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 the lesson then.

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

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

I'm gonna say them and I want you to repeat them back to me.

I'll say my turn, say the word.

Then I'll say your turn and it will be your turn to say it.

Ready? My turn, remainder, your turn.

My turn, decimal.

Your turn.

My turn, equivalent.

Your turn.

Okay, so that's how to say them, but what do these words mean? It's important we understand their definitions before we get going.

A remainder is an amount left after a division.

A decimal number has a decimal point followed by digits that show the fractional part.

Equivalent refers to when two or more things have the same value.

This is the outline of today's lesson.

We're gonna start by writing remainders as decimals.

Then we're gonna look at long division with money.

Sam and Andeep are gonna join us today.

They're gonna be discussing some of the math prompts that you see on screen so they can help us to learn.

Hi Sam, hi Andeep.

Are you ready? Are you ready? Let's get going then.

Andeep and Sam previously used long division to calculate 5,418 divided by 35.

You can see there jottings there on the right hand side of the screen.

We had a remainder of 28 when we calculated.

So they found that 5,418 divided by 35 is equal to 154 remainder 28.

They can use a fraction to represent the remainder.

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

Can you see that they have changed the remainder in that second equation? Instead of it being remainder 28, they've written 28 thirty-fifths.

We can simplify the fraction too.

28 thirty-fifths becomes four-fifths.

That's because both 28 and 35 have a common factor of seven.

That means that you can divide them both by seven.

28 divided by seven is equal to four and 35 divided by seven is equal to five.

So, the fraction simplified is four-fifths.

Long division can be used to give a decimal remainder.

28 is 28 ones, which can be regrouped as 280 tenths.

I can make eight groups of 35 tenths with 280 tenths.

So, we've got an eight in the tenths column, after the decimal point.

There is nothing left over, no remainder.

So, 5,418 divided by 35 is equal to 154.

8.

Andeep and Sam have three equivalent answers.

You can see them there.

154 remainder 28, 154 and four-fifths, 154.

8.

I know that four fifths is the same as eight tenths, which is 0.

8.

The whole number part is always 154.

I wonder when we'd use each answer.

When do you think you would use each answer? So, each of these answer is correct and they all have the same value, but the way that they've been written, the way they've been noted down is different and those ways could be different in different contexts.

So, I wonder what context they would be.

If we had people, we couldn't have a fractional part of a person.

No, that would be quite gruesome.

I agree, four-fifths of you isn't possible.

We'd use the remainder for people.

Four-fifths would be useful for something we can split like a cake.

Mm, cake.

So, if I had 154 cakes and four-fifths of a cake, I can imagine that.

Using a decimal would be good for measures, 154.

8 metres for example.

Or money.

We'd say 154 pounds 80, not 154 and four-fifths of a pound.

Okay, let's check your understanding so far then.

Write the remainder as a fraction.

Simplify, then write as decimal.

You've got 4,112 divided by 32 is equal to 128 remainder 16.

Pause the video and give that a go.

Welcome back.

Sam says remainder 16 is 16 out of the next group of 32.

So, it can be written as 16 thirty-twoths.

16 thirty-twoths can be simplified to one half as the numerator and denominator share a factor of 16.

One half is equal to five tenths.

So one half is equivalent to 0.

5 as a decimal.

So you can see there we've got a range of different answers.

Each of them has the same value, but they've been written with a different notation.

Pratchett the tortoise covers 2.

5 kilometres in 16 days.

How many metres does he travel each day? That's quite a long way for a tortoise to travel.

They must be speedier than we think they are.

We need to think about the units here.

The answer needs to be in metres.

2.

5 kilometres is equal to 2,500 metres.

Brilliant converting.

Well done, Sam.

We need to divide 2,500 by 16.

We could use long division.

Let's estimate first.

One hundred sixteens is equal to 1,600.

Two hundred sixteens is equal to 3,200.

I estimate around 150.

2.

5 kilometres is equal to 2,500 metres.

We need to divide 2,500 by 16.

2,500 divided by 16 is equal to 156 remainder four.

What does the answer mean? 156 remainder four what? It must be 156 remainder four metres in a day.

Okay, let's check your understanding so far.

Write the answer to the problem with the remainder expressed as a fraction, a fraction in its simplest form, a decimal.

And the question we've got was the one that we've just answered.

2,500 divided by 16 is equal to 156 remainder four.

Pause the video and give it a go.

Welcome back.

So Sam says the remainder of 4 is out of the next group of 16, so four-sixteenths.

So our first answer was 156 and four-sixteenth metres.

In its simplest form? Well 4 and 16 share a common factor of 4, so the fraction can be simplified to one quarter.

A fraction in its simplest form then? 156 and one quarter metres.

Lastly, a decimal.

Well, one quarter as a decimal is equal to 0.

25.

So as a decimal, it's 156.

25 metres.

156.

25 metres makes sense as the answer to a measure question.

Okay, it's time for the first practise task then.

I'd like you to write these remainders as decimals.

And Sam says, does simplifying the fractions help? You could then create an equivalent of tenths or hundredths.

Number two, complete the table to show how far each tortoise walks in a day.

Number three, order the tortoises from slowest to the fastest walker.

Pause the video here, give those a really good go and I'll be back in a little while with some feedback.

Good luck.

Welcome back.

Here's the answers for number one then.

The remainder could have been simplified in fraction form to three-fifths, and that would've given 123.

6 for A.

For B it could have been simplified to 123 and one half, which is the equivalent of 123.

5.

For C, it could have been 123 and three quarters, which is the equivalent of 123.

75.

For D 123 and one-fifth, that's 123.

2.

For E 123 and one quarter, that's 123.

25.

For F, we could have had 123 and eight-eightieths, which is equivalent to 123 and 1 tenth and that's 123.

1 Pause the video here if you need some time to catch up with that marking.

Welcome back.

Let's do number two then.

We needed to fill in this table.

Here's what it should have looked like.

Let's mark number two then.

I'll read the distance per day.

For Pratchett, it was 60.

5 metres.

For Bertie, it was 60.

6 metres.

For Hurricane, it was 60 metres, and for Clyde it was 60.

25 metres.

Here's the order then of the tortoises from the slowest to the fastest.

Hurricane, Clyde, Pratchett then Bertie.

Bertie holds the current world record as the fastest tortoise 2024.

Okay, let's move on to the second part of the lesson then.

We are used to seeing decimal places when we write money.

23 pounds 70, 22 pounds and one pence.

The decimal part represents a fraction of a pound.

22 pounds and one pence is 22 pounds and 100th of a pound.

I hadn't thought about it like that before.

23 pounds 70 is 23 pounds and seven tenths of a pound.

Okay, let's check your understanding of that.

Which of the following statements are true? And I'm gonna read them for you.

55 pounds 50 is equal to 55 pounds and five-tenths of a pound.

55 pounds and five pence is equal to 55 pounds and five-tenths of a pound.

55 pounds 55 pence is equal to 55 pounds and 55 hundredths of a pound and 50 pounds and five pence is equal to 50 pounds and five hundredths of a pound.

You've got A, B, C, and D there.

Which of those statements are true? Pause the video and decide.

Welcome back.

A was true and C was true.

D was also true.

Oak Academy's Class 6 raised money so they get to go to a sporting event.

Each child ticket costs the same.

They need 763 pounds for their class of 28 children.

How much is the cost of one ticket? Andeep says, "I think I can find the answer using long division.

I'm confident in this now." Andeep and Sam calculates 763 divided by 28 using long division.

I got the answer 27 remainder 7, but I don't think each ticket costs 27 remainder 7.

We could extend the long division to find a decimal remainder, but I think we can use what we know about fractions here.

Yes, we can express the remainder as 7 twenty-eighths, but that doesn't look like a price either.

How do you express a remainder when calculating with money? The simplified fraction remainder is one quarter, but we don't tend to use fractions for money.

I know one quarter is written as 0.

25 because one quarter is equivalent to 25 hundredths.

So each ticket costs 27 pounds 25 pence.

When dividing with money, you need to express the remainder as a decimal.

Adult tickets to the same sporting event cost more.

1,708 pounds is spent on 35 adult tickets.

How much is the cost of one ticket? When dividing with money you need to express the remainder as a decimal.

Andeep and Sam calculate 1,708 divided by 35 using long division.

This is tricky 'cause I had to think about 1,708 as 170 tens and eight ones.

I got 48 remainder 28.

I think we should think about the fraction remainder to answer the question.

Okay, so they know that one ticket costs 48 pounds, remainder 28, and they've expressed that as a fraction.

You can see 28 thirty-fifths.

The remainder as a fraction is 28 thirty-fifths.

The simplified fraction remainder is four-fifths but I'm not sure how to write this as a decimal.

What do you think? Okay, well, let's check your understanding.

Sam and Andeep calculated the cost of a ticket.

Write the cost of one ticket using decimal notation.

1,708 divided by 35 is equal to 48 and 28 thirty-fifths.

Andeep says, "Can you simplify the fraction first?" You should be able to.

Okay, pause the video here and give that a go.

Welcome back.

So four-fifths was the simplified fraction.

You may have noticed that four-fifths is equivalent to eight tenths, which is written as 0.

8.

1,708 divided by 35 is equal to 48 pounds and 80 pence.

This is the cost of an adult ticket.

Is that what you got? I hope so.

It's time for your second practise task then.

Number one, Andeep and Sam are helping to plan the transport for the trip to the sporting event.

How much does each coach cost per person? Express your answer as a decimal.

Elm Coaches, 56 seats, 700 pounds a day.

Ash Coach Hire, 64 seats, 848 pounds a day.

Rowan Bus Hire, 60 seats, 768 pounds a day.

Beech Buses, 65 seats, 858 pounds a day.

B, list the coach companies from the cheapest to the most expensive.

Okay, pause the video here and I'll be back with some feedback soon.

Good luck.

Welcome back.

Let's get some marking done then.

You can see here the Elm Coaches costs 12 pound 50.

Ash Coach Hire costs 13 pounds 25.

Rowan Bus Hire costs 12 pounds 80 and Beech Buses costs 13 pounds 20.

And all those prices I just gave were per person.

So if we list the coach companies for B from the cheapest to the most expensive, you should have had Elm Coaches, Rowan Bus Hire, Beech Buses, then Ash Coach Hire.

It's time for our end of the lesson summary then.

Fraction and decimal equivalents can be used to convert fraction remainders to decimals.

1 one is equivalent to 10 tenths, so a one can be exchanged for 10 tenths in the tenths column.

My name's Mr. Tazzyman.

I enjoyed that lesson today, I hope you did too.

See you again soon.

Bye for now.