Lesson video

Hello everyone, it's Mr. Millar here.

Welcome to the third lesson on percentages and in this lesson, we're going to look at "Converting from Fractions to Percentages." Okay, so first of all, I hope that you're all doing well.

And let's have a look at this Try This task so by first converting a fraction to a denominator of 100, we can write the fraction as the equivalent percentage.

So if we have a look at the first one, I know that 47 over 100 is going to be 47 percent because a percentage is something out of 100.

So to convert the other fractions to percentage, I'm going to need to make the denominator equal to 100, first of all.

So at the next one down, 11 twenty-fifths, I'm going to make the denominator change from 25 to 100.

So what do I have to do to the denominator here? Well, I have to multiply it by four.

So I'm going to have to do the same thing to the numerator.

Multiply that by four and 11 times by four gives me 44.

So 44 over 100 is just 44 percent, nice and straightforward.

Have a go at doing these for the rest of these questions.

Pause the video now and have a go.

Okay, great, so let's have a look at four-fifths.

So I, to go from five to 100, I times by 20, times by 20, so I'm going to have 80 over 100 or 80 percent.

To get from 20 to 100, I multiply by five.

So I'm going to have 55 over 100, 55 percent.

37 over 10, well, to get from 10 to 100, I'm going to have to multiply by 10 and 37 times by 10 is 370.

So it's going to be 370 percent.

And the next one, well, to get from 1000 to 100, I'm going to actually have to divide by 10 here.

So divide by 10.

So I get 3.

7 over 100, which is 3.

7 percent.

So you can see how easy this is, that when I, if I can change the denominator to 100, I can very easily find the percentage, but I cannot actually do this for all fractions.

So these fractions here I can.

Can you have a think about what is special about these fractions that allow me to change the denominator really easily to 100? Can you think what that is? Well, if you look at the denominators, you've got 25, 10, five, 20, and 1000.

1000's a little bit different, but still a similar thing.

So with all of these denominators, they are actually factors of 100.

So they go into 100, which makes converting the denominator to 100 really nice and easy because I can multiply it by a whole number.

However, if my denominator is not a factor of 100, let's say it's one over seven, then it's not as straightforward because seven doesn't go into 100.

It's not a factor of 100.

So I need to find out another way of doing this.

In the next slide, in the Connect slide, we're going to have a look at some examples of how we deal when the denominator, sorry, is not a factor of 100.

Let's have a look.

Okay, so here is the process for I'm converting from a fraction to a percentage, if we, if the denominator is not a factor of 100.

So the first one, one-third, I know that one over three is equal to one divided by three.

Now, I know how to do long division.

So if, for example, I asked you to do, I don't know, 465 divided by five, how would you do that? Well, you would set it up so that the five is outside the brackets here, and the 465 is inside here.

And then you would work it out.

So if you have one divided by three, where does the three go, and where does the one go? Well, if you have a look at the above example, you know that the three goes outside and the one goes inside like that.

Now three doesn't go into one.

So what I'm going to have to do is I'm going to have to create some more decimal points so that I can do this because now I can do three into 10.

So I put a zero here.

Three into 10 goes three times remainder one, and I've got three into 10 again.

That goes three times remainder one.

Three into 10 goes three times remainder one.

And I keep on going 0.

333333, et cetera, it goes on forever.

And this turns out, I can write this as a decimal.

If I've got 0.

3333 and it goes on forever, I can write that as 0.

3 recurring.

And this is what, this is how to write recurring.

I have the sort of a, a little point above the three.

That means that the three goes on forever.

0.

3333333.

So that is my decimal.

0.

3 recurring, and my percentage here, what do you think my percentage here is going to be? Have a look at the long division, and it's also going to need a recurring sign here, as well.

Well, if you have a look at the decimal, 0.

333, it's going to be 33.

3 and then we have the recurring above the three.

So 33.

3 recurring percentage is what one-third is.

Have a go at what you might do for one over six.

Have a go at one over six.

Well, again, this is one divided by six.

So I can write it as a six outside, a one on the inside, have some extra zeros, and now I do six into 10.

So I have zero point, and six into 10 goes one time remainder four.

And now I'm going to have six into 40, which goes six times with fours as a remainder.

Six into 40 again, six times with four as remainder, and we keep on going.

So my answer is going to be 0.

16666, et cetera, which I can write as a 0.

16 recurring with the recurring sign going over the six, because it's the six that keeps on going forever.

So as a decimal, 0.

16 occurring, and as a percentage, what do you think that's going to be as a percentage? If you haven't worked it out already? Well, it's going to be 16.

6 recurring percentage.

Okay, that is, that is all the Connect task I wanted to go through with you.

Want to, really, it might be a good idea to write down these examples.

So when you look at the independent task, you can come back to this for help if you need.

So when you're ready, let's move on to the independent task.

Okay, great, so here it is.

You have got eight questions to have a look at here, and you have a think about whether you can, first of all, convert the denominators to a, to 100, that would help you out.

But if you can't, you're going to need to use long division here.

So pause the video now, and have a go at these eight questions.

Okay, and when you're ready, let's move on to the answers, that, so here are all the answers.

Note that for the first four, you can convert them all to 100.

You don't need to convert the first one, but you can convert B, C, and D to 100.

You should notice a connection between your answers for E, F, and G; they are all recurring percentages.

And you'll notice that it's 11.

1 recurring, 22.

2 recurring, so that's an interesting thing there.

And then finally, for H, we've got three over eight.

So I can write that as three divided by eight.

And so I can complete this.

The eight goes outside, three goes inside, and I can fill in some extra zeros in case I need them.

Eight goes into, I have a zero point here, it goes into 30 three times, remainder six.

Eight goes into 60 seven times.

That gives me 56, so remainder four, and eight goes into 40 five times.

So I, I, I actually have 0.

375, which is, as you can see, 37.

5 percentage.

So when I use this method, this long division method, I don't always have a recurring decimal.

And actually, if you use this method for any of the ones in parts A to D, you would get the same answer, so if I looked at it for part B, for example, I do five outside and three inside.

That five goes into three zero times and five goes into 30 six times.

So I get 0.

6, which is 60 percent, so this long division method will always work, but you don't need to use it when you have a factor of 100 on the denominator.

Okay, great, when you're ready, let's move onto the Explore task.

Okay, so here is the Explore task today.

You have got to choose from the zero to nine digit cards to complete the equivalent fraction and percentage frame in five different ways.

So you can use the same digit card more than once.

So, but you need to use six of them, two on the top of the fraction, the numerator, two on the denominator, and then two make up the percentage.

So see if you can do it in five different ways.

It's a fun one; it's a bit of a fun one to explore.

So pause the video now and have a go at the Explore task.

Okay, great, so hopefully you found some that worked.

So for example, you could choose 25 in the denominator, and let's say 14 in the numerator.

And you can convert that to a percentage by multiplying both top and bottom by four.

14 times by four would give you 56 percent, so that would work for one of them.

So you could have 25 in the denominator, because that would give you a nice whole number as a percentage.

Or you could have 20 in the denominator.

For example, you could have 18 over 20, which would be 90 percent for example, or you could even have 50 in the denominator, as well.

It gets interesting if you say you can only use the digit card more than once.

So if I, if I said you can only use, use each digit card once, how many can you find? That would be interesting because for the first one, you couldn't actually have that because you're using the five here and the five here.

So you couldn't have that one.

So maybe I'll leave it up to you to see how many you can find if you can only use each digit card once.

Anyway, that is it for today's lesson.

I hope you've enjoyed it.

And I'll see you next time.

Thanks very much, and bye bye.