Lesson video

Hi, everyone.

My name is Miss 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 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/b, where a>b, are greater than one and so can convert from a mixed number to an improper fraction.

So let's have a look at some keywords.

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

For example, two over three, 2/3, 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, 7/5, 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, 3 1/3.

We have the integer three and the proper fraction 1/2.

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.

So 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 3/4.

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

I just wanna emphasise the example, 5/5.

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

Now when we have 5/5, 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 12/4 because a whole is represented as four equal parts.

So that means our three whole bars can actually be represented as 3 times 4/4, or three lots of 3/4, which we know is 12/4, 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 32/8.

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

Now we know we have four whole bars, so that means 32/8 is the same as four times our 8/8, or four lots of our 8/8, 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 8/4, but we also have two whole rectangles here.

So that means if each rectangle represents 4/4, we have two lots of 4/4.

This means we have 8/4, 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 9/3, 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 3/3, so that means three lots of 3/3 is the same as 3.

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

Well, the hole is represented as a circle, and it's broken into two parts.

And if you count, we actually have 10/2 in total.

Well, so let's have a look at our working out.

Well, this means we have five lots of 2/2, five, lots of 2/2, which gives me a final answer of 5.

Well done if you've 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 4.

We have some information here.

Eight over what gives us an answer of 4? Something over 10 gives an answer of 4.

12 over something gives an answer of 4.

Something over four gives an answer of 4.

80 over something gives an answer of 4.

Something over 16 gives an answer of 4, 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.

So let's move on to question three.

Place the following on the number line.

For A, it's 12/1.

For B, it's 12/2.

For C, it's 12/3.

For D, it's 12/4.

For E, it's 12/6, and for F it's 12/12.

To G, it wants you to estimate where do you think 12/5 would lie? And for H, it wants you to estimate where do you think 12/13 would lie? So 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 3, 4, 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.

So 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.

So let's move on to our answers.

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

So let's start with 12/2.

Hopefully you spotted that would be 6.

12 halves is exactly the same as 6.

15/3 is 5, 50/5 is 10, 9/9 is 1, 110/10 is 11, 24/12 is 2, and 300/15 is 20.

Really well done if you got that one right.

Let's have a look at question two.

Where you had to fill in the gap so that our answer evaluates to 4.

Let's start with eight over something.

Well, it should be 8/2.

Eight halves is exactly the same as 4.

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

40/10 is 4.

12/3 is 4.

16/4 is 4, 80/20 is 4, and 64/16 is 4.

For the remaining two, there are an infinite number of improper fractions which you evaluate to 4.

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, 12/1 is the same as 12.

For B, 12/2 is 6.

For C, 12/3 is 4.

For D, 12/4 is 3.

For E, 12/6 is 2.

For F, 12/12 is 1.

Now you're asked to estimate where would 12/5 lie? Well hopefully you spotted it should lie around about here.

You can either convert 12/5 into a mixed number, which would be 2 2/5, or you could have a look at D, which represents 12/4, and E, which represents 12/6 and position it in between that E and D.

Well done if you got this one right.

H wants you to estimate where would 12/13 lie? Well, 12/13 would lie here.

You might notice 12/13 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 closer 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.

So let's see how you got on.

So working out the cat first is 12, working out the hat next is 4, the dog gives you 3, 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 where 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, 3 1/2.

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

So 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 5 6/7 and understand what each part represents.

Well here, the 5 indicates we have five whole ones and the 6/7 represent an improper fraction with a numerator of 6 and a denominator of 7.

Now we can write five whole ones as an improper fraction using a denominator of 7.

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

You can write it as 35/7 because five whole seven over sevenths is 35/7.

So now we know our five represents 35/7 and we have our proper fraction of 6/7.

If we add these together, that means we have converted our mixed number into an improper fraction.

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 8/2 is equal to 8 X 2/2 + 1/2 = 16/2 + 1/2.

So that means the improper fraction is what? For B, you have 4 2/3 as equal to 4 X 3/3 + 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.

Well, hopefully you spotted the denominator was 2 for the mixed number 8 1/2.

So that means 8 needed to be multiplied by the 2/2, add our proper fraction of 1/2.

The 8 is now a 16/2.

Adding on our proper fraction gives us a final answer of 17/2.

For B, 4 2/3.

So that means you might spot the denominator is 3.

So that's why we multiplied our whole number by 3/3.

Adding on our proper fraction of 2/3 means we now need to write our 4 as an improper fraction.

This is the same as 12/3.

Adding on our proper fraction gives us 2/3, gives a final answer of 14/3 And for C, the denominator is 5.

So that means we need to multiply our whole number, 11, by 5/5.

Adding on our three over five gives us the integer of 11 is now represented as 55/5.

Adding on our 3/5 verifies the answer to be 58/5.

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 2/3, so look at that denominator over 3.

So we need to change our integer into a improper fraction with a denominator of 3.

That means we multiply our 10 by 3/3, adding our proper fraction of 2/3 gives us 30/3, add our 2/3, thus our improper fraction is 32/3.

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.

So let's see how you got on.

Well, we have a denominator of 5 in our proper fraction, so we need to change the integer 30 to an improper fraction with a denominator of 5.

That would be 30 multiplied by our five lots of 5, add our 3/5, thus making 30 the improper fraction of 150/5, still adding our 3/5 gives us 153/5.

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 1a 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 you can give it a go and press pause if you need more time.

Well done.

So 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.

So 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 46/5 and 10.

7.

So 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 116/5 and 124/5.

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 3/4 into an improper fraction.

Our denominator is 4, so that means we're multiplying 15 by 4/4.

Adding our 3/4 means our integer of 15 can be represented as 60/4.

Still adding on our proper fraction gives us 63/4.

For B, we have 7 2/9.

Looking at the denominator of 9, this means we multiply our integer, 7 by 9/9.

Adding on our 2/9 gives us 63/9 add our 2/9, verifying the improper fraction to be 65/9.

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

4 1/2 is 9/2, 11 3/5 is 58/5, 18 1/3 is 241/3, and 3 9/10 is 39/10.

Well done if you 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 3/5 or 3/7.

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 5/7.

Really well done if you got that one right.

Great work, everybody.

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

So 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 3/4 and 35/2.

Now Aisha says, "17 3/4 is greater than 35/2." But Izzy says "17 3/4 is less than 35/2." 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 3/4 is the same as 71/4.

Now you can make 35/2 have a common denominator as 71/4.

Thus we have 70/4.

So that means Aisha is correct.

You could have also converted 35/2 into 17 1/2.

So 17 1/2 is actually less than 17 3/4.

So 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 there are 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.

So hopefully you spotted we can write it as a fraction, 247/80.

This can be written as 3 7/80.

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 7/80 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 <, >, or = 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 49/5 metres, and the other gardener measures the width to be 4 1/5 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'll ask 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.

So let's go through these answers.

For question one, 13/4 is equal to 3 1/4.

If you convert 13/4 into a mixed number, you get 3 1/4, or you can convert 3 1/4 into an improper fraction, thus giving you 13/4.

For B, we should have 24/5 is less than 5 1/5.

Converting our mixed number into an improper fraction, we'd have 26/5, so 24/5 is less than 26/5.

For C, 92/4 is greater than 22 1/4.

Okay, converting our mixed number into an improper fraction, we have 83/4, so that means 92/4 is greater than 83/4.

And for D, 9/2 is greater than 25/6.

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

9/2 is the same as 4 1/2.

25/6 is the same as 4 1/6.

So that means 4 1/2 is greater than 4 1/6.

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, 4 1/5 + 49/5 + 4 1/5 + 49/5, It might just be easier to convert them all into improper fractions.

Converting them all into improper fractions means we have 140/5 which is 28.

So we need 28 fence panels.

Working out the cost of each fence panel, we multiply 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 is 11/4 to represent the 2 3/4, the 5 1/10 to represent the 51/10, the 23/4 to represent the 5 3/4, and the 20 1/2 to be the same as 41/2.

For B, 8/3 IS the same as 2 2/3, 24/5 is the same as 4 4/5.

This had to be 4 9/10.

Remember, they had to be in ascending order.

16/3, well, that'd have to be 5 1/3, and 5 2/5 is 27/5.

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

So 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, 3 1/2 is the same as 7/2.

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.