Negative Numbers

There are a number of rules you will need to know when working with negative numbers (sometimes called directed numbers).

Sign pairs

There are two signs in maths, a plus and a minus. If you every have a situation where you have two of these together, there is a rule that decides which to pick.

If the signs are the same, then replace them with a plus. If the signs are the different, then replace them with a minus.

\[5 +- 1\]

The +- has different signs, so replace it with a minus.

\[5 - 1 = 4\]

Addition

When adding with negative numbers, we use the number line. Start at the number, then count the 'jumps' to the right.

\[-4 + 3\]

Start at -4 on the number line and jump 3 to the right.

\[-4 + 3 = -1\]

Subtraction

We also use the number line when subtracting. Start at the number, then count the 'jumps' to the left.

\[2 - 5\]

Start at 2 on the number line and jump 5 to the left.

\[2 - 5 = -3\]

Multiplication

When multiplying with negative numbers, start by comparing the signs.

If the signs are the same, then the answer will be positive. If the signs are the different, then the answer will be negative.

\[-2 \times 5\]

The signs are different, so the answer will be negative. We can then multiply the 2 and the 5 to find the answer.

\[-2 \times 5 = -10\]

Division

Divisions follows the same rules as multiplications.

If the signs are the same, then the answer will be positive. If the signs are the different, then the answer will be negative.

\[-12 \div -4\]

The signs are the same, so the answer will be positive. We can then divide the 12 by the 4 to find the answer.

\[-12 \div -4 = 3\]