By Karen LoBello
Updated Aug 30, 2022
The set of integers includes all whole numbers, their opposites, and zero. Positive integers are greater than zero, negative integers are less than zero, and zero is neutral. Understanding how to perform the four basic operations with integers is essential for algebra and beyond.
Addition
- Visualize on a number line. Place a dot above the first addend. Move right for a positive number and left for a negative number. For example, adding –8 and –6: start at –8 and move six steps left to –14.
- Use matching symbols. Draw an X for each positive integer and an O for each negative integer you add. Pair X’s with O’s and cross them out. The remaining symbols show the sign of the result. For (–9) + 7, you cross out seven X’s with seven O’s, leaving two O’s, giving –2.
- Memorize the rule. When both numbers share the same sign, add their absolute values and keep that sign. When the signs differ, subtract the smaller absolute value from the larger and adopt the sign of the number with the larger absolute value.
Subtraction
- Convert to addition. Change the subtraction sign to an addition sign and flip the sign of the subtrahend. For example, (–10) – (+7) becomes (–10) + (–7).
- Apply addition rules. Add the two numbers as in the previous section. (–10) + (–7) equals –17.
- Remember the mantra. "Change the sign…Change the sign." This helps you remember to alter both the operation and the second number’s sign.
Multiplication & Division
- Multiply or divide the absolute values. Treat the numbers as if they were positive. For (–8) × (+9), compute 8 × 9 to get 72.
- Determine the sign of the result. If both numbers have the same sign, the result is positive; if the signs differ, the result is negative.
- Seek additional resources. Visit the Khan Academy pre‑algebra video section for in‑depth explanations and practice.
Warning
Without a solid grasp of integer operations, you will face significant challenges in higher‑level mathematics. Master these fundamentals now to set yourself up for success.
