Integers — English demo

Published: 1 Nov 2026

Introduction

Integers are positive and negative whole numbers, including zero: $-3, -2, -1, 0, 1, 2, 3$.

Values increase as you move right on a number line. Values decrease as you move left.

Integers on a number line

When two integers have the same sign, add their absolute values. Keep the common sign.

$\begin{aligned}(-4)+(-3)&=-(4+3)\\&=-7\end{aligned}$

To subtract an integer, add its opposite: $5-(-2)=5+2=7$.

Like signs give a positive product or quotient. Unlike signs give a negative result: $(-3)\times(-4)=12$ and $12\div(-3)=-4$.

$\frac{\cancel{3}\times4}{\cancel{3}}=4$

Division by zero is undefined.

Integers are closed under addition, subtraction and multiplication. They are not closed under division: $1\div2=\frac12$ is not an integer.

Addition and multiplication are commutative: $a+b=b+a$ and $ab=ba$.

$\sqrt{25}=5$, $2^3=8$, $\log_{10}(100)=2$, $\begin{pmatrix}1&2\\3&4\end{pmatrix}$.

Try these: $(-6)+4$, $3-(-5)$ and $(-7)\times2$. Then check your answers.

$-2$, $8$, $-14$.

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