Integers and Absolute Value
Understand integers as the set of whole numbers and their negatives. Define absolute value as distance from zero on the number line, and use it to compare and order integers including in real-world contexts like temperature and elevation.
A lesson of Pre-Algebra, in Number Sense & Operations, about 10 minutes.
By the end of this lesson, you will be able to define integers, find absolute values, and order integers on a number line.
Integers
Integers: the set ${\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots}$ — all whole numbers and their opposites.
Negative integers are less than zero (to the left of 0 on the number line).
Positive integers are greater than zero (to the right).
Zero is neither positive nor negative.
Absolute Value
$$|a| = \text{distance from 0 on the number line (always } \geq 0\text{)}$$
$|7| = 7 \qquad |-7| = 7 \qquad |0| = 0$
$|-15| = 15$ (distance is always positive)
Evaluate: $|3 - 8| = |-5| = 5$
Solve: $|x| = 4 \to x = 4$ or $x = -4$
Comparing and Ordering Integers
Farther right = greater. So $-1 > -8$ (even though 8 looks bigger, on the number line −1 is to the right of −8).
Order from least to greatest: $-5, -2, 0, 3, 7$
Opposites
The opposite of a number is the same distance from 0 on the other side.
Opposite of $-4$ is $4$. Opposite of $9$ is $-9$.
Double negative: $-(-5) = 5$
Summary
Integers: whole numbers + their opposites.
Absolute value: $|a|$ = distance from 0; always non-negative.
Comparing: right = greater; $-1 > -100$.
Opposites: same distance from 0, opposite side.