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Hello and welcome to another video.

In this lesson, we'll be looking at equal and non-equal priority.

My name is Mr. Maseko, and before you start this lesson, make sure you have a pen or pencil and something to write on.

Okay, now that you have those things, let's get on with today's lesson.

First thing, try this activity, pause the video here and give this a go.

Okay, now that you've tried this, let's see what you have come up with.

So I'm going to use the numbers two, three and four once to fill in the calculation frames.

What different calculations can you make? Well, we could say, let's say we could have two times three, add four.

Or you could have two times three add four.

Now, how many different answers are possible? Well, that all depends on the order that you write this in.

Now, in this one, two times three add four, the multiplication gets done first, two multiply by three, that gives you six, add four, that gives you 10.

Whereas here, we do what's in the brackets first, So three add four, that gives us seven, and then two multiplied by seven, that gives us 14.

Now, we're going to be talking about this idea that some operations like multiply have priority over other operations like addition.

But when we use brackets, we can give priority to other operations that would otherwise not have priority.

So if we look at this, this are all the different answers we could have gotten by using the numbers two, three and four.

What you'll notice is that some of the answers are repeated.

Now this is due to the fact that multiplication and addition are commutative.

So if you look at the repeated ones, so two multiplied by three is the same as three multiplied by two.

And two multiplied by four is the same as four multiplied by two.

We've just written them the other way around.

Multiplication is commutative, so whether you write two times four, or four times two, that's the exact same thing.

Same thing with addition, whether we write three add four, or four add three, that is the same thing.

That is why some answers are repeated.

So really, they're only what one, two, three, four, five distinct answers for these calculations.

Now, let's look at some function machines.

We can represent what happened, what we're doing in these calculations using function machines.

Now, if we look at this first calculation, so two multiply by three, add four.

So we start with the number two, we first multiply by three and then add four, for our final answer of 10.

Plus two multiplied by three, that gives us six, six add four is 10.

Whereas in this calculation, three add four, well, that gives us seven, and seven times two, well, that gives us 14.

Now, if you look at this, on that second calculation, we need to use brackets whereas in the first one we don't.

Why is that? Well, that's because when we talk about priority of operations, if we look at this calculation, we do multiplication first, because multiplication always has priority over addition.

So you always do multiplication first, before you do addition or subtraction, you first do multiplication and division.

So it's just a priority that is set.

But if you want to do addition before multiplication, you have to use brackets to show that you want to do that first.

That is why some calculations need brackets whereas others don't.

There is no point in let's say doing this.

Because this, adding those brackets has not changed the order you are going to do things.

Because you're always going to do multiplication first, so that is an improper use of brackets.

You only use brackets to give priority to operations that would otherwise not have priority.

Let's look at some other function machines and see what we can do.

Well, if we look at this function machine, these are some cards that we can use.

Now, how many different function machines can you make? Which function machines would give the same answers? When do function machines give different answers? And can you write each function machine as an equation? As an example we could do, put, add six here and then take away four.

So we can write 12 add six takeaway four.

12 add six, well, that's 18, takeaway four that gives us 14.

So that's one way we could do this.

Now, what other way can you arrange these cards? Pause the video here and give this a go.

Okay, now that you've tried this, let's see some of the calculations you could have come up with.

Well, if you look at these, these are all the different calculations you could have come up with.

I want you to pay particular attention to the ones that give the same answers.

What do you notice? Well look, when you just have a mixture of addition and subtraction, it doesn't matter which way they're written because these have no priority over each other cause they would give the same answer at the end.

So when you have a mixture of addition and subtraction, there is no priority.

So it doesn't matter which way you write these.

It's the same thing when you have multiply and divide only.

Whatever way you write them, you'll still get the same answer.

So these also have no priority over each other.

But when things start being different is when you mix a multiply sign with an addition or with subtraction, or a divide sign with an addition or a subtraction.

Now, when you start mixing multiplication with addition and subtraction or division with addition and subtraction, then order matters.

Because depending on which order you do the operations in, the answers will be different.

Look at this, if we do 12 take away four which is eight, times three gives us 24.

But if we do 12 multiply by three first, that's 36, take away four, that gives us 32.

We've used the same numbers, but the order we've done the operations has changed our answer.

Now, because multiplication has priority over subtraction, we have to use brackets, see, now we've used brackets to show that we want to do the subtraction first.

When you've mixed multiplication with addition and subtraction, or division with addition and subtraction, order matters.

The order you do the operations matters because the answers will be different and one operation will have priority over the other one.

So how do we use brackets? We use brackets to give priority.

Let's read it again, that's here.

So remember, we use brackets to give priority to operations that would otherwise not have priority.

Now, here's an independent task for you to try.

Pause the video here and give this a go.

Okay, now that you've tried this, let's see what you've come up with.

Well, two multiply by three add seven.

Well, two times three those first, so that's the six, add seven, that should give you 13.

Four multiplied by five take away three.

Well, the five take away three has priority.

So five take away three, well, that gives us two.

And then four times two that gives us eight.

And then eight divided by four times two.

Remember, division and multiplication have no priority over each other, so eight divided by four is two, times two, that gives us four.

Or eight divided by four add four, division has priority.

Eight divided by four is two, add four that gives us six.

Here, the four add four now has priority.

So that gives us eight, then eight divided by eight is one.

Do you see what's happened? When we added the brackets, we gave priority to the addition which changed the answer we got.

Now for these questions, we're adding brackets to make this true.

Remember, we use brackets to give priority where priority would otherwise not be given.

So we want to give priority to the three add five.

So that will give us two multiplied by three add five, that is eight, so two times eight is 16, good.

And then here, well, we're going to give priority to the two add three and priority to the four add five, and that is five multiplied by nine, which gives us 45.

So now that's true.

Now here's an explore task.

Consider each of the following statements and equations.

Decide for each if it is always, sometimes or never true and explain your answer.

Now, pause the video here and give this a go.

Okay, now that you've tried this, let's see what you've come up with.

Well, it's one add four divided by two always the same as one add four first then divide by two? Well, no, because on this side, we have to do four divided by two first, that would give us two, and then one add two, that would be three.

Whereas on this side, the brackets give priority to one add four, one add four would be five, and five divided by two, that will be 2.

5.

So that is never the case because we've mixed addition with division, so the order we do the operations in matters.

When you mix addition with multiplication or division, or subtraction with multiplication and division, order matters, because one operation has priority over the other one.

Now let's look at this, triangle add square take away diamond, square take away diamond add triangle.

This is just addition and subtraction, does it matter which order we do them in? No, because there is no priority.

So this one is always true, because there is no priority given to addition over subtraction.

And now this, a multiplied by seven add three is the same as 10 multiplied by a.

Well, if we look at the left hand side, what we do first? What we do is seven add three first, so that is 10.

And a multiplied by 10, well, that is always the same as 10 multiplied by a.

Remember, multiplication is commutative, so you can write it in either order and it's the same answer.

So this one is always true.

That is always true.

And then this last one, it goes five divided by a is equal to a divided by eight take away three.

But what is eight takeaway three? Well, eight takeaway three is five.

So is five divided by a the same as a divided by five? Is there a scenario where that would be true? Well, let's put some numbers in there.

Let's say one, if a was one, what's five divided by one? Would that be equal to one divided by five? Well, no, it's not.

Remember, division isn't like multiplication.

Division, no it's not, because division is not commutative.

Multiplication is commutative, you can write it in either order, but division isn't.

Five divided by one is five.

One divided by five, well, that is 0.

2.

Not the same thing.

But is there a number that would give us the same answer? Well, yes, if a was equal to five, that would be five divided by five, which is equal to five divided by five.

So this is sometimes true.

So this one, this one is sometimes true.

And it's only ever true when a is equal to five.

Okay, now really well done if you've got any of those answers, and you're getting quite good at this.

Just exploring with different numbers and just trying different things and we'll do more of this orders of operations stuff in the next few lessons.

Now, if you want to share anything you've done today, ask your parent or carer to share your work on Twitter tagging @OakNational and #LearnwithOak.

Thank you for participating in today's lesson.

Bye for now.