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Hello.
My name is Mr. Tilstone.
I'm a teacher.
I hope you're having a lovely day today, filled with success and happiness.
Let's see if we can make it even more successful and even happier by having a great maths lesson all about percentages.
If you're ready, I'm ready.
Let's begin.
The outcome of today's lesson is this: I can convert percentages to decimals and fractions with a denominator of 100.
Our key words.
If I say them, will you say them back, please? My turn.
Percent.
Your turn.
My turn.
Percentage.
Your turn.
What do those words mean? Percent means the number of parts in each hundred, and it literally translates to "for every hundred".
And a percentage is a proportion of a whole.
Our lesson today is split into two parts or two cycles.
The first will be writing percentages as fractions, and the second, writing percentages as decimals.
So let's start by writing percentages as fractions.
In this lesson, you're going to meet Aisha and Lucas.
Have you met them before? They're here today to give us a helping hand with the maths.
Aisha counts using 1/100, and she says, "I'm going to count in steps of 10/100." See if you can count along.
10/100.
20/100.
30/100.
Are you counting along? 40/100.
50/100.
60/100.
Keep going.
70/100.
80/100.
90/100.
100/100.
What could we say about 100/100? It's also the same as 1.
It's equivalent to 1.
One whole is equal to 100/100.
Aisha counts using percentages.
Count along.
She's going to count in steps of 10%.
Are you ready? 10%.
20%.
Right, pause there for a sec.
Is there anything that you've noticed so far? Hm? Let's keep going.
30%.
40%.
50%.
Stop there.
What could you say about 50%? Hm.
Keep going.
60%.
70%.
80%.
90%.
100%.
And what could we say about 100%? It's the same as one whole.
One whole is equal to 100%.
Aisha and Lucas compare fractions and percentages.
40/100 means 40 parts out of each 100.
40% also means 40 parts out of each 100.
So they're directly linked.
40/100 is equal to 40%.
They're exactly the same amount.
70/100 means 70 parts out of each 100.
What about as a percentage? 70% also means 70 parts out of each 100.
And the number lines help us to see that equivalence.
70/100 is equal to 70%.
Okay, let's have a little check.
The number lines are still there.
One is showing hundredths, one is showing percentages.
And the question is, what percentage is equal to 50/100? Pause the video.
The answer is 50%.
50% is equal to 50/100.
What else can we say about that? 50% is also equal to 1/2.
100 squares can also be used to represent fractions and percentages.
And perhaps you've got a 100 square in front of you now.
That's going to be a really useful tool if you have for exploring percentages.
There are 100 squares altogether, and 55 of them are shaded.
We could say 55/100 are shaded.
What else could we say? We could say this: 55% is shaded.
So 55/100 and 55% are the exact same amounts.
55/100 is equal to 55%.
They are equivalent.
What about now? What have we got here? There are 100 squares altogether, as before.
This time, 25 of them are shaded.
So we could say 25/100 are shaded.
And what else could we say? We could say 25% is shaded.
It's easy as that.
25/100 is equal to 25%.
25% is also equal to 1/4.
You can see 1/4 of that square is shaded.
What about now? What have we got here? Have a look.
There are 100 squares altogether.
This time, 72 of them are shaded.
Right, what can we say? How many hundredths is that? What percent is that? 72/100 are shaded.
72% is shaded.
So 72/100 is equal to 72%.
What about now? What have we got here? Well, we've got eight squares shaded.
There are 100 squares altogether.
Eight of them are shaded.
8/100 are shaded.
What about as a percentage? 8% is shaded.
It's as easy as that.
8/100 is equal to 8%.
Let's put that to the test.
Let's do a little check.
What fraction and what percentage is represented? Pause the video.
Well, I can see that 33 of those squares are shaded.
So 33 out of a hundred, so that's 33/100 are shaded.
Therefore 33% is shaded.
33/100 is equal to 33%.
And if you got that, well done.
You're on track and you're ready for the next part of the learning.
Aisha and Lucas find the missing numbers.
So, mm/100 is equal to 90%.
What do you think? 65/100 is equal to mm%.
What could it be? And then mm/100 equal to 5%.
Hmm.
90% is equal to 90/100, the same number.
65/100 is equal to 65%, the same number.
And then finally, 5/100 is equal to 5%.
Let's have another little check.
Who is correct? So have a look at that.
Mm/100 is equal to 2%.
Aisha says, "I think the missing numerator is 2." So 2/100.
Lucas says, "I think the missing numerator is 20." So 20/100.
So is Aisha right? Is Lucas right? Are they both right? Are they both wrong? What do you think? Pause the video.
Well, if it's 2%, then quite simply the missing numerator is 2.
It's 2/100.
So Aisha was correct.
2/100 is equal to 2%.
And well done to you if you got that.
It's time for some practise.
Number one, write the missing fractions and percentages represented by the 100 squares.
Number two, write the missing fractions and percentages.
And I predict you're going to work through that pretty quickly.
But let's find out.
Pause the video, and best of luck.
Welcome back.
How did you get on with that? Are you feeling confident? Are you feeling good about percentages? Let's have a look.
Let's give you some answers.
So for A, 80/100 is equal to 80%.
For B, 41/100 is equal to 41%.
And for C, 9/100 is equal to 9%.
And A, 60/100 is equal to 60%.
For B, 75/100 is equal to 75%.
C, 39/100 is equal to 39%.
D, 11/100 is equal to 11%.
E, 19/100 is equal to 19%.
F, 93/100 is equal to 93%.
G, 66/100 is equal to 66%.
H, 3/100 is equal to 3%.
And I, 100/100 is equal to 100%.
Well done if you got those.
I think you're ready for the next cycle.
In fact, I know you are.
And that's writing percentages as decimals.
Let's go.
100 squares can also represent decimal numbers.
So Aisha says, "1% of the 100 square is shaded." Would you agree? "Each square also represents 1/100." Yes, it does.
"1/100 can also be written like this, 0.
01." And that, by the way, can also be read as 1/100, or it can be read as 0.
01.
So 1% is equal to 1/100, which is equal to 0.
01, or 1/100.
What about this? What have we got here? Well, this time, 39% of the 100 square is shaded.
So that also represents 39/100, and that can be written as 0.
39.
And once again, that can be read as 0.
39, or it can be read as 39/100.
So 39% is equal to 39/100, which is equal to 0.
39.
They are all the same value.
Aisha and Lucas write percentages as decimal numbers.
See if you can predict what they're going to write before they write it.
So we've got 75%.
What could that be as a fraction? What could it be as a decimal? Well, "I know," says Aisha, "that 75% is equal to 75/100." Yeah, 75, 75.
And, "I know," says Lucas, that 0.
75, or 75/100, is equal to 75/100.
0.
75 is equal to 75/100.
What about this? 11% is a percentage, 11/100 is a fraction.
And the decimal? Now, we don't say zero point 11, do we? We say zero point one one.
So Lucas says, "I know that 0.
11 is equal to 11/100." and Aisha says, "I know that 11% is equal to 11/100." Let's see how you're getting on and if you're understanding this.
So the percentage is 66%.
What's the fraction and what is the decimal? Pause the video.
So that percentage, 66%, tells us that it's part of a whole.
So the fraction will too, it's part of a whole.
It's it's 66/100.
And the decimal will also show that it's part of a whole.
So a number less than one.
And that's zero point six six.
And remember, that's how we read it, not zero point 66.
So 0.
66.
And we could also read that as 66/100.
"66%," says Lucas, "is also equal to 0.
66." What happens if the hundredths column contains zero? Hm.
And this is a good example of that.
What can we see here? This is 50%.
50% is equal to 50/100.
Hmm.
This can also be written as 0.
50, which can be read as 50/100.
But what do you notice? "Hang on a moment," says Aisha.
"We don't need to write zero in the hundredths column." In maths, we keep things simple, and the zero makes no difference to the number, it's simply a placeholder.
So 50% is equal to 0.
5, and we could treat each of those 10/100 as 0.
1 and count it 0.
1, 0.
2, 0.
3, 0.
4, 0.
5.
0.
5 is equal to 5/10.
And 0.
5 can be read as 5/10.
0.
5 is also equal to half.
And hopefully you can see that there.
Half is shaded.
So 50% is equal to 50/100, which is equal to 0.
5.
So the lesson there is you don't need to write the zero on the end of that 0.
5.
Aisha counts using decimal numbers.
See if you can count along.
"I'm going to count in steps of 1/10," she says.
Lucas says, "Each step of 10% is equal to a step of 1/10, or 0.
1." So 0.
1, count along.
0.
2, 0.
3, 0.
4, 0.
5, 0.
6, 0.
7, 0.
8, 0.
9, and then 1.
So you can use that double number line to see the equivalence between percentages and decimals.
Aisha and Lucas compare the numbers.
So 30% we can see is equal to 0.
3.
90% is equal to 0.
9.
Let's have a check what amounts are represented by the 100 squares.
So two different amounts.
Can you say it in different ways? So which percentage is represented, and which decimal number is equal to the percentage? Pause the video.
Starting with that first one, then, you can count 70%, and that's to 0.
7, which we can read as 7/10.
So 70% is equal to 7/10, or 70/100 if you like.
And then this next one is 7%, and that's equal to not 0.
7 'cause that would be 7/10, but 0.
07, which is 7/100.
So 7% is equal to 7/100.
Percentages can be used to describe money too.
Aisha says, "There are 100 pennies in 1 pound.
1 pence is equal to 1% of 1 pound.
And Lucas says, "What percentage of 1 pound does each amount represent?" Let's look at that first one.
What percentage is that of a pound? So it's 50p, that's what it's equal to, and it represents 50% of one pound.
And what about the next one? What we've got here? Well, that's 73p, so that's 73% of 1 pound.
And what's about the final one? Perhaps a little bit trickier.
That's 3p, 3 pence.
This represents 3% of 1 pound.
Let's have a check.
Write each length as a percentage of 1 metre.
Pause the video.
Let's see.
So 0.
91.
Well, there are 100 centimetres in one metre.
One centimetre is equal to 1% of 1 metre.
So just like 1 penny is 1% of 1 pound, 1 centimetre is 1% of 1 metre.
So it might help to write each measurement in centimetres first.
So this is equal to 91 centimetres, and that represents 91% of 1 metre.
And 0.
19 metres, that's equal to 19 centimetres, or 19% of 1 metre.
And what about the last one? There's 7/100 of a metre there.
That's 7 centimetres, and that represents 7% of one metre.
Well done if you got those.
You're ready for some final practise, I can tell.
Number one, write the missing percentages and decimal numbers represented by the 100 squares.
So the first one, A, that's 17%.
What's that? Zero point what? And B, what percentage is that, and what decimal? This time, there's no clue there.
And the same for C.
And number two, "Complete the table".
So we've got some percentages, some fractions, and some decimals, so can you complete the equivalent trios? Write in the missing percentages, fractions and decimal numbers.
And number three, complete each statement.
And Aisha says, it's just a little reminder, "One pence is equal to 1% of a pound." And Lucas says, as a reminder, "One centimetre is equal to 1% of 1 metre." Pause the video, and away you go.
Welcome back.
How confident are you feeling about percentages and their equivalences? Well, let's give you some answers and you can check.
So, A, 17% is equal to 0.
17.
B, 36% is equal to 0.
36.
C, 90% is equal to 0.
9.
Now, if you wrote 0.
90, that's not incorrect, but we don't need that extra zero.
Number two, 77% is equal to 77/100, which is equal to 0.
77.
16% is equal to 16/100, which is equal to 0.
16.
30% is equal to 30/100, which is equal to 0.
3.
And 6% is equal to 6/100 hundredths, which is equal to 0.
06.
30% only needs to be written to one decimal place, so 0.
3 is just fine.
And 3.
A, that's equal to 45% of 1 pound.
B, that's equal to 99% of 1 pound.
C, that's equal to 86% of 1 metre.
D, that's equal to 27% of 1 metre.
E, 83 pence is equal to 83% of 1 pound.
And F, 0.
04, or 4/100 of a metre, is equal to 4% of one metre.
Then Aisha says, "For F, four centimetres is equal to 4/100 of 1 metre.
Zero is written in the 10th column of the decimal number to show there are no 1/10 of 1 metre." So that's really important.
That place holder is vitally important there.
We've come to the end of the lesson, and you've been brilliant, so well done you.
Today, we've been explaining how to convert percentages to decimals and fractions with a denominator of 100.
Percentages can be written as fractions with a denominator of 100.
Percentages can also be written as decimal numbers.
So we can create trios.
Percentages that are multiples of 10 are usually written to one decimal place, eg, 90% is equal to 0.
9, which we could read as 9/10.
Very well done on your achievements and your accomplishments today.
You've made good progress and it's been a pleasure working with you.
I hope you have a great day, and I hope to get the chance to spend another maths lesson with you in the near future.
But until then, take care, and goodbye.
