Most students can tell you the rules of directed numbers (which is just a fancy way of saying positive and negative numbers) but many students struggle when applying these rules. Why? Because the rules differ for addition and subtraction compared with multiplication and division.

**The rules:**

Two positives make a** positive****.**

A positive and a negative makes a **negative.**

A negative and a positive makes a **negative.**

Two negatives make a** positive.**

Adding negative numbers:

The thing that students get wrong when they add negative number is that they only affect each other if they are together.

So in the sum 3 + - 5, the signs** would** affect each other because they're together.

However, in the sum -3 + 6, the signs **would not **affect each other as they are not together.

**Example 1: Work out the value of**

3 + - 5

In this question we have a + and a - together, so they will affect each other and will become a negative overall, this means we can rewrite the sum as;

3 - 5

To do this, we can now read from left to right. - 5 means go 5 to the left, so if we start on a number line at 3 and go 5 to the left, we get;

3 - 5 = -2

**Example 2: Work out the value of**

- 2 + - 4

In this question we have a + and a - together, so they will affect each other and will become a negative overall, this means we can rewrite the sum as;

- 2 - 4

To do this, we can now read from left to right. - 4 means go 4 to the left, so if we start on a number line at -2 and go 4 to the left, we get;

-2 - 4 = -6