Albert Teen

YOU ARE LEARNING:

Negative Numbers

# Negative Numbers

### Negative Numbers

Addition, subtraction, multiplication and division of negative numbers requires us to follow certain rules.

1

Select the two options that are true for negative numbers.

You can select multiple answers

2

Negative numbers are all the numbers which come before zero.

These continue to infinity in the negative direction.

3

We represent this with an arrow

On a number line, we use the arrow to represent a range of numbers. The open circle shows that zero is not included.

4

Negative numbers closer to zero are greater

So $-2$ is greater than $-5$, we can also write this as $-2>-5$.

5

Which number is greater: $-4$ or $-3$?

Here we subtract from a positive number: $6-11$

1

Start from $6$ on the number line

Move left, when you have moved five times you are at zero because $6-6=0$

2

Subtract $5$ more from $0$ by moving another five to the left. What is $0-5$ ?

3

Nice!

The final answer is $-5$ 👍

1

Let's look at $6 - 11$ using counters

We start with $6$ positive counters.

2

We want to subtract $11$ counters

So we need to include $11$ negative counters.

3

One positive counter and one negative counter make a zero pair.

These cancel each other out as $1-1=0$.

4

Now we can cancel out "zero pairs"

This will leave us with five negative counters, so $-5$.

Let's try adding a positive to a negative: $-5 + 8$

1

Start at $-5$ on a number line

Adding 8 means to move "right" 8 times

2

We need to go past zero

This is because $8$ is bigger than $-5$'s zero pair

3

What is $-5+8$?

1

Let's have a look at $-5 +8$ using counters

We will start with $5$ negative counters.

2

Add $8$ positive counters

Now we can see the zero pairs.

3

Cancel out five zero pairs

We are left with $3$

1

We can rewrite $-5 + 8$ as $8-5$ and the answer is still $3$.

This is because addition is commutative.

2

Commutative means that it doesn't matter what order we put our numbers in, we will get the same answer.

$2+7=9$ and $7+2=9$

3

When doing this with negative numbers, make sure the negative sign stays with the right number! What is another way of writing $-4+6$?

What is $-8 + 5$?

Let's now look at subtracting from a negative number: $-2 - 5$

1

We start at $-2$ on our number line

Subtracting means to move left along the number line

2

Move $5$ along the number line in the negative direction.

What is $-3 - 6$?

1

Sometimes we will need to subtract a negative number, which will result in two minus signs next to each other:

$3-(-2)$

2

Subtracting a negative is the same as adding a positive.

So we can rewrite the question as $3-(-2)=3+2$.

3

So what is $3-(-2)$?

What is $12-(-11)$?

What is $53-(-12)$?

1

We may also need to add a negative number, resulting in a plus and minus sign next to each other:

$3+(-2)$

2

Adding a negative number is the same as subtracting a positive:

$3+(-2)=3-2$.

3

What is the answer to $3+(-2)$ or $3-2$ ?

What is $-11+(-7)$?

1

If you multiply or divide two negative numbers then the answer will always be...

2

What is $-6\times-3$ ?

3

What is $\dfrac{-21}{-7}$ ?

1

In multiplication and division,

if only one number is negative then the answer is always negative.

2

What is $-6 \times 7$?

3

What is $\dfrac{-50}{5}$ ?

Summary!

1

Negative numbers sit to the left of zero on a number line.

For example, $-3$ is a negative number.

2

Move left on the number line when adding a negative number.

This is the same as subtracting a positive number. $6+(-2)=6-2=4$

3

Move right on the number line when subtracting a negative number.

This is the same as adding a positive number. $(-8)-(-10)=(-8)+10=2$

4

Multiplying and dividing:

When both numbers are negative, the answer is positive. $(-2) \times (-3) = 6$

5

Multiplying and dividing:

When one number is negative and the other positive, the answer is negative. $18 \div (-3)=-6$.