Negative Numbers

Negative numbers are numbers less than zero. They appear on the left side of zero on a number line and are written with a minus sign (−) in front. Together with positive numbers and zero, they form the set of integers.

What Are Negative Numbers?

When we count up from zero (1, 2, 3 …), we get positive numbers. When we count down past zero (−1, −2, −3 …), we get negative numbers.

← −5 −4 −3 −2 −1 0 1 2 3 4 5 →

Real-Life Contexts for Negative Numbers

Context	Negative Meaning	Example
Temperature	Below zero (freezing)	−10°C in winter
Altitude	Below sea level	Dead Sea at −430 m
Finance	Debt / overdraft	−£200 in a bank account
Sport	Under par (golf)	−3 in a golf round
Floors	Below ground level	Basement = Floor −1

Ordering Integers

On the number line, numbers increase from left to right. So any number to the right is greater.

−7 < −2 < 0 < 3 < 8

Absolute Value

The absolute value of a number is its distance from zero, always positive. Written as |n|.

|−6| = 6 |6| = 6 |0| = 0

Adding and Subtracting Negative Numbers

Operation	Rule	Example
Adding a negative	Same as subtracting the positive	5 + (−3) = 5 − 3 = 2
Subtracting a negative	Same as adding the positive	5 − (−3) = 5 + 3 = 8
Negative + Negative	Add and keep the minus sign	−4 + (−2) = −6

Multiplying and Dividing

Signs	Result	Example
Positive × Positive	Positive	3 × 4 = 12
Negative × Positive	Negative	−3 × 4 = −12
Negative × Negative	Positive	−3 × −4 = 12

Key Points

Negative numbers are less than zero; positive numbers are greater than zero.
On a number line, smaller numbers are always to the left.
A larger absolute value does not mean a larger negative number (e.g., −10 < −2).
Two negatives multiplied or divided give a positive result.

Practice: Calculate with Negative Numbers

Work out the result below. If you get it wrong (or leave it blank), we'll walk through the sign rules together.

Calculate:

Summary

Negative numbers extend our number system below zero and are essential for describing temperatures, debts, depths, and many other real-world measurements. They follow clear rules for arithmetic, and understanding them is a prerequisite for algebra, coordinate geometry, and beyond.