A negative number is a value below zero, used for things like temperatures below freezing, debts, or depths below sea level. Picture a number line with zero in the centre, positive numbers increasing to the right, and negative numbers decreasing to the left — moving right always makes a number bigger (less negative or more positive), and moving left always makes it smaller.

Adding a negative number is the same as subtracting the positive version of it; subtracting a negative number ("a double negative") is the same as adding the positive version.

The sign of the answer depends only on whether the two numbers have the same sign or different signs — it has nothing to do with the actual size of the numbers.

The identical rule applies to division: $(-10) \div (-2) = 5$, but $10 \div (-2) = -5$.

Treat each negative number as a single quantity in brackets, and apply BIDMAS as normal — negatives don't change the order in which you do things, only how you simplify once you reach that step.

Example: $(-5) \times 3 + (-12) \div 4$.

1. Multiplication first: $(-5) \times 3 = -15$ (different signs → negative).
2. Division next: $(-12) \div 4 = -3$ (different signs → negative).
3. Add the results: $-15 + (-3) = -18$.

The temperature in a town was $-6°\text{C}$ at midnight. It fell by $4°\text{C}$ over the next three hours, then rose by $9°\text{C}$ by midday. What was the temperature at midday?

1. Start: $-6$.
2. A fall of $4°\text{C}$ means subtracting: $-6 - 4 = -10$.
3. A rise of $9°\text{C}$ means adding: $-10 + 9 = -1$.
4. The temperature at midday was $-1°\text{C}$.