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Hi, everyone.

My name is Ms. Coo, and I'm really happy to be learning with you today.

It's going to be fun and really interesting lesson, and I'm so excited to be learning with you.

You'll come across some new keywords and maybe some keywords you've already come across before.

Now we're going to work really hard today, but I am here to help, and we can learn together.

In today's lesson from the unit arithmetic procedures with integers and decimals, we'll be looking at the priority operations with positive and negative integers and decimals.

By the end of the lesson, you'll be able to calculate using the priority of operations, including brackets, powers, and exponents, with positive and negative integers and decimals.

So let's have a look at some keywords, starting with the additive inverse.

Remember, the additive inverse of a number is a number that, when added to the original number, gives the sum of zero.

For example, eight is the additive inverse of negative eight, and negative 4.

5 is the additive inverse of 4.

We'll also be looking at commutativity.

In other words, an operation is commutative if the value it's operating on can be written in either order without changing the calculation.

For example, negative three add four add 10 is exactly the same as 10 add negative three add four.

Today's lesson will be broken up into two parts.

First, we'll be looking at the priority operations with negatives, and the second part is where we'll be looking at the priority operations with negatives and decimals.

So let's make a start on the first part of our lesson, which is the priority operations with negatives.

Now the priority operations is really important, as it ensures that everybody can understand and approach a mathematical problem the same way.

This image represents the priority of operations.

We start from the top and we work our way down.

The priority applies to both positive and negative numbers.

When using negatives, we will be using addition with the additive inverse, and rewriting the calculation in a more efficient way.

For example, here we have 12 add negative three subtract five subtract the negative 10.

So what I'm going to do is rewrite the calculation so we're only using addition.

Well, let's have a look at what we have.

Well, I'm going to change that subtraction of five into the addition of negative five.

I'm also going to change the subtraction of negative 10 into add 10.

Thus, our calculation is 12 add negative three add negative five add our 10.

Then summing up all our positives, we have 12 add 10 is 22, and summing up all the negatives, we have negative three add negative five is negative eight.

Thus, we know summing up our values, we have 22 add negative eight.

So let's mix negative and addition with other operations.

Here we have 20 subtract negative five multiply by 10.

Well, which operation do you think we do first? Using the priority of operations image, hopefully you spot we do the multiplication first.

So we're going to do the multiplication of negative five by 10 to give us negative 50.

Then we end up with 20 subtract negative 50.

Now we're going to rewrite the calculation.

Can you rewrite this calculation but only using addition and your knowledge on additive inverses? Well, hopefully you've spotted the additive inverse of negative 50 is positive 50.

So therefore, we end up with 20 add our 50, giving us an answer of 70.

Now let's move on to a check.

Question one wants us to work out the answers of the following, ensuring that we show all our working out.

So remember to use the priority of operations, and when subtracting, we need to use the addition of the additive inverse.

See if you can give it a go and press pause if you need.

Great work.

So let's have a look at question 1A.

Hopefully you spot we do the multiplication first.

So the negative six multiply five gives us negative 30.

Then we have 100 add the negative 30.

Well, working this out gives us an answer of 70.

For B, hopefully you can spot we do the division first, so it's negative 20 divided by five, which gives us negative four.

So we end up with 100 subtract the negative four.

Now using our knowledge on additive inverse, this is the same as 100 add four, which gives us 104.

For C, which operation do you think we do first? Well, it's the multiplication.

Negative three multiply by negative 10 is 30.

So our calculation is 900 subtract 30.

Remember, we're replacing the subtraction with the addition of the additive inverse to give me 900 add negative 30, which is 870.

Great work if you got this one right.

Now let's look at two operations on the same row.

With addition and subtraction, we know it's easier and more efficient to use the additive inverse and keep all the operations as addition.

But what about multiplication and division? Well, with multiplication and division, they have the same priority, but it is better to rewrite the division as a fraction.

So let's have a look at an example where we're using both multiplication and division.

We have 80 subtract negative 12 divided by four times two.

Can you rewrite the division as a fraction? Well, hopefully you can spot it's the same calculation as 80 subtract negative 12 over four multiply by two.

Now what do you think the next step is? Well, hopefully you can spot we can work out the negative 12 over four to being negative three.

Well, our calculation is now 80 subtract our negative three times two.

So now do you think you can spot the next operation? Well, it's negative three multiply by our two to give us negative six.

So our calculation is 80 subtract negative six.

Using our knowledge on the addition of the additive inverse, this is 80 add six, which is 86.

Now let's have a look at a check question.

Here, Jun created a question for his friends.

100 add, in brackets, four squared add four, close bracket, divided by that negative two, add the square root of 20 subtract that negative five.

Aisha says it's 115.

Izzy says it's 95.

And Jacob said it's impossible because I can't square root a negative number.

Who's correct? And ensure you show your working out.

Well done.

So let's see what you've got.

Well, it's Izzy who is correct.

So let's have a look at her working out.

First of all, we have brackets.

You can clearly see the brackets for four squared add four.

And remember those implicit brackets because we have that extended line.

So that means we had to work out the 20 subtract the negative five.

So our first line of working out is 100 add the 16 add four, still in our brackets, divided by our negative two.

And then the 20 subtract that negative five is 20 add five.

Working out our brackets, we now have 100 add 20 divided by the negative two add the square root of 25.

Now remember the priority of operations.

We apply the roots first from our calculation.

So that means we have 100 add 20 divided by negative two add our five.

The next operation to apply is division, but we're going to write this as a fraction.

100 add 20 over negative two add five.

Working that fraction out, we have 100 add negative 10 add five, which gives the answer that Izzy gave, which is 95.

This was a great question.

Now let's have a look at your task.

What you have to do is fill in the blanks to make the calculation in the centre 24.

See if you can give it a go and press pause if you need.

Great work.

So let's look at question two.

Question two wants you to work out the following, ensuring to show your working out.

Remember those implicit brackets and the priority of operations.

See if you can give it a go and press pause if you need.

Great work.

So let's move on to question three.

Question three is a pyramid, and remember the number above the block is the sum of the two below.

See if you can give this one a go and press pause if you need more time.

Great work, everybody.

So let's go through our answers.

For question one, let's start on the top right.

Negative 240 divided by negative 10 would give us our 24.

Then four add the negative two times negative 10 would give us our 24.

We have 40 add eight times negative two would give us our 24.

20 subtract the negative eight divided by two would give us our 24.

And the 60 add the negative 12 times by three.

They were great questions.

Question two, we had to show our working out.

So for A, remember those implicit brackets.

So let's have a look at what goes on in this square root.

Well, we have a subtraction of negative 21.

Remember to use addition and the additive inverse.

So we have 100 add the root of 100 add 21, all divided by negative 11.

Then we have those implicit brackets, so I'm going to work out 100 add 21 is 121.

So our calculation is 100 add root 121 divided by negative 11.

Then we have 100 add our 11 divided by minus 11.

Rewriting as a fraction is 100 add 11 over negative 11, giving us 100 add negative one, which is equal to 99.

That was a great question.

Well done if you got that one right.

For B, you can spot our brackets.

So let's apply our brackets first.

For question B, we have 50 subtract negative 100 add 149, close bracket, divided by negative seven.

I'm going to rewrite what's in those brackets just to really emphasise that negative 100.

So it's 50 subtract the 149 add the negative 100 and divide it by the negative seven.

Remember, we're using the additive inverse.

Then we can work out what's in our brackets.

Well, this is 50 subtract 49 divided by the negative seven.

Division can be written as a fraction.

So 50 subtract 49 over minus seven gives us 50 subtract that negative seven.

Remember, we're changing the subtraction to the addition of the additive inverse to give us 50 add seven, which is 57.

For question three, you had to fill in the pyramid.

If you've got any of these answers, a huge well done, as it was really tricky.

So let's move on to the second part of our lesson.

We'll be looking at the priority of operations with negatives and decimals.

Now remember, the priority operations applies to both positive and negative numbers, whether they are decimals or integers.

So when using negatives, remember, we'll always be using the addition of the additive inverse and rewriting the calculation in a more efficient way.

Now let's have a look an example using decimals.

Well, we have 12 subtract 3.

2 add 7.

86.

I'm going to change the subtraction of 3.

2 into the addition of the negative 3.

So we have 12 add negative 3.

2 add our 7.

Then we're going to sum our positives.

Summing our positive values, we have 12 add our 7.

86.

Notice how I've used the column method here to carefully add our decimals.

Then we simply add the positives with our negative.

So we have 19.

86 add the negative 3.

Showing my working out, you can see I end up with 19.

86 in a column method with our 3.

2, giving me an answer of 16.

66.

Using the addition of the additive inverse just makes the calculation a little bit more easier.

So let's have a look at a check.

Here we have 8.

2 subtract 3.

4 multiply by that negative two add 12 over the 2.

5 add 7.

See if you can give it a go and press pause if you need.

Well done.

So which operation do you think we're applying first? Well, hopefully you can spot we have implicit brackets.

The 2.

5 and the 7.

5 had to be added together because of that extended line.

So we end up with 8.

2 subtract 3.

4 times negative two add 12 over 10.

Now let's work out this fraction.

So we end up with 8.

2 subtract 3.

4 times negative two add our 1.

2, because 12 divided by 10 is 1.

The next operation to apply is multiplication.

2 subtract the negative 6.

8 add to the 1.

Then using the addition of the additive inverse gives us 8.

2 add 6.

8 add our 1.

Remember using the column method for addition, we can carefully add up our decimals, giving us 16.

This is a great question.

Well done if you got this one right.

So let's have a look at a harder question.

In this question, we'll still be using the priority of operations with decimals and negatives.

We'll also be looking at more complicated calculations, which will require a little bit more work.

So let's have a look at what I mean.

You have 4.

5 add 2.

3 multiplied by 9.

1 subtract the three over the one plus nine.

So what do you think the first step is? Well, hopefully you can spot the first step will be using those implicit brackets.

You had to sum up the one add the nine because we have that extended line of our fraction.

Now what do you think the next step is? Well, the next step would be the multiplication.

You have 2.

3 multiplied by 9.

This is a little bit harder because you have the multiplication of decimals.

So what I'm going to do is I'm going to show 2.

3 multiplied by 9.

1 as 23 times 0.

1 multiply by 91 times 0.

Then working this out, I can work out 23 multiply by 91.

Then multiply that answer by 0.

01 to give me 2.

3 times 9.

So using the multiplication grid, I've worked out 23 multiply by 91 is 2,093.

And this is the level of working out required.

There are different ways in which you can multiply integers.

I'm just choosing this grid method.

Now we know 23 multiplied by 91 is 2,093.

That means I know 23 multiplied by 91 multiplied by 0.

01 is 20.

93.

So now, I have 4.

5 add my 20.

93 subtract my 0.

Then we're going to use that additive inverse.

5 add our 20.

93 add the negative 0.

We're going to sum up our positive values.

So using the column form, 4.

5 add 20.

93 gives me 25.

43.

And then we're going to add it to that negative 0.

3 to give me 25.

13.

It's a huge question, and you've got lots of different elements.

First of all, you have to use the priority operations, your knowledge on additive inverse, multiplication of decimals or multiplication of integers, and addition of decimals.

So now let's move on to your task.

Here, you've got to work out the following, ensuring you show all your working out.

For question one, we have 3.

4 subtract 7.

6 add 11.

And for question two, you have 13.

45 subtract 2.

4 add 3.

2 subtract 1.

See if you can give it a go and press pause if you need.

Great work.

So let's move on.

For question three, you have to work out the following, ensuring you show all your working out.

184.

2 subtract the negative 45.

2 multiply by 16 and then divide by negative four.

See if you can give it a go and press pause if you need.

Fantastic work.

So let's move on to question four.

Question four is a little bit harder.

I want you to work out the following, ensuring you're showing all your working out.

Look at all those operations.

We have 10.

2 subtract 1.

4 multiply by our negative 3.

2 add the 12 squared all divided by the square root of 25 add 75.

That's a tough question.

And question five wants you to create your own two questions using a combination of operations and decimals.

But your answer has to be 24.

You must use decimals and ensure to check your calculation with a calculator.

See if you can give these a go.

Press pause if you need.

A huge well done.

These were really tough.

So let's see how you got on.

So starting with question one, the question was 3.

4 subtract 7.

6 add 11.

So replacing the subtraction with the addition of the additive inverse, we have 3.

4 add the negative 7.

6 add our 11.

Remember to sum those positives first.

So we would've had 14.

6 add that negative 7.

6 gives us seven.

For question two, we have 13.

45 subtract 2.

4 add 3.

2 subtract 1.

Remember, we're replacing the subtraction with the addition of the additive inverse.

So we have 13.

45 add the negative 2.

4 add the 3.

2 add the negative 1.

Summing together all the positives, we have 16.

65.

And summing together all those negatives, we have negative four, thus giving us an answer of 12.

65.

Well done if you got that one right.

Let's have a look at question three.

Now question three wants us to work out 184.

2 subtract the negative 45.

2 multiplied by 16 divided by negative four.

So let's rewrite the division with a fraction.

Well, we have 184.

2 subtract the negative 45.

2 times the 16 over negative four, thus giving us 184.

2 subtract the negative 45.

2 multiplied by negative four.

Then the next operation is multiplication.

So we're going to work out 45.

2 multiplied by four.

By converting into integers, we have 452 multiplied by four multiplied by 0.

Working this out, I'm choosing this method, gives me an answer of 1,808.

Thus, the answer to 45.

2 multiplied by four is 180.

So now I have 184.

2 subtract our 180.

Working this out using the column method, I now have an answer of 3.

This was a great question and lots of work and skills are behind it.

Now let's move on to question four.

Question four was 10.

2 subtract 1.

4 multiplied by negative 3.

2 add 12 squared over the square root of 25 add 75.

So did you manage to spot those implicit brackets? Well, hopefully you spotted you needed to sum the 25 and the 75 first.

Then we're going to work out the answer to the square root of 100 is 10 and 12 squared is 144.

The next operation we're going to apply is multiplication.

So let's have a look at that 1.

4 multiply by 3.

Well, using our multiplication techniques, hopefully you've spotted 1.

4 multiplied by 3.

2 is 4.

48.

And then from here, we've also worked out the 144 divided by 10, which is 14.

Summing our values using the column method, we have 29.

08 as our final answer.

Massive well done if you got that one right.

Great work today.

Remember, the priority of operations is so important, as it ensures that everyone can understand and approach a mathematical problem the same way.

This priority applies to positives, negatives, and decimals.

Fantastic work, everybody.

A huge well done.

I've finished the video