Lesson video

Hi, I'm Mr. Tazzyman.

Today I'm gonna teach you a lesson from a unit that's all about multiplying, and dividing by two-digit numbers.

There might be lots of steps that you encounter here, but it's really important for you to understand not just the steps but the maths behind those steps as well.

So, sit back, listen well, it's time to learn.

Let's go.

Here's the outcome for today's lesson, then.

By the end, we want you to be able to say I can use long division and give the remainder as a fraction.

These are the key words that you might expect to hear during the lesson.

I'll say them, I want you to repeat them back to me.

Remainder, fraction.

Okay, but what does each of these terms mean? Because it's important for us to understand them as well as to be able to say them.

Well, a remainder is an amount left after a division.

A fraction shows us how many parts in a whole.

It is a number.

This is the outline for today's lesson then.

We're gonna start by writing remainders as fractions.

Then we're gonna look at simplifying fraction remainders.

Sam and Andeep are gonna join us today.

They're gonna help us by discussing some of the maths that you'll see on screen.

They'll give us some hints and tips, and they might even be able to reveal some of the answers later on.

Hi Sam, hi Andeep.

Okay, let's get started.

Sam and Andeep previously solved this problem.

3,600 apples are put into bags.

Each bag contains 28 apples.

How many bags can be filled? They use long division.

You can see their jottings there on the right-hand side.

They ended up with 128 remainder 16.

Ah yes, we had a remainder, says Andeep.

128 means 128 full bags of apples.

There were 16 apples left over.

The remainder can be represented in a different way.

16 apples could partly fill a bag.

I can show this as a model.

You can see there we've got in total 28 squares, but only 16 of those have been filled.

The whole bag is 28 and my remainder is 16.

I could say that this is 16 twenty-eighths of a bag.

So, 3,600 divided by 28 is equal to 128 and 16 twenty-eighths.

3,600 apples are put into bags.

Each bag contains 28 apples.

So, 128 full bags and 16 twenty-eighths of a bag.

The remainder can be written as a fraction of the divisor.

Okay, your turn.

Write the remainder as a fraction.

We've got 900 divided by 26 is equal to 34 remainder 16.

Can you write the remainder as a fraction? Pause the video and give it a go.

Welcome back.

900 divided by 26 is equal to 34 and 16 twenty-sixths.

So, the remainder as a fraction would have been 16/26.

The remainder can be written as a fraction of the divisor.

Haggis has a bag of 500 biscuits.

He eats 12 biscuits a day.

How many days will the biscuits last for? You can see Haggis there, and you can see the bag.

How many groups of 12 are in 500? I wonder if we will have a remainder.

I know 4 multiplied by 12 is 48.

So, 40 multiplied by 12 is equal to 480, and he writes that out.

He takes 500 and partitions it into 480 and 20.

480 we know is 40 groups of 12.

20 is 8 more than one group of 12.

So, 20 is equal to one group of 12 with a remainder of 8.

500 divided by 12 is equal to 41 remainder 8.

But what does that mean for Haggis? The 8 is the number of biscuits left over.

But he could still eat them, right? The 8 biscuits are 8/12 of a day's biscuits.

So, he has biscuits for 41 and 8/12 days.

500 divided by 12 is equal to 41 and 8/12.

The remainder can be written as a fraction of the divisor.

Okay, it's your turn.

Let's check your understanding so far.

Sam completes a long division and writes 5400 divided by 35 is equal to 153 remainder 45.

Then he tries to express that remainder as a fraction.

5400 divided by 35 is equal to 153 and 45/35.

Sam is incorrect.

Explain why.

Pause the video and give that a go.

Welcome back.

Did you manage to spot something here? The remainder is greater than the divisor, and the fraction is improper.

One more group of 35 can be made from 45.

So, the quotient is 154, and the remainder can be written as 10/35.

Okay, it's time for your first practise task.

Andeep and Sam have solved some equations.

Rewrite their answers so that the remainders are expressed as fractions.

Number two.

Solve each of the word problems using long division where appropriate.

Represent the remainder as a fraction.

I'm gonna read these for you.

A.

3840 apples are put into bags.

Each bag contains 28 apples.

How many bags are used? B.

4900 pears are put into bags.

Each bag contains 32 pears.

How many bags are used? And C.

Cooper the dog has a bag of 800 biscuits.

He eats 14 biscuits a day.

How many days do the biscuits last? Pause the video and give those questions a go.

I'll be back soon with some feedback.

Good luck.

Welcome back.

Here's number one, then.

Did you remember that the remainder can be written as a fractional part of the divisor? The numerator is the remainder, and the denominator is the divisor.

So, here's A rewritten.

412 divided by 32 is equal to 12 and 28/32.

B.

709 divided by 18 is equal to 39 and 7/18.

And C.

498 divided by 15 is equal to 33 and 3/15.

Pause the video here if you need extra time to check those carefully.

Here's number two, then.

Did you use an appropriate strategy to calculate? Well, the answer was 137 with a remainder of 4, but of course we wanted to express that as a fraction.

So, it was 137 and 4/28.

137 and 4/28 of bags are used.

Here's B.

The answer was 153, and 4/32 of bags are used.

And here's C.

The answer was that the biscuits last 57 and 2/14 days.

Pause the video here if you need some extra time to mark those more carefully.

It's time for the second part of the lesson now.

Simplifying fraction remainders.

Haggis has a bag of 500 biscuits.

He eats 12 biscuits a day.

How many days will the biscuits last for? I can simplify the fraction, says Andeep, and he's looking at the jottings on the right.

We've worked this out already, and we know that 500 divided by 12 is equal to 41 and 8/12.

8/12 is equivalent to 2/3, so we can also write 41 and 2/3 as our answer.

So, he has enough biscuits for 41 and 2/3 days.

On day 42, he won't have enough biscuits.

Poor Haggis.

Haggis's doggie daycare looks after 16 dogs in total.

Their jumbo sack of treats has 564 treats in.

How many treats does each dog get? So, we've got an expression that's been written here.

564 divided by 16, and there's an equal sign next to it, but we don't have an answer yet.

It's unknown.

We've got to calculate it.

I think we can use long division for this.

Andeep and Sam start with multiples of 16, and it's this trick again of writing out the first 10 multiples.

A really, really important and useful skill.

Double 4 groups is 8 groups, so double 64 is 128.

5 groups of 16 is half of 160, which is 80.

6 groups is 16 more than 80, which is 96.

96 plus 16 is equal to 112.

3 groups is 16 more than 32, which is 48.

9 groups is 16 less than 160, which is 144.

How do multiples of 16 help us to estimate? Well, there are 564 treats and 16 dogs.

I think each dog will get between 30 and 40 treats.

30 multiplied by 16 is less than 564, and 40 multiplied by 16 is greater than 564.

Andeep and Sam calculate 564 divided by 16 using long division.

564 is equal to 35 groups of 16 with a remainder of 4.

We can show the remainder as a fraction of the divisor.

4/16.

Now they've got themselves an answer.

564 divided by 16 is equal to 35 and 4/16.

I can simplify the fraction, says Andeep.

I wonder how.

We've got 4/16 as our remainder.

If we divide the numerator and the denominator by 4, then it's equal to one quarter.

So, the answer with a simplified fraction is 35 and 1/4.

So, each dog gets 35 treats and one quarter of a treat.

Okay, let's check your understanding then.

You've got to simplify these fractions.

Pause the video and give it a go.

Welcome back.

12/36.

Well, they both were multiples of 12, and if you divided both the numerator and denominator by 12, you would end up with 1/3.

For 13/52, you could divide both the numerator and denominator by 13, and that would give you 1/4.

Okay, let's check your understanding with your second practise task.

You've got to use an appropriate strategy to calculate each problem.

Give the remainder as a fraction in its simplest form.

I'll read the questions to you.

Number one.

Penguins at the zoo eat 15 fish a day.

That's a lot of fish.

How many days will 500 fish last for? Number two.

Bandit the dog has a bag of 600 biscuits.

He eats 11 biscuits a day.

How many days will the bag last for? Number three.

At doggie daycare, 798 treats are shared equally amongst all 36 dogs.

How many treats does each dog get? Number four.

If the answer to a division problem is 22 and 1/4, what could the question be? Can you write a worded problem? Sam gives us a little tip here.

Think about fractions that are equivalent to one quarter.

The denominator could be the divisor.

Okay, pause the video here and give those questions a good go.

I'll be back soon with some feedback.

Enjoy.

Welcome back.

Let's look at number one to begin with.

We've got 500 fish, and they've been partitioned into 450 and 50.

450 represents 30 groups of 15, and 50 is 3 groups of 15 with a remainder of 5.

So, 500 divided by 15 is equal to 33 remainder 5, but we know that we need to show the remainder in fraction form.

So, we've got 500 divided by 15 is equal to 33 and 5 fifteenths, but we need its simplest form, and that would be 33 and one third because 5 and 15 can both be divided by 5, and that will give you a 1 for the numerator and a 3 for the denominator.

500 fish will last for 33 and 1/3 days.

Here's number 2, then.

600 biscuits will last for 54 and 6 elevenths days.

Number 3 each dog gets 22 and 1/6 treats, and for number 4, well, here's one example.

One quarter is equivalent to 4/16.

16 is the divisor.

Something divided by 16 is equal to 22 remainder 4.

22 multiplied by 16 is equal to 352.

So, 352 divided by 16 is equal to 22.

Adding 4 to the dividend will leave a remainder of 4.

356 divided by 16 is equal to 22 remainder 4 or 22 and one quarter.

So, here's the context that we could use then.

365 metres of wood is divided into 16 equal lengths.

How long is each length? It is 22 and one quarter's metre long.

A bunny rehoming centre has 365 carrots.

There are 16 rabbits.

How many carrots does each rabbit get? It is 22 and one quarter carats.

Pause the video here if you need time to check what you've written gives you an answer of 22 and 1/4.

Okay, we've reached the end of the lesson.

Here's a summary of the learning.

When giving the remainder as a fraction, the denominator is the same as the divisor.

If the remainder can be simplified, then the denominator will be a factor of the divisor.

The fraction can be interpreted as a fraction of the unit of the dividend or the divisor, depending on the context.

My name is Mr. Tazzyman.

I enjoyed that today, and I hope you did as well.

Bye for now.