Adding and Subtracting Integers

Adding and subtracting integers is movement along the number line: adding a positive moves you right, subtracting a positive moves you left.

Two rules cover every case:

1. Same signs — add the digits and keep the sign. $-3 + (-5) = -8$.
2. Different signs — subtract the smaller digit from the larger and keep the sign of the larger. $6 + (-9) = -3$.

Subtracting is adding the opposite. $5 - (-8)$ means $5 + 8 = 13$. Two minus signs side by side cancel into a plus.

Worked example. Overnight it was $-4\,°\text{C}$; by afternoon it had risen $11\,°\text{C}$. New temperature: $-4 + 11 = 7\,°\text{C}$.

Exam checkpoint

Keep two ideas separate: the sign attached to a number tells you its direction, while the operation tells you what to do. Rewrite subtraction as addition of the opposite when the signs become crowded. Then decide whether the movements cancel or reinforce each other. A line of working makes sign errors easy to spot.

Short worked example. A scuba diver is at $-6$ m and rises 9 m: $-6+9=3$. A later drop of 5 m gives $3-5=-2$ m.