Integer Operations Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Integer Operations.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Adding, subtracting, multiplying, and dividing integers—numbers that include positive values, negative values, and zero.
Think of a number line with zero in the middle. Positive numbers go right, negative numbers go left. Adding a positive moves right; adding a negative moves left. Multiplying two negatives gives a positive because reversing a reversal brings you back to the original direction.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: The sign rules are consistent patterns, not arbitrary: (-1) \times (-1) = +1 because negating a negation restores the original.
Common stuck point: Subtracting a negative is the same as adding: 5 - (-3) = 5 + 3 = 8. Students often forget this double-negative rule.
Sense of Study hint: Draw a number line with zero in the middle and use arrows: right for positive, left for negative, to trace the operation.
Worked Examples
Example 1
easySolution
- 1 Notice the addends have different signs, so this becomes a subtraction problem.
- 2 Subtract the smaller absolute value from the larger: 8 - 5 = 3.
- 3 Keep the sign of the number with the larger absolute value (-8): the answer is -3.
Answer
Example 2
mediumExample 3
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyBackground Knowledge
These ideas may be useful before you work through the harder examples.