Integers - Addition and Subtraction of Integers on a Number Line

Integers consist of whole numbers and their negative opposites, represented on a horizontal number line where $0$ is the origin. Positive integers like $1, 2, 3 \dots$ are placed at equal intervals to the right of $0$, while negative integers like $-1, -2, -3 \dots$ are placed to the left.

The value of an integer increases as we move from left to right on the number line. Conversely, the value decreases as we move from right to left. For example, $-1$ is greater than $-5$ because it is positioned further to the right.

To add a positive integer, move to the right on the number line. For example, to solve $2 + 3$, start at $2$ and jump $3$ units to the right to land on $5$.

To add a negative integer, move to the left on the number line. Adding a negative is equivalent to subtraction. For example, to solve $4 + (-6)$, start at $4$ and move $6$ units to the left to land on $-2$.

To subtract a positive integer, move to the left on the number line. For instance, to find the result of $1 - 4$, start at $1$ and move $4$ units towards the left to reach $-3$.

To subtract a negative integer, move to the right on the number line. Subtracting a negative is the same as adding its positive counterpart. For example, for $-2 - (-5)$, rewrite it as $-2 + 5$. Start at $-2$ and jump $5$ units to the right to land on $3$.

The additive inverse of an integer $a$ is $-a$, such that $a + (-a) = 0$. On a number line, this represents moving from a point back to the origin ($0$) by traveling an equal distance in the opposite direction.