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Hello.
How are you today? My name is Dr.
Shorick, and I am really excited to be learning with you today.
You have made a great choice to learn maths with me and I'm here to guide you through the learning.
Today's lesson is from our unit "Calculating with Decimal Fractions." The lesson is called "Explain the Relationship Between Multiplying by 0.
01 and Dividing by 100." As we progress through the learning today, we are really going to deepen our understanding of this connection between multiplying by 0.
01, an one-hundredth, and dividing by 100.
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 guide you through the learning if the going gets tough.
So, let's get started, shall we? How can we explain that relationship between multiplying by 0.
01 and dividing by 100? Our key word for the learning today is hundredth.
You might have heard that word before, but it's always good to practise.
Let's have a go.
My turn, hundredth.
Your turn.
Nice.
And when we say one-hundredth, we mean one part in 100 equal parts.
We're going to start our lesson today thinking about how we find one-hundredth.
And we have Lucas and Sofia to guide us.
Let's look at this.
Lucas and Sofia are investigating different pieces of string.
Lucas' string is two metres long.
"My string," Sofia is saying, "is one-hundredth times this length." So, we can represent Lucas' string as two metres.
And to find the length of Sofia's string, we need to find one-hundredth of two metres.
And one-hundredth is written as 0.
01.
So, we need to multiply two metres by 0.
01 to find one-hundredth times the size of two metres.
When we multiply by one-hundredth, the digits move two places to the right.
So, two metres multiplied by one-hundredth is equal to 0.
02 metres.
So, one-hundredth of two metres is 0.
02 metres.
One-hundredth of two metres, we could also say is two hundredths of a metre because 0.
02 is two hundredths.
The length of Sofia's string is 0.
02 metres or two hundredths of a metre.
The children look at some other lengths of string where Sofia's is always one-hundredth times the length of Lucas' string and they have presented their results in a table.
We can see they looked at when Lucas' string was two metres, 12 metres or 200 metres, and then they could work out the length of Sofia's string by finding one-hundredth times the length of Lucas'.
So you can see they are multiplying each length by 0.
01 or one-hundredth.
So, we can say that one-hundredth of mm metres is mm hundredth of a metre or mm.
So for example, one-hundredth of two metres is two hundredths of a metre or 0.
02.
One-hundredth of 12 metres is 12 hundredths of a metre or 0.
12.
One-hundredth of 200 metres is 200 hundredths of a metre, or two.
So to summarise, to find one-hundredth, we can multiply by 0.
01.
To multiply by 0.
01, we move the digits two places to the right and we can use the stem sentence to support us.
One-hundredth of mm metres is mm hundredth of a metre or mm.
Let's check your understanding with this.
Lucas has a 46 metre length of string.
Sofia's string is one-hundredth times the length.
Complete the stem sentence to determine the length of Sofia's string.
One-hundredth of mm metres is mm hundredths of a metre or mm.
Pause the video, maybe talk to somebody about this and say the sentence to each other.
And when you are ready to go through the answers, press play.
How did you get on? Did you say the stem sentence one-hundredth of 46 metres is 46 hundredths of a metre or 0.
46.
Well done.
Let's look at this.
Lucas has a 10 metre length of string.
Is there another way to find one-hundredth? We know we could multiply by one-hundredth or 0.
01, but is there another way? Ah, thank you Sofia.
We can also write one-hundredth as a fraction, as a unit fraction where the numerator is one and the denominator is 100.
And we know that when we multiply by a unit fraction, it is the same dividing by the denominator of that fraction.
In this case, our denominator is 100.
so multiplying by one-hundredth would be the same dividing by 100.
When we divide by 100, the digits move two places to the right, so one-hundredth of 10 metres is 10 hundredths of a metre or 0.
1.
So, we can say that each of these expressions represent the same relationship.
If we multiply by 0.
01 or multiply by one-hundredth or divide by 100, they are all the same.
They all represent ways that we can find one-hundredth of 10 metres.
So, we could write them in one long equation because they are all equal to each other.
Let's check your understanding with this.
Which of these equations represent finding the length of a piece of string that is one-hundredth times the length of a 400 metre length of string? You've got four options, A, B, C and D, and it says which equation or equations, so there could be more than one.
Pause the video while you have a go, and when you are ready for the answers, press play.
How did you get on? Did you say, "Well, it can't be A, can it?" Because there, we're multiplied by 0.
1 or 1/10, so we're finding 1/10 times.
B is correct.
We've got 400 metres and we are multiplying by 0.
01, or one-hundredth times.
What about C? Well, C is correct, isn't it? Because we know multiplying by one-hundredth is the same as dividing by 100, and D is also correct, because when we multiply by 0.
01 it is the same as multiplying by one-hundredth.
How did you get on with those? Well done.
Let's look at this on a place value grid.
We've got the number 300.
We know when we divide by 100 or multiply by one-hundredth, the digits move two places to the right.
300 multiplied by one-hundredth or divided by 100 is equal to three.
We had three hundreds.
We now have three ones.
Let's look at this number on a place value grid, 120.
120 multiplied by 0.
01 is equal to 1.
2, or divided by 100 is also equal to 1.
2.
What do you notice? That's right.
When we divide by 100 or multiply by one-hundredth, the digits move two places to the right.
We had one hundred and two tens.
We now have one one and 2/10.
What about this number, 92? Well, when we divide by 100 or multiply by one-hundredth, the digits move two places to the right, so 92 metres made one-hundredth times the size is 0.
92.
We must remember to put that placeholder at the front in the ones position because there are no ones.
One-hundredth of 92 metres is 92 hundredths of a metre or 0.
92.
What about this number? About number four? When we divide by 100 or multiply by one-hundredth, the digits move two places to the right.
We had four ones.
We now have four hundredths.
We can write the equations four multiplied by 0.
01 or four divided by 100.
They are equivalent actions, so we equal 0.
04, and again, we must remember those placeholders in the ones and in the tenths to show us that there are no ones and no tenths, but we have got those four hundredths.
So, we can say that when a number is multiplied by 0.
01 or one-hundredth, the digits move two places to the right, but also when we divide by 100, the digits move two places to the right, so they are equivalent actions.
When we multiply by 0.
01 or one-hundredth and divide by 100, they are equivalent actions.
Let's check your understanding with this.
Could you complete these two related equations that represent finding one-hundredth of 105 metres? Pause the video while you do that.
When you are ready to go through the answers, press play.
How did you get on? Did you say, "Well, to find one-hundredth, we need to multiply by 0.
01 or we can divide by 100." You may have written one-hundredth as a unit fraction in place of my 0.
01.
We can say that when we divide by 100 or multiply by one-hundredth, the digits move two places to the right.
These are equivalent actions.
It's your turn to practise now.
For question one, could you fill in the missing numbers? Explain any pattern that you spot, and then if you finish, could you make up your own group of equations that have a similar connection? For question two, could you complete these equations by filling in the blanks? Pause the video while you have a go at both questions and when you are ready to go through the answers, press play.
How did you get on? Let's have a look.
For question one, we had to fill in the missing numbers.
So, we had 150 divided by 100.
Well, when we divide by 100, the digits move two places to the right, that would be 1.
5, and 15 divided by 100 would be equal to 0.
15.
Then we had 700.
Well, we know when we're multiplying by 0.
01, the digits move two places to the right.
That would be seven.
70 multiplied by one-hundredth would be 0.
7.
Seven multiplied by one-hundredth, 0.
07, and 0.
7 multiplied by one-hundredth would be seven thousandths or 0.
007.
You might have explained that when the multiplicand becomes 10 times smaller, then the product becomes 10 times smaller if the multiplier remains the same.
You might then have made up a group of equations where the multiplicand became 10 times smaller like this.
I chose to start with 900 and then I made it 10 times smaller, 90, 10 times smaller, nine, and 10 times smaller, 0.
9.
And you can see my product is 10 times smaller each time, as well.
For question two, you are asked to complete these equations.
50 multiplied by 0.
1.
Well, that's equivalent to divided by 100.
So, both of those answers will be 0.
5.
The same with 91 when we multiply by 0.
01.
It's the same as divided by 100, so both of those answers are 0.
91.
And then here we started with 80.
We multiply by 0.
01, and that's the same as divided by 100.
Both answers are 0.
8.
And then we had here 0.
53.
Well, that's equal to 53 multiplied by one-hundredth.
0.
21 is equal to 21 divided by 100.
620 multiplied by 0.
01 is 6.
2, and 62 divided by 100 would be 0.
62.
250 divided by 100 would be 2.
5, and then 25 divided by 100 would be 0.
25.
Remember when we divide by 100 or multiply by 0.
01, the digits move two places to the right.
Then we have 40 divided by 100.
Well, that's equal to 40 multiplied by one-hundredth.
72 divided by 100 is equal to 72 multiplied by one-hundredth.
84 divided by 100 is equal to 84 multiplied by one-hundredth.
Remember, they are equivalent actions.
So, eight divided by 100 is also equal to eight multiplied by one-hundredth.
How did you get on with those questions? Well done.
Fantastic learning.
I am really impressed with how hard you are working.
We're gonna move on now and have a little bit of a look at problem solving.
Let's look at this problem.
The distance from London to Sydney is about 16,900 kilometres.
The distance from London to Birmingham is roughly one-hundredth times this distance.
Can you visualise that? Can you see London to Sydney and then London to Birmingham? One-hundredth times this distance, so it must be 100th times smaller, mustn't it? What might the question be though? We haven't got a question so far.
What bit of information are we missing? That's right.
How far is it from London to Birmingham? We know the distance from London to Sydney and we know the distance from London to Birmingham is one-hundredth times this distance, but we don't know how far that is yet.
So, Lucas is saying that sometimes, we can't draw our models to scale because we can't draw something that's 16,900 kilometres.
So, he's going to sketch this representation instead.
You can see he's sketched London to Sydney is 16,900 kilometres, but we don't know the distance between London to Birmingham, but he knows it will be smaller, and we can use this information to form an equation.
The distance to Birmingham is one-hundredth times the distance to Sydney, and to find one-hundredth times the amount, we need to multiply by one-hundredth.
We've got 16,900 multiplied by one-hundredth or 0.
01.
And we know multiplying by one-hundredth is the same as dividing by 100.
And we know when we divide by 100, the digits move two places to the right.
16,900 divided by 100 is equal to 169.
So, we can say the distance from London to Birmingham is 169 kilometres.
Let's check your understanding on that.
Which equations represent finding one-hundredth of 13,400 metres? You've got options A, B, C and D.
Pause the video while you have a think about each option.
Remember there could be more than one because equations is plural, and when you are ready, pause the video, and when you are ready to find the answers, press play.
How did you get on? Did you say, "Well, it can't be A because when we multiply by 100, well, that's getting greater isn't it?" And we want one-hundredth, so we shouldn't be multiplying by 100.
B? Well, we're multiplying by 0.
1, which is 1/10.
So, we're finding 1/10 times the size, and we need to find one-hundredth.
C is correct, isn't it? We need to find one-hundredth times the size, and we are multiplying by one-hundredth or 0.
01, and the digits will move two places to the right.
So, 13,400 metres made 100 times smaller is 134 metres.
And what about D? Well, that's right.
D is correct because multiplying by one-hundredth or 0.
01 is the same as dividing by 100.
How did you get on with that? Well done.
Let's look at a different problem.
Sofia measures the length of her pet snake.
It is 64 centimetres long.
Can you visualise that? What if you might have a pet snake? That's what I can visualise in my head.
I've got a snake and it's 64 centimetres from the top of its head to the end of its tail.
What might the question be, though? We haven't got a question yet, have we? Ah, what is its length in metres? We know it's 64 centimetres, but what is its length in metres? We can use our known facts.
We know there are 100 centimetres in one metre, and we can use that to help us.
One centimetre we can say is one-hundredth of one metre.
So, to convert, we can find one-hundredth times the length given in centimetres, and we could also divide by 100 because metres are larger so there will be fewer of them.
And we know dividing by 100 is the same as multiplying by one-hundredth.
And when we divide by 100 or multiply by 0.
01, one-hundredth, the digits move two places to the right.
So, 64 divided by 100 is equal to 0.
64.
So, we could say Sofia's snake has a length of 64 centimetres, and that is equivalent to 0.
64 metres.
Let's have a go at working together with this one.
I'm going to convert 35 centimetres to metres and I would like you to convert 76 centimetres to metres.
So, I'm going to start by dividing by 100 because there are 100 centimetres in one metre, and we need to divide because centimetres are smaller so there will be fewer metres.
And I'm going to divide by 100, which is the same as multiplying by one-hundredth.
And we know the digits move two places to the right.
35 divided by 100 is 0.
35.
So, I can say 35 centimetres is equal to 0.
35 metres.
Now, it's your turn to have a go.
Can you convert 76 centimetres to metres using the same structure that I have done? Pause the video while you have a go and when you are ready for the answers, press play.
How did you get on? Did you say, "Well, it's 76 that we're looking to convert, isn't it?" So, the first equation must be 76 divided by 100.
We know that's the same as multiplying by one-hundredth.
And we know when we are dividing by 100 or multiplying by one-hundredth, the digits move two places to the right.
So, 76 divided by 100 is 0.
76.
So, we can say 76 centimetres is equal to 0.
76 metres.
How did you get on with those? Well done.
It's your turn to practise now.
Could you for question one solve these problems for part A? The actual length of a triceratops was 9.
1 metres.
A toy triceratops is one-hundredth times this length.
How long is the toy? Could you give your answer in centimetres? For part B, Lucas has 34 pounds.
Sofia has one-hundredth times this amount.
How much do they have all together? And could you give your answer in pounds? And for part C, the mass of a banana is 125 grammes.
The mass of a grape is one-hundredth times this mass.
How much heavier is a banana than a grape? And give you answer in grammes.
For question two, is this true or false, and could you give me some reasons to convince me that you are correct? Lucas has 49 pounds.
Sofia has 49 pence.
Sofia has one-hundredth times the amount of money that Lucas has.
Pause the video while you have a go at both of those questions, and when you are ready for the answers, press play.
Shall we see how you got on? For question one, you had some problems to solve about, the first one was about the length of triceratops, and we know the toy triceratops is one-hundredth times the length of the actual triceratops.
So, we need to do 9.
1 multiply by one-hundredth or 0.
01, and we know that is equivalent to divided by 100.
And when we divide by 100, the digits move two places to the right.
9.
1 divided by 100 is equal to 0.
091.
So, the length of the toy is 0.
091 metres.
There are 100 centimetres in one metre, so we need to multiply 0.
091 by 100 to convert, and that equals 9.
1 centimetres.
For part B, Lucas has 34 pounds, and Sofia has one-hundredth times this amount.
I can use that information to form an equation.
34 multiplied by 0.
01.
We know that's the same as dividing by 100 and the digits move two places to the right.
34 divided by 100 is 0.
34.
So, Sofia has 0.
34 pounds.
Altogether, we needed to add their amounts up, and we have 34 add 0.
34, which is equal to 34 pounds and 34 pence.
For part C, the mass of the banana is 125 grammes and the mass of the grape is one-hundredth times this mass.
So, I can form an equation from that.
125 multiplied by one-hundredth.
Well, that's the same as dividing by 100, and the digits move two places to the right.
125 divided by 100 is equal to 1.
25.
So, the mass of the grape is 1.
25 grammes.
But we needed to work out how much heavier a banana is than a grape.
The banana is 125 grammes, so we need to subtract that 1.
25 grammes, and that is equal to 123.
75 grammes.
And so, the banana is 123.
75 grammes heavier than the grape.
For question two, true or false, what did you think? Is 49 pence one-hundredth times the amount that Lucas has of 49 pounds? Well, you might have said that it is true and reasoned that to find one-hundredth, we need to divide by 100, and when we divide by 100, all the digits move to places to the right.
So, 49 divided by 100 is equal to 0.
49 and Sofia does have one-hundredth of the amount that Lucas has.
She has 0.
49 pounds and that is equivalent to 49 pence.
How did you get on with those questions? Well done.
Fantastic learning today.
I am really proud of how hard you have tried, and when we try really hard, that is when we can be successful.
We have really deepened our understanding of this relationship between multiplying by 0.
01 or one-hundredth and dividing by 100.
We know 0.
01 can be represented as the fraction 1/100.
We know multiplying by 0.
01 is the same as multiplying by one-hundredth, and multiplying by one-hundredth is the same as dividing by 100.
So, multiplying by one-hundredth or 0.
01 must also be the same as dividing by 100, and we can use our stem sentence to support us.
One-hundredth of mm metres is mm hundredths of a metre, or mm.
Very well done today.
I have had great fun learning with you, and I look forward to learning with you again soon.
