Lesson 1.2: Integers

New Concept

This lesson introduces integers, their opposites, and absolute values. You will learn to perform all basic arithmetic operations on them—addition, subtraction, multiplication, and division—which is essential for simplifying expressions and solving application problems.

What’s next

Next, you'll tackle interactive examples on adding, subtracting, multiplying, and dividing integers. Then, test your skills with a series of practice problems.

Property

The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero. Opposite Notation is written as $-a$ and means the opposite of the number $a$. The notation $-a$ is read as “the opposite of $a$.”

Examples

• The opposite of $15$ is $-15$, as they are both 15 units from zero.

• The opposite of $-9$ is $9$. We can write this as $-(-9) = 9$.

Property

The absolute value of a number is its distance from $0$ on the number line. The absolute value of a number $n$ is written as $|n|$ and $|n| \geq 0$ for all numbers. Absolute values are always greater than or equal to zero.

Examples

• The absolute value of $-18$ is $18$, because $-18$ is $18$ units away from $0$. This is written as $|-18| = 18$.

• To simplify $|-7| + |3|$, first find the absolute values: $7 + 3$, which equals $10$.

Property

$a - b = a + (-b)$

Subtracting a number is the same as adding its opposite.

Examples

• The expression $14 - 8$ can be rewritten as adding the opposite: $14 + (-8)$, which both equal $6$.

Property

$-1a = -a$

Multiplying a number by $-1$ gives its opposite.

Examples

• To find the opposite of $9$, you can multiply it by $-1$: $-1 \cdot 9 = -9$.