Negative Numbers

Introducing negative numbers on the number line, comparing them, and performing addition and subtraction.

What Are Negative Numbers?

Negative numbers are less than zero. We write them with a minus sign: $-3$ , $-7.5$ .

They appear in real life as temperatures below zero, floors below ground level, or debts.

Number line:

Comparing Negative Numbers

On the number line, numbers to the right are always greater.

$-2 > -5$ because $-2$ is to the right of $-5$ .

Adding and Subtracting

Same signs → add the values, keep the sign.

$(-3) + (-4) = -7$

Different signs → subtract the smaller from the larger, keep the sign of the larger.

$(-8) + 5 = -3$ (8 is larger, keep negative)

Subtracting a negative = adding a positive:

$6 - (-2) = 6 + 2 = 8$

Temperature

In the morning it was $-5°C$ . By noon it rose by $9°C$ . What is the new temperature?

$-5 + 9 = +4°C$

Warning

Two minus signs next to each other make a plus: $- (-3) = +3$

Real world: temperature below zero

On a winter night the temperature is $-8°C$ . By morning it has risen by $11°C$ . New temperature $= -8 + 11 = +3°C$ . Weather forecasters and skiers depend on negative numbers daily to describe sub-zero conditions.

Real world: bank overdraft

A student has €15 in their account and spends €40 online. Their balance becomes $15 - 40 = -25\text{ EUR}$ — an overdraft. The bank charges interest on the negative balance, so understanding negative numbers is essential for personal finance.

Real world: sea depth and elevation

A submarine dives to $-350$ m (below sea level) while a mountain peak stands at $+1200$ m. The total vertical difference is $1200 - (-350) = 1550$ m. Negative numbers allow geographers to measure depths below a reference level.

Tip Think of a number line: moving right always increases the value, moving left always decreases it. This works for temperatures, finances, and heights all at once.

Practice Problems

Place these numbers in order from least to greatest: -4, 2, -1, 0, -6

Show answer

-6, -4, -1, 0, 2.

Calculate: (-3) + (-7)

Show answer

-10.

Calculate: 5 − (−3)

Show answer

5 + 3 = 8.

The temperature is -8°C and drops by 4°C. What is it now?

Show answer

-8 − 4 = -12°C.