Adding and Subtracting Integers: Practice

Start at $5$ and step $2$ units to the left, since adding a negative moves left. The signs differ, so subtract the smaller distance from the larger.

$5 + (-2) = 5 - 2 = 3$

The larger distance belongs to the positive $5$, so the answer is positive.

A number and its opposite form a zero pair, and a zero pair cancels.

$(-6) + 6 = 0$

Starting at $-6$ and stepping $6$ units right lands exactly on zero.

Both numbers are negative, so the distances add and the sign stays negative.

$(-2) + (-9) = -(2 + 9) = -11$

The numbers $4$ and $-4$ are opposites, so they form a zero pair.

$4 + (-4) = 0$

Step $4$ units left from $4$ and you land on zero.

The signs differ, so subtract the smaller distance from the larger. The distances are $1$ and $9$.

$(-1) + 9 = 9 - 1 = 8$

The larger distance belongs to the positive $9$, so the answer is positive.

This is ordinary subtraction of whole numbers, a step of $3$ units to the left from $8$.

$8 - 3 = 5$

The signs differ, so subtract the smaller distance from the larger. The distances are $2$ and $6$.

$2 + (-6) = -(6 - 2) = -4$

The larger distance belongs to the negative $-6$, so the answer is negative.

Both numbers are positive, so both steps go right and the distances add.

$6 + 7 = 13$

The signs differ, so subtract the smaller distance from the larger. The distances are $10$ and $4$.

$(-10) + 4 = -(10 - 4) = -6$

The larger distance belongs to the negative $-10$, so the answer is negative.

Both numbers are negative, so the distances add and the sign stays negative.

$(-3) + (-8) = -(3 + 8) = -11$

The numbers $-12$ and $12$ are opposites, so they form a zero pair.

$(-12) + 12 = 0$

A number and its opposite always cancel to zero.

Subtracting $9$ is the same as adding its opposite, $-9$.

$5 - 9 = 5 + (-9) = -4$

The signs differ, so subtract the distances ($9 - 5 = 4$). The larger distance belongs to $-9$, so the answer is negative.