fraction represented here if each bar is worth a whole? Have a little think.

Well, hopefully you spotted we have 12 quarters, because a whole is represented as four equal parts.

That means our three whole bars can actually be represented as three times four quarters, or three lots of four quarters, which we know is 12 quarters, which we know is our three whole bars.

What I want you to do is have a look at this diagram.

Can you explain the improper fraction represented here? Well, hopefully you can spot we have 32 eighths.

This is because each whole is represented as eight equal parts.

Now we know we have four whole bars, so that means 32 eighths is the same as four times our eight eighths, or four lots of our eight eighths, which we know is four.

Now what I want you to do is have a look at these check questions, and I want you to fill in the missing gaps to write the improper fraction, identify the calculation, and work out the integer answer to each of the following.

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

Well done.

So, let's go through our answers.

Well, from the diagram you'll be able to see that we have eight quarters, but we also have two whole rectangles here.

That means if each rectangle represents four quarters, we have two lots of four quarters.

This means we have eight quarters, which is the same as two.

For B, you might be able to spot we have our triangle represented as a whole, and the triangle is broken to three equal parts.

Counting up those equal parts, well we have a nine thirds, so that's our first improper fraction.

Now linking it back into our working out, you'll notice, well, how many triangles do I have? We have three whole triangles, three lots of three thirds, so that means three lots of three thirds is the same as three.

For C, let's look at the diagram, and let's see what represents a whole.

Well, a whole is represented a circle, and it's broken into two parts.

And if you count, we actually have 10 halves in total.

So let's have a look at our working out.

This means we have five lots of two over two.

Five lots of two over two, which gives me a final answer of five.

Well done if you got any of these right.

Now, let's move on to your task.

What I want you to do is match the improper fraction with the correct integer, so you can give it a go and press pause if you need more time.

Well done.

Let's move on to question two.

Question two wants you to fill in the gaps so that we can evaluate the answer to four.

We have some information here.

Eight over what gives us an answer of four? Something over 10 gives an answer of four.

12 over something gives an answer of four.

Something over four gives an answer of four.

80 over something gives an answer of four.

Something over 16 gives an answer of four.

And we have two fractions where you're free to input anything you want, as long as the answer evaluates to four.

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

Well done.

Let's move on to question three.

Place the following on the number line.

For A, it's 12 over one.

For B, it's 12 over two.

For C, it's 12 over three.

For D, it's 12 over four.

For E, it's 12 over six, and for F it's 12 over 12.

To G, it wants you to estimate where do you think 12 over five would lie? And for H, it wants you to estimate where do you think 12 over 13 would lie? See if you can give it a go, and press pause if you need more time.

Let's move on to question four.

Question four is a nice little puzzle where you have to use the numbers three, four, 12 and 24.

So a cat can represent any one of these numbers.

A star could represent any one of these numbers.

A dog could represent any one of these numbers, and the hat could represent any one of these numbers, but it has to make the calculation correct.

A fraction add a fraction is equal to nine.

Fraction subtract a fraction has to equal two, and a fraction add a fraction has to equal the dog to make the above calculations correct.

You need to work at the value of those images.

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

Well done.

Let's move on to our answers.

We had to match the improper fractions with the correct integer.

So let's start with 12 over two.

Hopefully you spotted that would be six.

12 halves is exactly the same as six.

15 over three is five.

50 over five is 10.

Nine over nine is one.

110 over 10 is 11.

24 over 12 is two, and 300 over 15 is 20.

Really well done if you got that one right.

Let's have a look at question two.

We had to fill in the gap, so that our answer evaluates to four.

Let's start with eight over something.

Well, it should be eight over two.

Eight halves is exactly the same as four.

Something over 10 is four, so that means it must be 40.

40 over 10 is four.

12 over three is four.

16 over four is four, 80 over 20 is four, and 64 over 16 is four.

For the remaining two, there are an infinite number of improper fractions which evaluate to four.

If you need to double check, you can use your calculator.

So now, let's have a look at question three.

A is indicated here.

12 over one is the same as 12.

For B, 12 over two is six.

For C, 12 over three is four.

For D, 12 over four is three.

For E, 12 over six is two.

For F, 12 over 12 is one.

Now you're asked to estimate where would 12 over five lie? Well, hopefully you spotted it should lie around about here.

You can either convert 12 over five into a mixed number, which would be two and two fifths, or you could have a look at D, which represents 12 over four and E, which represents 12 of six, and position it in between that E and D.

Well done if you got this one right.

H wants you to estimate where would 12 over 13 lie.

Well, 12 over 13 would lie here.

You might notice 12 over 13 won't give you a mixed number, and this is because it's a proper fraction.

12 is less than 13, so that means we know it will be less than one, because 12 is fairly close to than number 13.

We know it'll be closer to one than it will be closer to zero.

Well done if you got that one right.

For question four, this was a great problem solving question.

Let's see how you got on.

Working out the cat first is 12.

Working out the hat next is four, the dog gives you three, and the star gives you 24.

That makes all the calculations correct.

Really well done if you've got that one right.

Well done, everybody.

So let's move on to the second part of our lesson.

We'll be looking at mixed numbers to improper fractions.

Well, a mixed number is an improper fraction written as an integer part plus the fractional part, where the fractional part is a proper fraction.

For example, three and a half, and it's sometimes important to convert mixed numbers into improper fractions, and vice versa.

Let's look at how we can efficiently and effectively convert a mixed number into an improper fraction.

Well, let's have a look at five and six sevenths, and understand what each part represents.

Here, the five indicates we have five whole ones, and the six sevenths represent an improper fraction with a numerator of six and a denominator of seven.

Now we can write five whole ones as an improper fraction using a denominator of seven.

How do you think we can write this? Well done.

You can write it as 35 over seven, because five whole seven over sevenths is 35 over seven.

So now, we know our five represents 35 over seven, and we have our proper fraction of six sevenths.

If we add these together, that means we have converted our mixed number into an improper fraction, which is 41 over six.

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

Here, you need to fill in the blanks to show the working out, and the conversion from mixed number to an improper fraction.

For A, you have eight halves is equal to eight times two over two.

Add one half equals 16 over two add a half.

That means the improper fraction is what? For B, you have four and two thirds is equal to four times three over three add something, and then you need to work out the rest.

For C, you might notice you have less working out, but I think you can figure it out.

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

Well done.

So let's see how you got on with A.

Hopefully, you spotted the denominator was two for the mixed number eight and one half.

That means eight needed to be multiplied by the two over two.

Add our proper fraction of a half.

The eight is now a 16 over two.

Adding on our proper fraction gives us a final answer of 17 over two.

For B, four and two thirds.

So that means you might spot the denominator as three.

That's why we multiplied our whole number by three over three.

Adding on our proper fraction of two thirds means we now need to write our four as an improper fraction.

This is the same as 12 over three.

Adding on our proper fraction gives us two over three, gives a final answer of 14 over three, and for C, the denominator is five.

That means we needed to multiply a whole number, 11, by five over five.

Adding on our three over five gives us the integer of 11 is now represented as 55 over five.

Adding on our three over five verifies the answer to be 58 over five.

Really well done if you got this one right.

Now, I'm going to do a question with you, and you can do the second one on your own.

This question wants you to convert the following to an improper fraction showing our working out.

Now we have 10 and two thirds.

Look at that denominator of a three.

We need to change our integer into an improper fraction with a denominator of three.

That means we multiply our 10 by three over three, adding our proper fraction of two thirds gives us 30 over three, add our two thirds, thus our improper fraction is 32 over three.

Now I want you to have a go.

I want you to convert the following to an improper fraction, showing working out if you need.

See if you can press pause if you need more time.

Well done.

Let's see how you got on.

Well, we have a denominator of five in our proper fraction, so we need to change the integer 30 to an improper fraction with a denominator of five.

That would be 30 multiplied by our five lots of five, add our three fifths, thus making 30 the improper fraction of 150 over five.

Still adding our three fifths gives us 153 over five.

Well done if you got that one right.

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

Here, you need to fill in the blanks to show the working out, and the conversion from a mixed number to an improper fraction.

See if you can give one A and B a go.

Great work.

Let's move on to question two.

Question two wants you to convert the following to improper fractions, showing any working out that you need.

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

Well done.

Let's move on to question three.

Question three is a lovely little puzzle, and you have to work out the mixed number, given the clues for the integer and the proper fraction.

We know our mixed number has the integer, which is an even number, and the numerator and denominator of the proper fraction are odd and prime.

The mixed number is between 46 over five, and 10.

7.

Can you figure out what that mixed number is? For the second question, we know our mixed number has an even integer, and if it was written as an improper fraction, the numerator would be 173.

The denominator would be odd, and we know the mixed number lies in between 116 over five and 124 over five.

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

Well done.

This was a great question, and if you want to do a few more questions like this, why not write your own mixed number with clues? Now, let's go through our answers.

For question one, we had to convert 15 and three quarters into an improper fraction.

Our denominator is four, so that means we're multiplying 15 by four over four.

Adding our three quarters means our integer of 15 can be represented as 60 over four.

Still adding on our proper fraction gives us 63 over four.

For B, we have seven and two ninths.

Looking at the denominator of nine, this means we multiply our integer seven by nine over nine.

Adding on our two ninths gives us 63 over nine.

Add our two over nine, verifying the improper fraction to be 65 over nine.

For question two, you need to convert to improper fractions, showing any working out if you need.

Four and a half is nine over two.

11 three fifths is 58 over five.

18 and one third is 241 over three, and three and nine 10ths is 39 over 10.

Well done if you've got any of those correct.

For question three, this was a nice little puzzle, and for the first question, hopefully you figured out the integer is 10, and the numerator and denominator can be either three fifths or three sevenths.

Really well done if you got that one right.

Now, let's have a look at the second question.

We know the integer is even, and the improper fraction has a numerator of 173, so we should have got the only answer, which is 24 and five sevenths.

Really well done if you've got that one right.

Great work everybody.

Let's move on to the last part of our lesson, where we'll be comparing mixed numbers and improper fractions.

Being able to convert mixed numbers into improper fractions and vice versa is really important, because when numbers are converted, it makes them easier to order, or use in real life context.

For example, here are two numbers, 17 and three quarters and 35 over two.

Now Aisha says 17 and three quarters is greater than 35 over two, but Izzy says 17 and three quarters is less than 35 over two, and we're asked to explain who's correct and why.

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

Well done.

Well, hopefully you spotted that 17 and three quarters is the same as 71 over four.

Now you can make 35 over two have a common denominator, a 71 over four.

Thus we have 70 over four.

So that means Aisha is correct.

You could have also converted 35 over two into 17 and a half.

So 17 and a half is actually less than 17 and three quarters.

In either case, Aisha is correct.

Well done if you got this one right.

For the next check question, if a bus had 80 seats and 247 people, what would the calculation be to work out how many buses are needed? See if you can give it a go, and press pause if you need.

Well done.

Hopefully you spotted we can write it as a fraction, 247 over 80.

This can be written as three and seven over 80.

Well, the great thing about writing it as a mixed number is that you can clearly see in the context of this question, we need four buses, as we can't get seven 80ths of a bus.

Well done if you got this one right.

Now, let's move on to your task.

I want you to insert the symbol less than, greater than, or equal to, to make the following statements correct.

You have some improper fractions and some mixed numbers, and you need to compare.

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

Well done.

Let's move on to question two.

Question two is a nice context question.

Two gardeners are putting a fence around a rectangular garden.

One gardener measures the length to be 49 over five metres, and the other gardener measures the width to be four and one fifth metre.

Now, fence panels cost 22 pound per metre.

How many fence panels are needed, and what's the total cost? See if you can give it a go, and press pause as you'll need more time.

Question three shows we have some numbers, and they've been put in ascending order.

The mixed number is above, and the equivalent improper fraction is below.

And what we're asked to do is fill in the gaps.

Remember the numbers on the top are the mixed numbers, and the number on the bottom are the equivalent improper fractions, and they've been put in ascending order.

See if you can give A and B a go.

Well done.

Let's go through these answers.

For question one, 13 over four is equal to three and one quarters.

If you convert 13 over four into a mixed number, you get three and one quarter, or you can convert three and one quarter into an improper fraction, thus giving you 13 quarters.

For B, we should have 24 over five is less than five and one fifth.

Converting our mixed number into an improper fraction, we'd have 26 over five, so 24 over five is less than 26 over five.

For C, 92 over four is greater than 22 and one quarter.

Converting our mixed number into an improper fraction, we have 83 over four, so that means 92 over four is greater than 83 over four.

And for D, nine halves is greater than 25 over six.

This is a nice question, because it might be easier to convert both of them into mixed numbers.

Nine over two is the same as four and one half, 25 over six is the same as four and one sixth.

That means four and a half is greater than four and one sixth.

Well done if you got this one right.

For question two, let's see how many fence panels are needed.

Well, if you added all of these numbers together, four and one fifth, add 49 over five, add four and one fifth, add 49 over five.

It might just be easier to convert them all into improper fractions.

Converting them all into improper fractions means we have 140 over five, which is 28, so we need 28 fence panels.

Working out the cost of each fence panel, we multiplied 28 by 22, giving us 616 pounds.

Well done if you got this one right.

Question three: remember question three shows numbers in ascending order.

The numbers on the top are the mixed numbers and the numbers below are the equivalent improper fractions.

So what you should have got got is 11 over four to represent the two and three quarters, the five and one tenths to represent the 51 over 10, the 23 over four to represent the five and three quarters, and the 20 and a half to be the same as 41 over two.

For B, eight thirds the same as two and two thirds.

24 over five is the same as four and four fifths.

This had to be four and nine-tenths.

Remember, they had to be in ascending order.

16 over three, that has to be five and one third, and five and two fifths is 27 over five.

This is a great question if you got this one right.

In summary, an improper fraction is a fraction where the numerator is greater than or equal to the denominator, and we can write an integer as an improper fraction.

A mixed number is an improper fraction written as its integer parts, plus the fractional part where the fractional part is a proper fraction.

For example, three and a half is the same as seven over two.

It's sometimes important to convert mixed numbers into improper fractions and vice versa.

It's so we can compare them.

It was great learning with you today.

Well done.