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Hello, my name is Dr.
Shorrock.
I am really looking forward to 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.
This lesson is called divide decimal fractions by one digit numbers using written methods.
As we move through the learning today, we'll start by thinking about how we can use scaling to convert the decimal fraction to a whole number and then use a written method.
And then we will look at what happens if we don't use scaling.
Can we still use a written method? Now, sometimes new learning can be a little bit tricky, but I'm here to guide you when the going gets tough and I know if we work really hard together, then we can be successful.
Let's get started then, shall we? How can we divide decimal fractions using a written method? These are the key words for the learning today.
We have estimation and scaling.
Let's practise those words together.
My turn estimation, your turn.
Nice.
My turn scaling, your turn.
Fantastic.
Now when we estimate we find a value that is close enough to the right answer.
Usually we have to have a little bit of a think about it or some sort of calculation.
And scaling is when a given quantity is made hmm times the size and maybe 10 times the size or 100 times the size.
And it can be used to adjust the size of a factor.
And in this lesson, scaling will involve making values 10 or 100 times the size.
Let's get started with our learning today thinking about how we can divide decimal fractions using written methods, starting by thinking about how we can use scaling and then short division.
Throughout the learning today we have got Lucas and Sofia to guide us.
Lucas and Sofia are discussing how to calculate 6.
3 divided by 3.
How would you calculate? Sofia is saying that to divide 6.
3, we use scaling to convert this to a whole number by multiplying by 10.
6.
3 multiplied by 10 well, 63 tenths multiplied by 10 would give us 63 ones because we move the digits of the decimal fraction one place to the left until we get the whole number.
Then we can divide.
But 63 divided by 3 is not a known fact, is it? So we can use short division.
First let's set up our short division algorithm.
Six tenths divided by 3 is equal to two tenths.
Three ones divided by 3 is equal to one 1.
63 divided by 3 is equal to 21.
But this is not the answer to our original equation.
We need to divide the answer by 10 to solve the original equation.
21 divided by 10.
We know when we divide by 10, we need to move the digits one place to the right.
So 6.
3 divided by 10 is equal to 2.
1 63 ones divided by 3 is 21 ones.
So 63 tenths divided by 3 must be 21 tenths and that is equal to 2.
1.
It's then always really sensible to check your answer using estimation.
We know 6.
3 is slightly greater than six, so we could perform the calculation using six instead of 6.
3.
Six divided by 3 is equal to 2.
So 6.
3 divided by 3 must be slightly greater than 2 and it is, isn't it? 2.
1 is slightly greater than two.
So our answer looks reasonable.
Lucas and Sofia then discuss a different calculation.
0.
85 divided by 5.
How would you do that? Sofia is saying that to divide 0.
85, we can use scaling to convert this to a whole number and this time we need to multiply by 100.
Do you know why? That's right it's because we've got 85 hundredths.
So if we multiply by 100, we will form a whole number or 85 and when we multiply by 100 the digits of the decimal fraction move two places to the left, then we can divide.
But this is not a known fact, is it? So we need to use short division.
First let's set up the short division algorithm.
85 divided by 5.
8 tens divided by 5 is 1 ten with a remainder of 3.
35 ones divided by 5 is equal to 7 ones.
So 85 divided by 5 is equal to 17, but this is not the answer to the original equation.
Now we need to divide by 100 to solve the original equation.
17 divided by 100.
When we divide by 100 the digits move two places to the right.
0.
85 divided by 5 is equal to 0.
17.
We can say that 85 ones divided by 5 is equal to 17 ones.
So 85 hundredths divided by 5 is equal to 17 hundredths or 0.
17.
And then we know we need to sense check our answer using estimation.
We know 0.
85 is just slightly less than one.
We could do the calculation with one one divided by 5.
Well that's equal to 0.
2.
We could use the fact that 10 divided by 5 is equal to two and then make that 1/10 times the size.
So 0.
85 divided by 5, it must be slightly less than 0.
2.
And 0.
17 is slightly less than 0.
2.
So our answer is reasonable.
Let's have a go working together now to calculate these, I'm going to model how to calculate 25.
5 divided by 5 and then I would like you to use my structure to calculate 15.
6 divided by 4.
Have you noticed something about these? That's right.
They're decimal fractions, aren't they, with tenths.
So I can multiply by 10 to form a whole number.
I get 255.
I can then use the short division algorithm to help me calculate 2 hundreds divided by 5 while I don't get any hundreds and I have a remainder of 2.
25 tens divided by 5 is five and then 5 ones divided by 5 is equal to one.
255 divided by 5 is equal to 51.
But that isn't the answer to my original equation.
I need to adjust my answer by dividing by 10.
51 divided by 10 is equal to 5.
1.
Okay, it's your turn to practise now using the structure that I've just used, could you calculate 15.
6 divided by 4? Pause the video while you do that and when you are ready to go for the answers, press play.
How did you get on? Did you notice that 15.
6 was a decimal fraction so you needed to transform it into a whole number by multiplying by 10, which is 156.
You could then use the short division algorithm to calculate 156 divided by 4 is equal to 39.
Then we needed to adjust the answer to solve the original equation by dividing by 10.
39 divided by 10 is 3.
9.
Let's have a go at sense checking our answers by estimating.
25.
5, well that's slightly greater than 25, isn't it? So if I did that calculation with 25, 25 divided by 5 is equal to 5.
So my calculation of 25.
5 divided by 5 should be slightly greater than 5 and it is.
So the answer is reasonable.
Could you sense check your answer by estimating, pause the video while you do that and when you are ready to go through the answer, press play.
How did you get on? Did you note that 15.
6 is slightly less than 16, so you could do the calculation with 16.
16 divided by four is a known fact and that's equal to four.
So 15.
6 divided by 4 should be slightly less than four and it is.
So your answer is reasonable.
Well done.
Let's then work together to calculate these.
I'm going to model how I would calculate 3.
56 divided by 4 and then I would like you to use my model to calculate 5.
45 divided by 5.
First have you spotted something? That's right.
The number we are dividing is a decimal fraction and it has hundredths.
So I'm to multiply by 100 to transform mine into a whole number, 356.
I can then use the short division algorithm to help me.
300 divided by four.
Well I can't make any hundreds, so I have a remainder of 3.
35 tens divided by four is 8 tens with a remainder of 3.
36 ones divided by four is equal to 9 ones.
So 356 divided by four is equal to 89.
But then I need to adjust my answer by dividing by 100 so that I can find the answer to the original equation.
3.
56 divided by four is equal to 0.
89.
It's your turn to practise now.
Could you use the structure I've shown you to have a go at calculating 5.
45 divided by 5? Pause a video while you do that and when you are ready to go through the answers, press play.
How did you get on? Did you notice that you also had to multiply by 100 to form a whole number? You could then use the short division algorithm to calculate 545 divided by 5 which is 109.
You then needed to adjust the answer by dividing by 100, which gives you 1.
09.
Let's then sense check our answers by estimating.
I know that 3.
56 is slightly less than four, so I can do my calculation using 4.
4 divided by 4 is equal 1 one.
So my answer to 3.
56 divided by 4 should be slightly less than one and it is.
So my answer is reasonable.
Have a go now at sentence checking your answer by estimating.
Pause the video while you do that and when you are ready to go through the answer, press play.
How did you get on? Did you notice that 5.
45 is slightly greater than 5 and if you did, your calculation with 5, 5 divided by 5 is equal to 1.
So your answer to 5.
45 divided by 5 should be slightly greater than one and it is so your answer is reasonable.
Well done.
It's your turn to practise now for question one.
Could you complete these calculations and then could you explain what you noticed? And did you have to calculate each of these or was there a pattern that you spotted? For question two, could you complete these calculations? Then sense check your answers to these calculations using estimation.
Pause the video while you have a go at both questions and when you are ready for the answers, press play.
How did you get on? Let's have a look.
For question one you had to complete these calculations and I wonder if you may be spotted a pattern.
You might have noticed that for each set of calculations the hole was made 1/10 times the size.
So for the first set of calculations, we started with 714.
That was made 1/10 times the size, 71.
4.
So then because the hole was made 1/10 times the size, but the number we were dividing by remained the same, the answer would be 1/10 times the size.
So actually for each set of equations, you only needed to calculate the first equation, then the could just have been made 1/10 times the size.
Well done if you spotted that.
For question two, you were asked to complete these calculations, then sense check your answers to the calculations using estimation.
31.
5 divided by 5.
Well, we can transform 31.
5 into 315 and then do the division using our short division algorithm, which gives us 63, we then need to adjust the answer by dividing by 10 to get 6.
3.
For part B, 7.
92 divided by 4, we needed to multiply by 100 to transform the decimal fraction into a whole number.
We could then use the short division algorithm to help us calculate 792 divided by four is 198.
We then need to adjust the answer by dividing by 100 to give us 1.
98.
For part C, 6.
12 divided by 3, we needed to multiply by 100 to transform the decimal fraction into a whole number.
We could then use the short division algorithm.
612 divided by 3 is equal to 204.
We then needed to adjust the answer by dividing by 100, 2.
04.
Then you are asked to sense check your answers using estimation.
We know 31.
5 is slightly greater than 30.
30 divided by 5 would be 6.
So our answer should be slightly greater than 6 and it is.
7.
92 divided by 4.
Well, 7.
92 is slightly less than eight.
8 divided by 4 is 2.
So our answer should be slightly less than 2 and it is.
6.
12 divided by 3.
Well, 6.
12 is slightly greater than six.
6 divided by 3 is equal to 2.
So our answer should be slightly greater than 2 and it is.
How did you get on with those questions? Well done.
Fantastic learning so far.
Really impressed with how hard you are trying.
We're going to move on now and have a look at short division with decimal fractions when we don't scale, is it possible? What do you think? Let's find out.
Lucas and Sofia discuss this calculation.
6.
3 divided by 3.
How would you calculate it? Sofia is saying "To divide 6.
3 we use scaling to convert this to a whole number by multiplying by 10." Hmm, but Lucas is respectfully challenging Sofia.
He's asking do we actually have to convert the decimal fraction to a whole number? Good question Lucas, what do you think? Let's look at a previous calculation to help us.
If we look at 85 divided by 5 is equal to 17 in the short division algorithm, what would 0.
85 divided by 5 equal 0.
7 look like in the short division algorithm? What do you think? Let's have a look.
This is what it would look like.
What do you notice? Did you notice that the decimal point in the answer is aligned with that in the decimal fraction? Let's revisit this calculation then.
Let's use short division with the decimal fraction rather than scaling.
So let's not do the scaling and see what happens.
First, let's lay out the calculation in our short division algorithm.
2.
55 divided by 5.
Then let's write the decimal point for the answer.
If we write it in now, we can't forget it, can we? Then let's perform the calculation using unitizing.
Two ones divided by 5 is equal to zero ones with a remainder of two.
We write the zero in the ones column and write two to the left of the tenths column to give 25 tenths.
25 tenths divided by 5 is equal to five tenths.
We write five in the tenths column.
Five hundredths divided by 5 is equal to one hundred.
We write one in the hundredth column.
2.
55 divided by 5 is equal to 0.
51.
We can use short division with decimal fractions and Sofia is agreeing.
We just need to remember to align the decimal point in the answer to that in the decimal fraction that we are dividing.
Let's check your understanding with this.
Which of these short division algorithms are laid out correctly for this calculation? 1.
65 divided by 5.
Is it A, B, or C? Pause the video while you look at each of those and make a decision.
When you are ready to hear the answer press play.
Did you spot that it must be C.
In A we've got 16.
5 and that's not what we are calculating with.
In B, the decimal points are not aligned so it must be C.
Well done if you spotted that.
Let's now have a go at calculating the answer.
We've set the short division algorithm up for you.
So pause the video while you have a go at calculating and when you are ready for the answer, press play.
How did you get on? Did you say that one divided by 5 equals zero ones with the remainder of one.
We write zero in the ones column and one to the left in the tenths column.
This gives 16 tenths.
16 tenths divided by 5 equals three tenths with a remainder of one.
We write three in the tenths place and one to the left in the hundredths place.
This gives 15 hundredths.
15 hundredths divided by 5 equals three hundredths.
We write three in the hundredths place.
1.
65 divided by 5 is equal to 0.
33.
How did you get on with that? Well done.
It's your turn to practise now.
For question one, could you calculate the answers using short division with the decimal fraction? You can see for parts A and B, I've set up the short division algorithm for you.
But for parts C and D, you need to do that yourself.
For question two, could you solve these problems? Sofia has 2.
52 litres of water.
Lucas has one third times this amount.
How much water does Lucas have for part B? Lucas has 9 pounds 42 and Sofia has won six times this amount.
How much money does Sofia have? And for Part C, Lucas grows some potatoes.
He has 27.
5 kilogrammes of potatoes altogether.
He packs them into five bags so that they have equal mass, which is the mass of each bag.
Pause the video while you have a go at questions one and two.
And when you are ready to go through the answers, press play.
How did you get on? Let's have a look.
For part A, 3.
95 divided by 5.
Well that's 0.
79.
For part B, 43.
2 divided by 3 is equal to 14.
4.
For part C 38.
4 divided by four is equal to 9.
6 and for part D, 5.
52 divided by 6 is equal to 0.
92.
For question two solving problems, we could represent these in a bar model.
Sofia has 2.
52 litres of water and Lucas has one third times this amount.
We can use that to form an equation.
2.
52 divided by 3.
I can use my short division algorithm.
It's 0.
84.
So Lucas has 0.
84 litres of water.
For part B Lucas has 9 pound 42 and Sofia has won six times this amount.
So we are dividing by six.
We can set up our short division algorithm.
9.
42 divided by six is equal to 1.
57.
So Sofia has 1 pounds 57.
For part C we know 27.
5 is our whole and there are five equal parts, so we are dividing by 5.
We can then set up our short division algorithm.
27.
5 divided by 5 is 5.
5.
So the mass of each bag is 5.
5 kilogrammes.
How did you get on with those questions? Fantastic.
Really impressed with how hard you have tried today in your learning.
I know you have deepened your understanding on how we can divide decimal fractions using written methods.
We know we could use scaling to convert the decimal fraction to a whole number.
And then if we've done that, we need to remember then to adjust the answer.
We know though that we could use short division with decimal fractions and if we do that, the decimal point in the answer must be aligned in the same position as in the decimal fraction being divided and we know that we should use estimation to sense-check our answers.
Fantastic learning today.
Well done.
I look forward to learning with you again soon.
