Lesson video

Hi, my name is Mr. Chan.

Today we're going to learn about simple percentages without a calculator.

Let's begin by looking at a bar model representing 100%.

If we were to split that bar model up into two equal pieces, let's think about what percentage that portion there would represent.

Well, we split the 100% bar model up into two, so, 100% divided by two, that would represent 50%.

So, in order to find 50% of an amount, we can think about halving or dividing by two.

Let's again think about, starting with the bar model representing a 100%, but this time we're going to split that up into four equal pieces.

So, what percentage would each piece there represent? Well, what we've done is split the 100% up into four, so, we would do 100% divided by four, and that gives you 25%.

So, what we found there is splitting up 100% and dividing that by four would be 25%, and we can think of 25% as being 1/4.

In this example, again, we're going to start with 100%, and we are going to split it up into 10 equal pieces this time.

So, what do you think the percentage represented in that portion of the bar model is now? So, to work that out, we can do the calculation, 100% divided by 10, and that would give us 10%.

So, what we can think of as when we try and work out 10% is, is 1/10 or simply dividing by 10.

Now, let's look at an example of finding a percentage of an amount.

Let's start with 120.

If we were to find the percentage of an amount of 120, let's think about what percentage this part of the bar model it would represent.

Well, we split that up into 10 equal pieces, so, that would represent 10% as we've covered previously.

So, in order to find 10% of 120, we can simply divide by 10.

So, 10% of 120, we can work out as 120 divided by 10 that would equal 12.

So, 10% equals 12.

Now.

we can use that to find further percentages of 120.

So, for example, if we wanted to find 20%.

If we know 10%'s amount, then we can simply double that to represent 20% like so.

20% of 120 would be the 10% value, in this case 12, multiply that by two, so, 20% would equal 24.

Here's some questions for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here are the answers for the first question.

You'll notice that all of the questions revolve around finding percentages of £150.

So, hopefully as you moved through the questions, you did use previous answers to help you.

So, for example, in part a and part b, you found 50% and 25%.

You could have used those by adding them together to find the answers to part c, 75%.

Because you know that 50 add 25 gives you 75.

Hopefully you got all those correct.

Here's another question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answers to this question.

This question poses a very common mistake people make with percentages, because they understand that to find 10% of a number, you would divide the amount by 10.

However that doesn't work with other percentages.

Think about finding 50% for example, you wouldn't divide by 50, you already know you divide by two.

So, Mia's wrong when he says to find 5% of a number, you divide by five.

In fact, if you do divide by five, you're actually finding 20% of that number.

Let's look at how we can understand percentages in a little bit more detail.

I've got 10 by 10 grid there, 100 squares.

We can say that represents 100%.

If we take one little square there, we can say that that would represent 1%.

So, what we've done there is we've divided the 100% up into one single square by dividing by a hundred.

So, what that tells us is, in order to find 1%, we can split that up by dividing by a 100.

If we know 1%, how would we find 7%? Well, to get from 7% we could just simply multiply the 1% by seven.

Similarly, if we wanted 95%, we could multiply by 95.

However, look at the portion that's not shaded there, we could simply find 5% and subtract that off the 100%.

So, that's lots of different ways we can find percentages, and sometimes your method may not correspond to somehow somebody else has found a percentage, but hopefully your answers will agree.

Let's look at this example.

We're told that 5% of 620, equals 31.

So, we're asked the question, find 20% of 620.

So, we already know from the card that 5% of 620 equals 31, but we have to find 20%.

Well, if I multiply 5% by four, that five multiply by four gets me 20.

So, it must be straightforward to multiply the 31 amount by four as well, to give me an answer 124.

So, we've used the information given to actually find what 20% of 620 is, and that would equal 124.

Here's some questions for you to try.

Pause the video to complete your task, resume the video once you're finished.

Here are the answers for question three.

Hopefully you've used all the information given.

Let's look at a few of these.

In part a, 3% of 1,020.

Well I'm told that 1% of 1020 equals 10.

2.

So, in order to find 3%, I just need to multiply that amount by three.

So, 10.

2 multiply by three gives me 30.

6.

In part b, I must find 3% of 781.

What information have I been given about 781? I'm told that 6% of 781, equals 46.

86.

So, what link does 3% have with 6%? Well, 3% is just half of the amount.

So, in order to find 3% of 781, I just simply need to divide 46.

86 by two.

46.

86 divided by two, equals 23.

43.

Here are some more questions for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here are the answers.

Question four is quite interesting because we're told that Ms. Hall has £700 in her bank account, and she spends 45% of her money on rent.

We're asked how much money does she have left? So, you could approach this question by finding 45% of £700, and then subtracting that amount from the £700 to give you an answer.

How many of you actually thought about finding 55% of £700? Because that would represent how much money she has left.

That's all for this lesson.

Thanks for watching.