Lesson video

Hello everybody, my name is Mr. Kelsall, and welcome to today's lesson on understanding percentages alongside fractions and decimals.

Now before we start, you are going to need a pen, a piece of paper, and somewhere quiet where you're not going to get disturbed.

Don't forget to remove any sort of distractions, for example put your mobile phone on silent or move it away completely.

Pause the video, and then when you're ready, let's begin.

Today's lesson is on understanding percentage as a fraction and as a decimal.

We're going to start by linking fractions and decimals.

We'll then be looking at identifying halves, quarters, and fifths as a percentage.

We'll then look at percent in context, and then it's quiz time.

Now I've mentioned already, you need a pencil and a piece of paper, and our star words for today are 'per-cent', which means 'per one-hundred'.

We'll use the percentage symbol.

We'll talk about divided and division.

We'll talk about equal parts.

We'll refer to fractions and decimals, and we'll talk about hundredths, and we'll also talk about how fractions can be equivalent.

Quick bit of revision, you know that 'cent' means 'one hundred', so 'per-cent' means 'per 100'.

Have a look at the task on the screen.

It says, "Complete the missing gap." One-half is equal to something over 100, is equal to something percent.

Pause the video.

When you're ready, press play to continue.

Well I've used my bead string to work out this, and if I remember, my bead string is 100 beads long.

If I count one, two, three, four, five.

.

.

One, two, three, four, five.

I know that halfway between 100 is 50.

So I know that half must be equal to 50 parts of 100, and I know that half is 50 percent.

And then ask, what is 50 percent as a decimal? Now if I remind myself about the place value, and how the number system works, I'm thinking that 50 parts of 100, well, what is that as a decimal? How many ones do I have? I don't have any ones.

How many tenths do I have? I have five tenths.

And I have zero hundredths.

So as a decimal, I know that 50 hundredths, or one half, is null point five zero.

However, if I think about this, this zero on the end doesn't actually mean anything.

It means I've got zero hundredths.

I could write zero, zero, zero.

It would stay exactly the same value.

It just has zero value.

So, actually, I can just write this as zero point five.

There's another way I can find out what decimal 50 percent is as a decimal.

I know that 50 percent is one-half, and one-half means one divided by two.

So let's try and do this.

Well how many twos go in one? I can't do that.

So I'm going to put zero.

I'm going to extend into my decimals, so I'm going to carry over my one.

How many twos go into 10? Five.

So straight away, I've used two methods to prove that 50 percent is the same as null point five as a decimal.

Let's see if you can have a go at using those two methods, and this time, can you transfer out 25 percent as a decimal, and 20 percent as a decimal? Pause the video, and then when you're ready, press play to continue.

Okay, one quarter.

Well my bead string has been cut into half, and then it's been cut into quarters.

And I can count on my bead string.

I've got 10, 20, five.

So I've got 25 out of 100.

So one quarter is equal to 25 out of 100, and I know that is 25 percent.

What's that in my place value? Well, if I draw out my place value grid again, I've got zero ones, I've got two tenths, and I've got five hundredths.

So 25 percent is null point two five.

I can do the same method as I did before.

I can say well what is one divided by four? I know I'm going to go into my decimals, so I'm going to add my decimals there.

How many fours go in one? Zero.

Carry the one.

How many fours into 10? Four, eight, goes two, and there's two leftover.

How many fours into 20? Four, eight, 12, 16, 20, goes five times.

So I know that one quarter is equal to null point two five.

Let's repeat that with one fifth.

This time, one fifth splits my beads into five parts, and in each part we're at 10, 20.

So one fifth is 20 out of 100, and I know that's 20 percent.

If I look at my place value, I'm asking myself how many ones do I have? Zero.

How many tenths I have? Two.

How many hundredths? Zero.

Now, like before, I can write this as null point two zero, null point two zero, zero, zero, but actually it's best just to write it as null point two.

And again, like before, I can ask myself well, what is one divided by five? I'm going into my decimals.

I like my decimals.

How many ones and five> Zero.

Carry the one.

How many five? I'll say that again.

How many fives in one? Zero.

How many fives go into 10? Two.

So again, I know that I have proof that one fifth is equal to null point two.

I know that one fifth is equal to 20 percent.

I know one fifth is equal to 20 over 100.

So just to recap, 25 percent as a decimal is null point two five.

As a fraction is one quarter, or 25 over 100.

20 percent as a decimal is null point two.

As a fraction is one fifth or 20 over 100.

So just to remind you that one bead is one part out of 100 equal parts, and so it's one percent of the whole bead string.

10 beads are 10 parts out of 100 equal parts, and so it's 10 percent of the whole bead string.

When we're looking at hundred grids, it's exactly the same.

One square is one percent out of 100 equal parts, and so it's one percent of the whole hundred grid.

And 10 squares are 10, 10 squares are 10 parts out of 100 equal parts, and so it's 10 percent of the whole hundred grid.

Now, have a look at these below.

What fractions, decimals, and percentages can you represent with your hundred grid? I will go through one or two, and then I'll let you explore some others.

Well, if I start with three quarters, I'm going to take my hundred grid and I'm going to split it into half, and then into half again.

And I know that I have quarters there, and if I've got one quarter, two quarters, three quarters, how many squares do I have, and therefore what's that as percentage? What's that as a decimal? Well, I know I've got one, two, three, four, five, by one, two, three, four, five.

So that's a five by five.

It's 25, 50, 75.

So I can say that three quarters is equal to 75 over 100.

And because I've got 75 of 100, I can go back to my place value.

I can say, well, how many ones do I have? Zero.

How many tenths do I have? Seven.

How many hundredths do I have? Five.

So I know that three quarters as a percentage is 75 percent, as a fraction is 75 over 100, and as a decimal is null point seven five.

If I look at the next one, six tenths, there's a few different ways I can do it.

I can do it on my hundred grid, and I can say well let me just do one tenth, two tenths, three tenths, four tenths, five tenths, six tenths.

So I can say that six tenths is equal to 60 parts out of 100.

And I can convert to a decimal, and I know that how many ones have I got? Zero.

How many tenths? Six.

How many hundredths? Zero.

So I don't need to write my zero, so six tenths is equal to null point six.

I know because I've shaded 60 parts out of 100, it's 60 percent.

I could also look at it on one of the other grids.

For example, my first grid, I have five equal parts.

Well, that doesn't help me.

So if I split this into two, I've now got 10 equal parts, and I want one, two, three, four, five, six of those 10 parts shaded.

I can look at it that way, and then I can revert back and say well actually, I've shaded three parts out of five, so six tenths is also equal to three fifths.

Okay, pause the video and have a look at the examples on the screen and see if you can explore what the rest of the fractions would be as a fraction out of 100, as a percentage, and as a decimal.

When you're ready, press play to continue.

And that brings us to our develop learning board today.

How many different ways can you explain that one fifth of the shaded shape, sorry, one fifth of the shape is coloured red? Pause the video.

When you're ready, press play to continue.

Okay.

So I'm thinking I've got one, two, three, four, five parts, and in total, I've got one, two, three, four, five, 10, 15, 20, 25.

So I've got five parts out of 25.

Well, what would that look like on a hundred grid? I could do my five parts in exactly the same shape, so in total, I've got four, eight, 12, 16, 20, so I know that five twenty-fifths is equal to 20 hundredths.

Think about that for a moment.

How have I found that equivalent fraction? If I multiply five by four, I get 20, and if I multiply 25 by four, I get to 100.

So I'm thinking about equivalent fractions.

Let's have a look in a different way.

I could move all these squares to here, and if I represented the same thing on the hundred grid, I now know that I've got 20 parts out of 100.

I also know I could split this equally into five parts, so I can say, well, I have one part out of five parts shaded.

So I know I've got one fifth.

Don't forget that I can still convert this to a decimal and a percentage.

If we start with one fifth, I know that means one divided by five, and I can say, well, how many fives go into one whole one? Zero.

So we'll carry the one.

How many fives go into 10 tenths? Well, goes two times, so I know one fifth is equal to null point two as a decimal.

I know that one fifth, if we remember, was equal to 20 over 100, which is 20 percent.

There are other ways, too.

Okay, in front of you, there are a list of fractions, decimals, and percentages that you need to know.

I divided them into a few different categories because some facts, you need to know, and some, you can work out from a fraction already.

So you need to understand that 100 percent is one whole one.

As a decimal, it's one, or one point zero.

As a fraction, it's one-one or one whole one.

If you half 100 percent, you get 50 percent.

As a decimal, 50 percent is null point five, and as a fraction, it's one half.

Don't forget, it's also 50 out of 100 and other equivalent fractions.

Now, if you know 50 percent, you can work out 25 percent because you can work out half of 50 percent is 25 percent.

Half of null point five is null point two five 'cause I can think what's half of null point five zero? Well, that's null point two five.

As a fraction, it's a quarter.

It's also 25 out of 100.

And if I know 25 percent, I then know 75 percent because it's just three times as big.

So 75 percent is null point seven five as decimal, and it's three quarters as a fraction.

Don't forget it's 75 out of 100 as well.

So these are the ones you normally learn first.

You normally learn 50 percent, 25 percent, 75 percent.

We then extend that to 20 percent.

So 20 percent is equal to null point two, and it's one fifth, or it's 20 out of 100, and if you know 20 percent, you can work out 40 percent, 60 percent, 80 percent, and so on.

Take a moment.

Pause the video, and spend some time memorising, learning, and using these facts.

When you're ready, press play to continue.

We can also look at using calculations within fractions, decimals, percentages.

So I've got an example here.

I've got two fifths, Add on 50 percent.

And I need to think how I can do this.

Now, I can convert them all to fractions, all to decimals, or all to percentages, whichever you feel most comfortable doing.

Let me show you all three, so you can see them.

'Kay.

Two fifths add a fraction.

50 percent as a fraction is one half equals what? Now, if you can't add fractions, that's absolutely fine.

You can convert them to decimals or percentage.

Let's try decimals next.

What's two fifths as a decimal? It's null point four.

What's one half as a decimal? Null point five.

I can add them together to get null point nine.

So sometimes you'll notice that fractions might seem quite difficult whereas decimals might seem quite easy.

Let's do the same thing with percentage.

Two fifths is 40 percent, and I'm adding on 50 percent, which gives me 90 percent.

Again, percentages, like decimals, in this case, is quite easy, and it's an easy number to work with.

Well since we've done found decimals quite easy last time, let's continue to use decimals.

I'm going to do null point two five, and I'm adding on null point.

.

.

And what's three fifths as a decimal? As one fifth is point two, two fifths is point four, three fifths is point six, so I'm adding on null point six.

Now some people add this up, and they get null point three one, and that's incorrect because what they've done is they've added the six to the five to give them one, and carry the one, which gives them 31, so they think 25 add six is 31.

However, that's incorrect.

I'm about to show you how to add this up in column addition, and I can add my null point six.

Do you remember we talked about our place holder before? Well, I'm going to put a placeholder in there.

That zero means nothing, but it helps us add up correctly.

So five add zero gives us five.

Two add six is eight.

Zero and zero is zero.

So null point two five add on null point six gives us zero point eight five.

In the same way, I can add my percentages.

25 percent add on 60 percent gives me 85 percent, and you can see with this time, actually, percentages are a little bit easier than decimals because I'm not confusing the, the place value of the six.

So you might find that percentage is easier on this occasion.

Let's have a look what it is as a fraction.

I'm adding one quarter add three fifths.

Now I know that to add these fractions, I need to convert and find the common denominator, and that's going to be quite complicated, so I'm not going to look at adding fractions at the moment.

Just want to give you one example of where adding a fraction might be relatively easy.

If I have two fifths add on one fifth, I know that that gives me three fifths, and that might be a little bit easier than saying null point four add null point six, sorry, I've made a mistake there, haven't I? Not null point six.

It's null point two.

So null point four add null point two gives me null point six.

Now you might find that fractions are a little bit easier there, but you decide which is most appropriate.

And now it's time for our independent task.

Look at the questions on the screen, and complete the calculations.

When you're ready, press play to continue.

So I've given most of my answers in percentages.

Converted everything to percentages, and the first one is 75 percent, 75 percent, 85 percent, 70 percent, 75 percent, 70 percent, 125 percent, and I'll come back to this, zero percent, and 75 percent.

Something to be aware of.

Many people think that 100 percent is the maximum thing that you can have.

Whereas actually, you can go above 100 percent, and this is quite common if you're saying that the prices increased by something.

So for example, house prices.

Let's say you buy a house for 100 pounds, and the price increases, and it's now worth 225 pounds.

That is an increase of 125 percent.

So most of the time percent is within 100, but sometimes it can be above 100.

Congratulations on completing your task.

If you'd like to, please ask your parent or carer to share your work on Twitter, tagging @OakNational and also #LearnwithOak.

And before we go, please complete the quiz.

So that brings us to the end of today's lesson on understanding percentages alongside fractions and decimals.

A really big well done for all the learning that you've achieved.

Now, before you finish, perhaps quickly review notes and try to identify the most important part of your learning from today.

Well, all that's left for me to say is thank you, take care, and enjoy the rest of your learning for today.