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Hello, my name is Dr.

Sheikh , and I am so happy to be learning with you today.

You have made a great choice to learn maths with me and I am here to guide you through the learning.

Today's lesson is from our unit calculating with decimal fractions.

The lesson is called multiply one digit numbers by decimal fractions using written methods.

As we progress through our learning today, we will deepen our understanding of how we can use the short multiplication algorithm to help us calculate with decimal fractions.

First by using scaling, and then we will move on to thinking about how we do it without scaling.

Along the way, we will also be sense checking our answers using estimation.

Now sometimes new learning can be a little bit tricky, but I know if we work really hard together then we can be successful.

And I'm here to help you when the going gets tough.

Let's get started then, shall we? How can we use the written method of short multiplication to help us calculate with decimal fractions? These are our key words for the learning today.

We have estimation and scaling.

I'm sure you may have heard those words before, but it's always good to practise.

So let's have a go.

My turn estimation.

Your turn.

Nice, my turn.

Scaling.

Your turn.

Fantastic.

When we estimate we find a value that is close enough to the right answer, usually with a bit of thought or calculation and scaling is when a given quantity is made a certain amount of times the size, so maybe 10 times the size or 100th times the size and it can be used to adjust the size of a factor, which is what we are going to look at today.

And in this lesson, we will use scaling to make values 10 or 100 times the size.

So let's get started shall we? We're going to first think about how we can use scaling then short multiplication to multiply with decimal fractions.

In this lesson we have Lucas and Sofia to help us.

Lucas and Sofia are discussing how to calculate 5.

7 times by three.

And sofia is saying that to multiply by 5.

7 because it's a decimal fraction, we can use scaling to convert this to a whole number by multiplying by 10.

And we know that when we multiply by 10, the digits of the decimal fraction will move one place to the left until we get a whole number in this case 57.

Then we can multiply.

But what do you notice? That's right, 57 multiplied by three is not a known fact is it? We only know to 12 times three.

So we're going to have to calculate now and this time we are going to use short multiplication.

First, we can lay out our short multiplication algorithm and we are doing 57 multiplied by three.

Seven ones multiplied by three is 21 ones, we write one in the ones column, and we write two underneath the tens column.

Three multiplied by five tens is 15 tens.

Add those extra two tens is 17 tens.

We know now that 57 multiplied by three is 171, but, we need to work out the answer to the original equation.

So we need to divide the product by 10 to solve the original equation.

171 divided by 10.

Well we know we need to move the digits one place to the right, that's 17.

So we can say that 57 ones multiplied by three is equal to 171 ones.

So 57 tenth multiplied by three is 171 tenths, or 17.

Lucas and Sofia then discuss how to check their answer using estimation.

It's always a good thing to do is to check your answer to make sure you are about in the right place.

We know that 5.

7 is just slightly less than six.

So if we calculated with six, six threes they are 18.

So 5.

7 multiplied by three must be slightly less than 18 and it is, isn't it? So our answer looks reasonable.

Lucas and Sofia then discuss a different calculation, 0.

62 multiplied by eight.

to multiply by 0.

62, we first need to use scaling to convert this to a whole number.

We've got 6,200, so we're going to multiply by 100 when we multiply by 100, the digits of the decimal fraction move two places to the left until we get a whole number, in this case 62.

Then we can multiply.

But 62 multiply by eight is not a known fact.

So again, we can use short multiplication.

So we can start by laying out our short multiplication 62 multiplied by eight.

We've got two ones multiplied by eight is 16 one.

So we can write the six in the ones column and the one under the tens column.

Eight multiplied by six tens is 48 tens, add the extra 10 is 49 tens.

So 62 multiply by eight is equal to 496.

But, we need to work out the product for the original equation, don't we? So we need to divide this by 100, 496 divided by 100.

While the digits will move two places to the right, we get 4.

96.

And we can say that 62 ones multiply by eight is 496 wands.

So 62 hundredths multiplied by eight is 496 hundredths or 4.

96.

Lucas and Sofia then discuss how to sense check their answer using estimation.

While we know 0.

62 is slightly greater than six tenths, so we could do the calculation with six tenths.

Six 10th times eight is 48 tenths or 4.

So 0.

62 times eight is slightly greater than 48 tenths, and it is.

So our answer looks reasonable.

Let's work together on one.

I'm going to have a go at 12.

7 multiplied by six, and once I finish I'd like you to have a go at 14.

5 multiplied by four.

So we are calculating with a decimal fraction.

So the first thing I need to do is change that into a whole number by scaling, this time I'm going to multiply by 10, I get 127.

Then I'm going to use the short multiplication algorithm to help me.

I've got seven ones multiplied by six is 42 ones.

So I write the two in the ones column and the four underneath the tens column.

Then I've got six multiplied by two tens is 12 tens.

Add that four tens, it's 16 tens.

I can write the six in the tens column and the one in the under the one hundreds column.

Six multiplied by 100, add that extra 100 gives me seven hundreds.

127 multiplied by six is equal to 762.

But, we need to remember to adjust to find the original product.

I multiplied by 10, so now I'm going to divide by 10, 762 divided by 10 is 76.

Now, using my structure, I'd like you to have a go at calculating 14.

5 multiplied by four.

Pause the video while you do that.

When you are ready for the answers, press play.

How did you get on? Did you notice that we were multiplying by a decimal fraction so we needed to multiply by 10 to form it into a whole number, the 145.

We can then use the short multiplication algorithm to help us.

145 multiplied by four is 580.

We then needed to divide by 10 to solve the original equation.

14.

5 multiplied by four is equal to 58.

Let's work together to sense check our answers by estimating.

we know 12.

7 is slightly less than 13 and 13 multiplied by six.

While I can use the distributive law to help me because 13 is composed of 10 and three, 10 sixes are 60, 3 sixes are 18.

If I sum those I get 78.

So 12.

7 multiplied by six should be slightly less than 78 and it is.

So our answer is reasonable.

I wonder if you can use that structure to sense check your answer by estimating, pause the video While you do that, maybe find someone to chat to about this.

When you are ready for the answer, press play.

How did you get on? Did you notice that 14.

5 is slightly less than 15 and if you did 15 multiply by four using the distributor law, 10 fours are 40, 5 fours are 20, sum those you get 60.

So 14.

5 multiplied by four should be slightly less than 60 and it is, you've got 58.

So the answer is reasonable.

So always worth sense checking your answers by estimating to check that you are as accurate as you can be.

Let's have a go at these questions together.

I'm going to show you how I would calculate 3.

25 multiplied by six, and then I'd like you to have a go at 4.

56 multiplied by four.

So this time I've noticed I've got a decimal fraction.

This time I've got hundredth, so I'm going to multiply by 100 to give me a whole number 325 multiplied by six.

I'm going to use the short multiplication algorithm because 325 multiplied by six is more than my timestables.

It's more than my known facts.

So I've got six multiplied by five.

Ones is 30 ones.

So I write the zero in the ones column and the three under the tens column.

I've got six multiplied by two tens is 12 tens.

Add those three tens is 1510s.

So I can write my five in my tens column and the one underneath my hundreds column and then six multiplied by three hundreds is 18 hundreds.

Add the extra hundred 19 hundreds.

So 325 multiplied by six is 1,950.

But I need to adjust that, don't I? To solve the original equation.

We multiply by 100, so I need to divide by 100.

1,950 divided by 100 is 19.

Using that structure, I wonder if you can have a go at multiplying 4.

56 multiplied by four.

Pause a video while you have a go.

When you are ready for the answer, press play.

How did you get on? Did you multiply by 100 first to form a whole number? Then use the short multiplication algorithm to calculate 456 multiplied by four, which is 1,824.

Then you needed to adjust the product to solve the original equation by dividing by 100, 18.

24.

We then need to sense check our answers by estimating.

25 multiplied by six was equal to 19.

Well we know 3.

25 is slightly more than three, so I can calculate with three.

Three multiply by six is 18.

So 3.

25 multiplied by six should be slightly more than 18 and it is.

So our answer is reasonable.

I wonder if you can sense check your answer to 4.

56 multiplied by four equals 18.

24 using the structure that I've shown you.

Pause the video while you do that.

When you are ready for the answer, press play.

How did you get on? Did you notice that 4.

56 is slightly less than five? Five fours would be 20.

So 4.

56 multiplied by four should be slightly less than 20 and it is.

So the answer is reasonable.

How did you get on with that estimation? Well done.

Your turn to practise now.

For question one, could you use Sofia's method of scaling by 10 or 100 to calculate these? And then for part two, could you sense check your answers to these calculations using estimation.

Pause the video while you have a go at those questions.

When you are ready to go through the answers, press play.

How did you get on? So we were asked to use scaling to calculate these because we've got a decimal fraction.

So 19.

4 I'm going to multiply by 10 to get 194.

I can then use the short multiplication algorithm to calculate 194 multiplied by five is 970.

Then I need to adjust that to solve the original equation.

So divide by 10 would give me 97.

For the second question, I need to multiply by 100 to get a whole number 319.

I can then use the short multiplication algorithm to calculate three multiplied by 319 is 957.

And then we need to adjust that to solve the original equation by dividing by 100.

So 9.

57.

And we can then sense check those answers.

19.

4, well it's slightly less than 20.

20 fives would be 100.

So our answer should be slightly less than 100 and it is, so the answer is reasonable.

And then three multiplied by 3.

19, 9.

57, while 3.

19 is slightly greater than three.

If we do three threes, it equals nine.

So our answer should be slightly greater than nine and it is.

So the answer is reasonable.

Let's have a look at the other calculations.

91.

Well we need to adjust it to make it a whole number by scaling, multiplying by ten 915.

We can then use the short multiplication algorithm to calculate 915 multiplied by six is 5,490.

Then I need to adjust by dividing by 10 to solve the original equation, 549.

And then five, multiply by 6.

27.

Again, I need to adjust by multiplying by 100 to get 627.

I can then use the short multiplication algorithm to help.

627 multiplied by five is 3,135.

We then need to adjust by dividing by 100 to solve the original equation.

31.

35.

We can then sense check our answers.

We know 91.

5 is slightly greater than 90.

If we did 90 multiplied by six, well nine six is a 54.

So 90 sixes are 540.

Our answer should be slightly greater than 540 and it is.

So our answer is reasonable.

And for the last calculation, we know 6.

27 is slightly greater than 6, five sixes are 30.

So our answer should be slightly greater than 30 and it is.

So our answer is reasonable.

How did you get on with those questions and sense checking your answers? Well done.

Fantastic learning so far everyone.

You are working really hard.

We're now going to move on and look at how we can use short multiplication with decimal fractions.

So Lucas and Sofia discussed this calculation, 2.

46 multiplied by three.

And sofia is saying, well to multiply by 2.

46, we need to scale to convert this to a whole number by multiplied by 100.

Oh, but Lucas is respectfully to challenging Sofia.

He is asking if we actually have to convert the decimal fraction to a whole number.

What do you think? Do we need to scale by 100, or could we just use the decimal fraction? Let's find out.

So let's look at a previous calculation to help us work out the answer to that.

So we've got 127 multiplied by six is 762.

What would happen if we wrote this? 12.

7 multiplied by six equals 76.

2 in the short multiplication algorithm? What would it look like? That's right.

It would look like this, wouldn't it? Hmm? What do you notice? Is there anything that is the same? Anything that is different? That's right.

The decimal point in the product, 76.

2, is aligned with that in the decimal fraction, isn't it? 12.

7 they're aligned, they're in the same place.

Do we notice anything else? Well, Sofia noticed that the multiplier in this case, six, well it's not written in the ones column is it's not written under the two.

We know it's six ones, but it's just usual to write it on the right of the written method.

So let's revisit this calculation that Sofia and Lucas were looking at at the start.

Let's use short multiplication with the decimal fraction.

So let's not do the scaling to convert into a whole number.

Let's see what happens.

First, let's lay out the calculation.

Okay, 2.

46, multiply by three.

And then Lucas is saying, "Well, let's just write that decimal point in for the product and see what happens.

And then we can perform the calculation as we would usually using the unitizing." Three times six hundredths is equal to 18 hundredths.

18 hundredths is one 10th and eight hundredths.

Three times four tenths is equal to 12 tenths.

12 tenths plus that one 10th is 13 tenths.

13 tenths is one one and three tenths.

Three two ones equals six ones.

And we need to add the extra one, don't we? Which is seven ones.

So 2.

46 multiplied by three is equal to 7.

38.

So we can use short multiplication with decimal fractions.

And Sofia agrees.

We just need to remember to align the decimal point in the product to that in the decimal fraction that we are multiplying with.

So it's really important when we set up that short multiplication algorithm that if we've got a decimal point in the number we are multiplying that we put it straight into the product in that same position so they are aligned.

And we need to remember to write the multiplier under the digit with the lowest place value.

It might not necessarily be in the ones column.

Let's check your understanding with this.

Take a look at these short multiplication algorithms, A, B, C, and D.

Can you tell me which are laid out correctly for this calculation? Five multiplied by 1.

67.

Pause the video while you have a look at them and when you think you know, press play.

How did you get on? Did you say it must be C? It can't be A because there are no decimal points.

It can't be B because the decimal points are not aligned, and it can't be D because we've got 16.

7 and we are meant to be calculating 1.

67.

Did you spot that C was correct? Well done.

It's your turn to calculate the product now, we've got 1.

67, we've set up the short multiplication for you and the decimal point has been aligned in what will be the product and in our decimal fraction, 1.

67.

Pause the video while you have a go.

When you are ready to go through the answers, press play.

How did you get on? Did you start off by saying five times seven Hundredths is 35 hundredths and 35 hundredths is three tenths and five hundredths, then five times six tenths equals 30 tenths plus those three tenths is 33 tenths, and 33 tenths is three ones and three tenths? And then five times one one equals five ones plus those three ones equals eight ones.

So five multiplied by 1.

67 is 8.

35.

How did you get on with that? Well done.

Your turn to practise now for question one, could you calculate these products using short multiplication? A and B have been set up for you, but for C and D you will need to write the short multiplication algorithm for yourself.

For question two, could you solve these problems using short multiplication? Sofia has 2.

48 litres of water.

Lucas has three times this amount.

How much water does Lucas have? Part B, Lucas has five pounds 32, and sofia has six times this amount.

How much money does sofia have? And for part C, Lucas buys four magazines each costing two pound 34.

How much change does he get from 10 pounds? Pause the video while you have a go to all of those questions.

When you are ready to go through the answers, press play.

How did you get on? For question one, you are asked to calculate products using short multiplication.

38, multiply by five is 6.

90.

25.

8 multiplied by three is 77.

Again, you notice how the decimal point is aligned in the decimal fraction and in its product.

For part C, you had to actually set up the short multiplication algorithm.

43.

7 multiplied by five is 218.

And for D 3.

96 multiplied by four is equal to 15.

84.

For question two, you had some problems to solve.

Sofia has 2.

48 litres of water and Lucas has three times this amount.

So my bar model has got three parts and the hole is unknown.

I can use that to form an equation, 2.

48 times three.

I can then use the short multiplication algorithm to do the calculation for me.

Lucas has 7.

44 litres of water.

For part B, Lucas has five pound 32 and sofia has six times this amount.

The hole is unknown, I have six parts.

Each part is worth five pound 32.

I can use this to form an equation, 5.

32 times six.

I can then use the short multiplication algorithm to calculate.

And we work out that sofia has 31 pounds, 92 pence.

For Part C, Lucas has four magazines.

So my bar model has four parts.

Each part is worth two pounds 34.

And I need to calculate the total cost to begin with.

I can form an equation 2.

34 multiplied by four.

And then to calculate it, I can use the short multiplication algorithm.

36.

So he spends nine pounds 36.

But, the question is asking is how much change he gets from 10 pounds.

So we still need to work out the change.

So we've got 10 pounds and we're going to subtract nine pound 36.

So I'm going to adjust, I'm going to adjust the 10 pounds into nine pounds 99 and adjust the nine pound 36 into nine pound 35.

I can then do the calculation and get 64 pence change.

How did you get on with those questions? Well done.

Fantastic learning today, you've really deepened your understanding on using the written method of short multiplication with decimal fractions.

We know that to multiply one digit numbers by decimal fractions, we can use scaling to convert the decimal fraction to a whole number.

And then, after we've calculated though, we need to remember to use scaling to adjust the product.

We know that we can use short multiplication to multiply one digit numbers by decimal fractions as long as we remember to align the decimal point in the product with that in the decimal fraction.

And we also learn it's really important to estimate, to sense check our answers.

Really proud of how hard you have worked today.

I've had a lot of fun.

I look forward to learning with you again soon.

I've finished the video