# Negative Numbers

Search my site:

Level: Primary 6 / Grade 6 / PSLE

Here is a simple way that I use to explain Negative Numbers.

Before I introduce negative numbers to my students, I remind them of the number line. Numbers are usually written this way on a number line. Things to note:

• The line starts at 0
• The numbers increase as you move to the right of the line

Now I show them the number line with negative numbers added to it. Things to note:

• The number line has to beginning and no ending, indicated by the arrow on both ends of the line
• The negative numbers also increases digitally as you move to the left of the line, but the negative sign means the value of the number actually decreases

To help my students understand better, I tell them to think of negative numbers this way:

• The negative sign tells you how far away the number is from the zero.
• So -3 means you are 3 steps away from 0 and -5 means you are 5 steps away from zero.
• Therefore, -5 is smaller than -3 because you are further away from zero.

### Adding and Subtracting with Negative Numbers

When it comes to using negative numbers in addition and subtraction, using a number line is crucial for understanding how it all works.

The first thing to understand is the difference in the meaning between the subtraction symbol (-) and the negative number symbol (-).  They both look the same but have different meanings.

The subtraction symbol tells us which direction we want to go along the number line.  The negative symbol applies only to the number it is paired with.

The other thing to note is that the addition symbol (+) tells us to move to the right of the number line while the subtraction symbol (-) tells us to move to the left of the number line.

Let's look at some examples. Here is the number line again. Let's find the answer to: 1 subtract 3.

We write it as: 1 - 3.  The subtraction tells us to move to the left on the number line.

Starting at number 1, move 3 steps to the left on the number line. You will end up at negative two.

So,  1 - 3 = -2

Here is another way to look at it.

If I have 1 cookie (1) and I want to give you 3 cookies (-3), that means I owe you 2 cookies (-2).  The negative sign means I owe you.

1 - 3 = -2

Let's try another example.

Find the answer to -1 plus 3.

We write it as: -1 + 3.  The plus or addition sign tells us to move to the right on the number line.

Starting at -1, move 3 steps to the right on the number line.  You will end up at 2.

So,  -1 + 3 = 2

Here is the alternative explanation.

I owe you 1 cookie (-1).  Someone else gives me 3 cookies (+3).  I have to give you what I owe so I end up with only 2 cookies.

-1 + 3 = 2

Try a few more yourself.  Remember: To add - move to the right.  To subtract - move to the left.  Or think in terms of giving or receiving cookies.

1.  -2 + 5
2.   3 - 5
3.   0 - 3
4.   -1 - 2

### Exceptions to the Rule

When a negative number comes after the addition or subtraction sign, it means you have to reverse the normal direction.

That is, if a negative number comes after the addition sign, it means you move to the left instead of the right on the number line.

Vice versa, if a negative number comes after the subtraction sign, it means you move to the right instead of to the left on the number line.

Let's look at the example below. 2 + (-2)

You start at the number 2.  Then you move 2 steps to the left instead of the right and end up at 0.

This means that 2 + (-2) is the same as 2 - 2 which gives the answer 0.

2 + (-2) = 0

Here is another example. Let's find the answer to (-3) - (-1).

Start at -3. Then move 1 step to the right instead of the left. You will end up at -2.

So, -3 - (-1) is the same as -3 + 1  which gives the answer -2

-3 - (-1) = -2