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Hello everyone, it's Mr. Millar here.

Welcome to the sixth lesson on percentages.

And in this lesson, we're going to be looking at decimal multipliers.

So first of all, I hope that you're all doing well.

And let's have a look at the Try this task.

So you've got nine different kinds of mixtures or a mixture of percentage, fractions and decimals.

So your job is to find the equal values and then suggest some equivalent values if there are any which are not matched.

So pause the video and see how many matches you can find here.

Okay, great.

So let's go through some of these.

So first of all, you might notice that 50% and 5/10 are the same thing.

So that is one match.

Next you've got 23% and 23/100.

So that is going to be a second match.

And then 20% is the same as 0.

2.

So that is a third match.

And we can have a look at some of the other ones.

So 8/40, if I cancel that down, that is going to be 4/20, which is 1/5.

So actually that is going to be the same.

That's going to be another match for a 0.

2 and 20%.

Great, so next is if there are a couple of unmatched values.

So 0.

25.

We can think of that in a number of different ways.

That is 25% or it is 1/4.

And then 5/40.

Well, I can cancel that down to be 1/8.

And I know that as a decimal, that is 0.

125.

And as a percentage, it is 12.

5%.

You should know that 1/8, is 0.

125, but if you didn't, you could use long division, which we used a couple of lessons ago.

So that eight goes into one.

So it's going to be eight into 10 goes one time.

Remainder two.

Eight into 20 goes twice, remainder four.

And then you have 0.

125, but you should just know that 1/8 is equal to 0.

125.

Okay, great.

So I hope that this was a good reminder of some of the fractions, decimals, and percentages conversions that we've been doing over the last few lessons.

Now let's have a look at the next thing, the Connect task.

Okay, so let's have a look at the question.

Jack and Eloise are working out 30% of 220 and this problem and the diagram on the left-hand side is exactly the same as what we were doing last lesson.

So let's just recap how we did that.

Well, first of all, to find 10%, what do we need to do? Well, of course, we need to divide 220 by 10.

So divide that by 10.

And that gives me 22.

And then how do I find out what 30% is? Well, I'm going to need to multiply that by three and I get 66.

So that is doing it in two steps.

Finding out 10% first, and then timesing by three to get 30%.

But it turns out that if you actually look at the diagram on the right-hand side with the orange arrow, you can get 30% in just one step using what we call a decimal multiplier.

Let's find out how we get that decimal multiplier.

Well, first of all, instead of doing 220 divided by 10 times by three, we could just swap that around and do 220 times by three first and then divide by 10.

You would agree with me that that is not going to change the value of our answer.

Well, what's next? Well, if we just have a look at this three divided by 10, you should know that three divided by 10 is the same thing as three-tenths or 3/10, which as a decimal is equal to, what does is that as a decimal going to be? That's right, 0.

3.

So actually we can work out 30% of 220 in just one step by using a decimal multiplier.

This is 0.

3.

And if we put into our calculator 0.

3 times by 220, we would get the same answer as 66.

And it turns out that, as long as we have a calculator, this is a really useful method because it saves us a lot of trouble.

So let's have a look at two more examples.

How would we find 70% of 220? What we're going to have to do, 0.

7 times by 220.

And the reason is because 70% as a decimal is 0.

7 because it's 70/100.

What about 37% of 164? What we would do is we would do 0.

37 times by 164.

And we put that into our calculator and that's it.

We get the answer.

And this is so valuable because if we were to do 37% of 164 using the method that we looked at last time, that would take quite a long time.

'cause we'd have to work out 10% and then 30% and then 1%, and then 7% and add it all together.

And it would just take a long time.

And it turns out that this decimal multiplier is really useful because we can just do it all in one go.

So let's have a look at the independent task.

We're going to see some more examples.

Okay, so make sure that you have a calculator on hand to help you do this.

You might have one in front of you, but most phones and computers also have a calculator function so you should be able to do it on your phone or your computer if you don't have a calculator with you.

Even if you don't have a calculator, you can still do the calculations.

So the first one, 40% of 17 is going to be 0.

4 times by 70 because 40% as a decimal is 0.

4.

Pause the video now and have a go at the remaining answers.

And if you have a calculator, go ahead and work out the answers.

Pause the video now for a couple of minutes to do this.

Okay.

And let's have a look at the answers then.

Okay, great.

So here are the answers then.

Well done if you got these and it's just worth going over the last one here, 145% of 94, because if we think of 195%, that is going to be, 145%, sorry.

So it's going to be 145/100, and I know that if I divide by 100, I move two decimal places back.

One, two.

So I get 1.

45.

So that is why it's 1.

45 times by 94.

Great.

Let's move on to the final slide of today, which is a nice one.

It's the Explore task.

So for the Explore task you need to think how many different ways can you work out 25% of 300.

So I am pretty confident hopefully that you can work it out, but over the last few lessons, we have learned a number of different ways to do it.

So there are some suggestions in the boxes.

Pause the video to see how many different ways you can work out 25% of 300.

Okay.

So let's go through these.

First of all, you could draw 25% of 300 as a bar model because you know that 25% is equal to 1/4.

So you could split 300 into quarters here.

And so the whole thing is 300.

So to find out what 1/4 was, you could do 300 divided by four, which would be equal to 75.

So each of these bars would be 75.

So that's the first method.

The next method to work out 25% of 300, I start by calculating 10%.

Yeah, I could do this as well.

So 10% of 300 would just be 30.

So I need to find out what that 25% of it is.

So I could do 20% next, which would be double 30, which would be equal to 60.

And then what have I got left? Well, I got 5% left and that is equal to 15.

So I just add 20 plus five, 25%.

And that would be 75.

The final way.

I could use a decimal multiplier.

This is what we did in today's lesson.

And that is just going to be 0.

25 times by 300.

And I didn't even need a calculator for this.

It's worth saying that you can use your knowledge of place value.

So this is equivalent to, imagine moving the decimal place forward to here, moving it back to here.

This is equivalent to 25 times by three, which is equal to 75.

So a number of different ways that we have worked out how to find the percentage of an amount.

You should feel confident with all of them.

But the good news is that usually if you're doing this on a non-calculated paper, you would use the second method here.

It's nice and straightforward, but whenever you have a calculator, always just use the decimal multiplier because it's really quick and straightforward.

That is it for today.

And next lesson, we're going to be looking at increasing an amount by a percentage.

Thanks very much for watching.

Hopefully you've enjoyed this video.

And I will see you next time.

Thanks very much.

Bye bye.