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Hello, how are you today? My name is Dr.
Shorrock and I'm really excited that you have chosen to learn maths with me today.
We are gonna have great fun as we move through the learning together.
Today's lesson is from our unit calculating with decimal fractions.
This lesson is called divide decimal fractions by one digit numbers.
As we move through the learning today, we are going to deepen our understanding of how we can use unitizing and our known facts to divide these decimal fractions.
We are then going to apply this learning to solve problems. Now, sometimes new learning can be a little bit tricky, but it is okay.
I am here to guide you and I know if we work really hard together, then we will be successful.
So let's get started, shall we? How do we divide decimal fractions? These are our key words for the learning today we have unitizing and integer.
Let's practise saying those words.
My turn.
Unitizing.
Your turn.
Nice.
My turn.
Integer.
Your turn.
Lovely.
And unitizing means treating groups that contain or represent the same number of things as ones or units, particularly important when we handle money and in understanding place value, it helps us to think multiplicatively one 50 Pence coin is equal to 50 one-pennies that are unitizing.
The 50 p is a unit and an integer is a whole number.
It's got no fractional part to it.
So for example, zero one fourteen, 103 decimal numbers such as 3.
4 are not integers.
Let's start our learning today by looking at how we divide decimal fractions using unitizing and known facts.
And we have Lucas and Sofia to guide us through the learning today.
Let's have a look at this problem.
Lucas has a 12 metre length of string.
Can you visualise that? He cuts it up into three equal pieces.
Can you see that? What is the length of each piece? Good idea, Lucas.
Let's represent this in a bar model.
Our hole is known 12.
The piece of string is 12 metres long and we know that Lucas cuts it into three equal parts and we can use the bar model to form an equation.
We've got 12 is our hole and we are dividing into three equal parts and we can use our known facts to solve this.
We know three fours are 12, so 12 divided by three must be equal to four.
The length of each piece of string is four metres.
Now let's have a look at this.
I wonder if you can make a connection with this problem and the previous problem, Sofia has a 1.
2 metre length of string.
She also cuts it up into three equal pieces.
What is the length of each of those pieces? Good idea, Sofia.
Let's represent this in a bar model.
We know our hole is 1.
2 and we know the hole has been cut up into three equal parts and we can use that bar model into form an equation.
We have 1.
2 and we are dividing by three.
Sofia has spotted something, have you? Sofia has spotted that there is a relationship between this equation 1.
2 divided by three and the equation that Lucas formed 12 divided by three is equal to four.
Can you spot something that is the same or something that is different? Sofia has noticed that 1.
2 is one-tenth times the size of 12, and when we find one-tenth, we can multiply it by 0.
1 or divide by 10.
If 1.
2 is one-tenth times the size of 12, well what does that mean? That's right.
It means that 1.
2 divided by three must be one-tenth times the size of 12 divided by three.
So we can use our 12 divided by three equation to help us solve our 1.
2 divided by three equation.
So we can use the four to determine the answer to 1.
2 divided by three.
When we multiply by 0.
1 or divide by 10, the digits move one place to the right.
Four divided by 10 is equal to 0.
4.
We can summarise and say that 1.
2 is one-tenth times the size of 12.
So 1.
2 divided by three must be one-tenth times the size of 12 divided by three.
So if 12 divided by three is equal to four, 1.
2 divided by three must be equal to 0.
4.
Let's check your understanding with this.
Could you use this unitizing strategy and the stem sentence to calculate 2.
4 divided by three and the stem sentence is 2.
4 is one-tenth times the size of 24.
So 2.
4 divided by three is one-tenth times the size of 24 divided by three.
Pause the video while you work out 2.
4 divided by three using the known fact that I've given you there.
And when you're ready to go through the answers, press play.
How did you get on? Did you work out? It must be 0.
8.
2.
4 is one-tenth times the size of 24.
So 2.
4 divided by three must be one-tenth times the size of 24 divided by three and that is equal to eight.
One-tenth times the size of eight is 0.
8.
How did you get on with that? Well done.
Let's look at these equations then.
Got 12 divided by three is equal to four and 0.
12 divided by three is equal to something.
What do you notice about those equations? Is there something that's the same or something that's different? Sofia has noticed that there is a relationship between these equations.
She's noticed that 0.
12 is one-hundredth times the size of 12, and when we find one-hundredth we can multiply by 0.
01 or divide by one-hundredth.
They are equivalent actions.
If 0.
12 is one-hundredth times the size of 12, then 0.
12 divided by three must be one-hundredth times the size of 12 divided by three.
We know 12 divided by three is equal to four, so we need to find one-hundredth times the size of four and to do that we can multiply by 0.
01 or divide by 100 and when we divide by 100 the digits move two places to the right.
So four divided by 100 is 0.
04.
We can summarise and say 0.
12 is one-hundredth times the size of 12, so 0.
12 divided by three must be one-hundredth times the size of 12 divided by three and that's equal to four.
So 0.
12 divided by three must be equal to one-hundredth times the size of four or 0.
04.
Let's summarise our learning.
We know 12 ones divided by three equals four ones, so 1.
2 divided by three, well that's 12 tenths and dividing it by three would equal four tenths or 0.
4 and then 12 hundredths or 0.
12 divided by three must be equal to four hundredths or 0.
04.
Let's solve this equation, 5.
6 divided by eight.
How would you solve this equation? Hmm? Is there something that you spot, something that you recognise, something that might be a little bit familiar to you? Thank you Lucas.
To divide 5.
6, we can first convert this to a whole number by multiplying by 10.
5.
6 multiplied by 10 is equal to 56.
Do you recognise something there with the 56 and the eight? That's right.
It's a known fact, isn't it? We know eight sevens are 56, so 56 divided by eight must be seven.
But this isn't the answer to the original equation, is it? What do we need to do? That's right, we need to divide the answer by 10 to solve the original equation.
Seven divided by 10 is 0.
7.
So you can see how we use scaling to create a whole number from our decimal fraction.
Then we used our known facts, but then we had to adjust the answer to solve the original equation.
So 56 wands divided by eight is equal to seven ones.
So 56 tenths divided by eight is equal to seven tenths.
And we can say that if the hole is one-tenth times the size, the answer will be one-tenth times the size.
Let's solve this equation.
0.
56 divided by eight.
Well to divide 0.
56, we can first convert this to a whole number by multiplying by 100.
We've got 56 hundredths.
If we multiply by 100, we will get 56 ones.
And then this is a known fact so we can calculate with the whole numbers.
We know eight sevens a 56, so 56 divided by eight must be seven.
But this is not the answer to the original equation.
We then need to divide the answer by 100 to solve the original equation because originally we multiplied by 100, so we need to adjust the answer as well.
Seven divided by 100 is 0.
07.
We can say that 56 ones divided by eight is equal to seven ones.
So 56 hundredths divided by eight is equal to seven hundredths or 0.
07.
We can say that if the whole is one-hundredth times the size, the answer will be one-hundredth times the size.
So 0.
56 is one-hundredth times the size of 56.
So the answer is one-hundredth times the size of seven.
Let's check your understanding with this.
Using this unitizing strategy and the stem sentence calculate 0.
54 divided by six and the stem sentence is 54 ones divided by six is equal to nine ones.
So 54 hundredths divided by six is equal to mm hundredths or mm.
Pause the video while you have a go at this and when you are ready to go through the answers, press play.
How did you get on? Did you use your known fact? 54 divided by six is equal to nine.
And then from that we can determine the answer to the original equation.
0.
54 had been multiplied by 100 to form a whole number 54, so we needed to adjust our answer by dividing by 100 to give us 0.
09.
We could say 54 ones divided by six is equal to nine ones.
So 54 hundredths divided by six is equal to nine hundredths or 0.
09.
How did you get on with that? Well done.
We've got a different example here.
We've got 0.
4 divided by eight.
How should we solve this? Well, Lucas says he's going to start by making the whole 10 times larger.
We've got four tenths, so if we make it 10 times larger, we'll transform it into a whole number, won't we? And we can then calculate 0.
4 made 10 times large is four, so we have four divided by eight.
Hmm, is there something that you notice here that's slightly different to the calculations we've looked at previously? That's right.
This is not a known fact, is it? The whole four is smaller than the number we are dividing by? Four is smaller than eight.
Hmm.
What are we going to do then? Ah, Lucas has an idea.
We can multiply by 10 again.
Good idea Lucas four multiply by 10 is 40 and this is now a known fact, isn't it? We know eight fives are 40, so 40 divided by eight must be five.
So we can solve the equation but instead of multiplying by 10 and 10 again we could just have multiplied by 100 to start with if we had spotted that.
But what do we need to do to solve the original equation? That's right.
We know 40 divided by eight is equal to five, but we've got 0.
4 divided by eight, so we need to divide the answer by 100 to solve the original equation.
Five divided by 100 is 0.
05.
It's your turn to practise now using the structure that I just used for 0.
4 divided by eight, could you calculate 0.
3 divided by five? Pause the video while you have a go and when you are ready to go through the answers, press play.
How did you get on? Did you first transform the 0.
3 into three by multiplying by 10? And realising though that three divided by five is not a known fact, so you needed to multiply by 10 again to get 30 divided by five.
That is a known fact and we know that 30 divided by five is six.
And then what did you do to calculate the answer to the original equation? That's right.
You needed to divide by 100.
So six divided by 100 is 0.
06.
So 0.
3 divided by five is equal to 0.
06.
How did you get on with that? Brilliant.
Let's look at these equations.
We've got 0.
3 divided by five, 0.
35 divided by five and 3.
5 divided by five.
We know we need to use scaling to transform the decimal fraction into an integer, but how do we know when to scale by 10 or 100? When do we multiply by 10? When do we multiply by 100 to transform the decimal fraction into a whole number? Sofia thinks she knows.
Sofia is saying if the decimal fraction has hundredths, then we multiply by 100 to transform it into an integer.
So 0.
35.
If we multiply that by 100, we get 35.
If the decimal fraction has tenths, then we multiply by 10 to transform it into an integer 3.
5.
If we multiply by 10, we get 35.
Unless this makes an initiative that is smaller than the number we are dividing by, in which case we need to multiply by 10 again or have multiplied by 100 in total so that we've then got a known fact that we can use.
It's your turn to practise now for question one, could you solve these equations by using the relationships that you spot? And then could you make up a set of your own equations using this pattern? For question two, could you solve these equations.
First, make the decimal fraction a whole number and then calculate using your known facts and adjusting the answer accordingly.
And for question three, could you solve these equations? See what you spot about them.
Make sure that you transform the decimal fraction to a whole number that is greater than the number we are dividing by.
Pause the video while you have a go to all three questions and when you are ready to go through the answers, press play.
How did you get on with these questions? Let's have a look.
For question one, you were asked to solve these equations by using the relationships that you spot.
We were given 24 divided by six is equal to four.
Now the hole was made one-tenth times the size, so if the hole is made one-tenth times the size, then the answer will be one-tenth times the size or 0.
4, then the hole was made one-hundredth times the size 0.
24.
So the answer must also be made one-hundredth times the size, 0.
04.
99 divided by nine is a known fact that equals 11 and our whole was made one-tenth times the size 9.
9, so the answer must be one-tenth times the size 1.
1.
Then 99 was made one-hundredth times the size so the answer needed to be made one-hundredth times the size, 0.
11.
15 divided by five is equal to three.
It's a known fact and 15 was then made one-tenth times the size to 1.
5, so the answer must be made one-tenth times the size 0.
3.
Then 15 was made one-hundredth times the size to 0.
15 so the answer needed to be made one-hundredth times the size 0.
03.
We know five sixes are 30, so it must be 30 divided by five is equal to six.
Then the answer was one-tenth times the size.
So we know the whole had to be made one-tenth times the size three, then the answer was one-hundredth times the size of six.
So we know the hole had to be made one-hundredth times the size of 30 or 0.
3.
You might then have made up your own set of equations like this.
I chose the known fact four seven to 28 and I created some of my own equations.
28 divided by seven is equal to four.
I made my whole one-tenth times the size 2.
8, so the answer needed to be made one-tenth times the size 0.
4.
Then I made my whole one-hundredth times the size to 0.
28, so the answer needed to be made one-hundredth times the size 0.
04.
For question two, you were asked to solve these equations by making the decimal fraction a whole number first, 0.
32 or 32 hundredths.
We can multiply by 100 to make a whole number 32.
This is then a known fact.
32 divided by eight is equal to four.
Then we need to adjust the answer by dividing by 100, 0.
04.
0.
6 divided by two, I could make the 0.
6 10 times larger to six.
Six divided by two is equal to three, so then I needed to adjust the answer by dividing by 10, 0.
3.
0.
48 divided by eight, I've got 48 hundredths so I can make the decimal fraction into a whole number by multiplying by 100.
48 divided by eight is equal to six, but then I need to remember to adjust the answer by dividing by 106 divided by 100 is 0.
06, 0.
36 divided by three I can multiply the 0.
36 by 100 to form a whole number 36.
36 divided by three is equal to 12.
I then needed to adjust the answer by dividing by 100, 0.
12.
4.
2 divided by seven.
I've got 42 tenths, so if I multiply by 10, I can form a whole number 42.
42 divided by seven is equal to six.
Then I need to adjust the answer by dividing by 10, 0.
6 4.
5 divided by nine.
I've got 45 tenths so I can multiply by 10 to form a whole number 45.
45 divided by nine is equal to five, but then I need to adjust the answer by dividing by 10, 0.
5.
0.
35 divided by five I've got 35 hundredths so I can start by multiplying by 100 to form a whole number 35.
35 divided by five is equal to seven, but then I need to adjust the answer by dividing by 100, 0.
07.
For question three, you were asked to solve these equations and first you had to transform the decimal fraction to a whole number that is greater than the number we are dividing by.
0.
4 divided by five, but if I only multiplied by 10, that would be four divided by five and then the whole would not be greater than the number we are dividing by.
So I needed to multiply by 100.
40 divided by five is equal to eight, so that means that I can then adjust the answer by dividing by 100, 0.
08.
0.
3 divided by six.
I can multiply 0.
3 by 100 to form a whole number that is greater than the number we are dividing by, 30 divided by six is equal to five.
Then I can adjust the answer by dividing by 100, 0.
05, 0.
2 divided by five.
I can transform the 0.
2 into a whole number by multiplying by 100.
20 divided by five is equal to four.
I can then adjust the answer by dividing by 100, 0.
04.
0.
1 divided by two.
I can transform 0.
1 into 10 by multiplying by 100, 10 divided by two is equal to five.
Adjusting the answer by dividing by 100, 0.
05.
0.
1 divided by five.
I can transform the 0.
1 into 10 by multiplying by 100 and then 10 divided by five is equal to two.
I can then adjust the answer by dividing by 100, 0.
02.
0.
2 divided by four.
I can transform the 0.
2 into a whole number by multiplying by 100, 20 divided by four is equal to five.
Adjust the answer by dividing by 100 and we get 0.
05.
How did you get on with those questions? Brilliant.
Brilliant learning so far.
I can see how hard you are trying and that's what's really important.
We're going to move on now and have a look at how we can divide decimal fractions when we are problem solving.
Let's look at this problem.
Lucas lives 2.
8 kilometres away from school.
I wonder how far away from school you live.
I wonder if you know.
Sofia lives one quarter times that distance.
So if she lives one quarter times that distance, it's a shorter distance, isn't it? How far away from school does Sofia live? Good idea, Lucas.
Let's represent this as a bar model.
We know Lucas lives 2.
8 kilometres away from school and Sofia lives one quarter times the size.
So we know we have four equal parts and we can use the bar model to form an equation.
2.
8 divided by four.
To divide 2.
8 we can convert this to a whole number by multiplying by 10, 2.
8 multiplied by 10 is equal to 28.
We can then use our known facts to calculate this.
We know four sevens of 28, so 28 divided by four is equal to seven and then we need to divide the answer by 10 to solve the original equation.
Seven divided by 10 is 0.
7.
This tells us that Sofia lives 0.
7 kilometres away from school.
Let's look at a different problem.
Sofia has 0.
35 kilogrammes of flour and she shares this between five containers.
Can you visualise that? And we want to know how much flour is in each container and yes, good idea Sofia.
We should always represent a word problem as a bar model.
We know our whole is 0.
35 and we know it the flour is shared between five containers, so we have five equal parts and we can use the bar model and to form an equation.
0.
35 divided by five and to divide 0.
35, we can first convert this to a whole number by multiply by 100.
We've got 35 hundredths.
If we multiply by 100, we get 35 ones and we can then use our known times table facts.
We know five sevens are 35, so 35 divided by five must be seven.
And then we need to divide the answer by 100 to solve the original equation.
Seven divided by 100 is 0.
07.
So this means there is 0.
07 kilogrammes of flour in each container.
Let's work together now to solve these problems. My hole is 0.
18 and it is going to be divided into three equal parts.
I can see that from the bar model.
0.
18 divided by three.
So what do I need to do first? That's right.
I need to convert the decimal fraction into a whole number.
I've got 18 hundredths, so I'm going to multiply by 100 to give me 18.
This is now a known fact.
Three sixes are 18, so 18 divided by three must be equal to six.
I can then transform my answer by dividing by 100 to answer the original equation, 0.
06.
Now it's your turn.
Can you look at your bar model and the structure that I have used and form a calculation and then solve it.
Pause the video while you have a go and when you are ready for the answers, press play.
Did you notice that your bar model was composed of six equal parts? So your equation was 0.
66 divided by six.
We've got 66 hundredths, so we need to multiply by 100 to make 66 ones and if we divide that by six, we get 11.
We can then adjust the answer by dividing by 100 to help us answer the original equation.
11 divided by 100 is 0.
11.
How did you get on with that? Well done.
It's your turn to practise now.
You've got some problems to solve.
Represent them in a bar model to support you to form an equation that you can then solve.
Question A, Lucas bought a bag of apples that has a mass of 0.
36 kilogrammes.
Each apple had the same mass and there were three apples in the bag.
What is the mass of one apple? Part B, Sofia has a 1.
6 metre length of ribbon.
She cuts it into four equal lengths.
What's the length of each piece? And for part C, Sofia has made a cake that has a mass of one point kilogrammes.
Lucas has made a cake that has a mass one third times this mass.
How much heavier is Sofia's cake? Pause the video while you have a go at those three questions and when you are ready to go through the answers, press play.
How did you get on our first question about the bag of apples? We know the hole is 0.
36 and we know there are three parts.
We can use this to form an equation.
0.
36 divided by three.
We've got 3600th, so we're going to multiply by 100 to form a whole number and then we can use our known facts.
36 divided by three is 12.
We then need to adjust the answer by dividing by 100.
12 divided by 100 is 0.
12.
So the mass of one apple is 0.
12 kilogrammes.
For question two, we know the hole is 1.
6 metres and the ribbon was cut into four equal lengths and we can use that to form an equation.
1.
6 divided by four, I've got 1.
6, I've got 16 tenths so I can multiply by 10 to form a whole number.
And this is then a known fact.
16 divided by four is equal to four, and then we need to adjust the answer by dividing by 10.
Four divided by 10 is 0.
4.
So the length of each piece is 0.
4 metres.
For part C, Sofia has made a cake that has a massive 1.
8 kilogrammes and that is our whole.
Lucas's cake had a mass of one third.
So there are three equal parts and we can use that to form an equation.
1.
8 divided by three, I've got 18 tenths, so I'm going to multiply by 10 to form a whole number 18.
This is then a known fact.
18 divided by three is equal to six.
Then we need to adjust the answer by dividing by 10.
Six divided by 10 is 0.
6.
Lucas's cake has a mass of 0.
6, but that's not the answer is it? The question was how much heavier is Sofia's cake? So we need to find the difference 1.
8 subtract 0.
6 is equal to 1.
2.
So Sofia's cake is 1.
2 kilogrammes heavier than Lucas's.
How did you get on with those questions? Well done.
Fantastic learning today, everybody.
You have really made a lot of progress with your understanding of how we can divide decimal fractions by one digit numbers.
We know that when we divide decimal fractions by one digit numbers, we make the decimal into a whole number by multiplying by 10 or 100.
We can then use unitizing and known facts to divide.
And then we need to remember that the answer must be adjusted by dividing.
So you should be really proud of how hard you have worked today.
I've had a lot of fun learning with you, and I look forward to learning with you again soon.
