Integers & Number Lines
Positive and negative numbers, ordering and operations
What are Integers?
Integers are all whole numbers including negatives: … −3, −2, −1, 0, 1, 2, 3 …
On a number line, numbers increase as you move right and decrease as you move left.
Ordering Integers
Larger numbers are always to the right on a number line.
Example: Order −5, 3, −1, 0, −8 from smallest to largest:
→ −8, −5, −1, 0, 3
Adding and Subtracting Integers
- Adding a positive number → move right on the number line
- Adding a negative number → move left (same as subtracting)
- Subtracting a negative number → same as adding a positive
e.g. 5 − (−3) = 5 + 3 = 8
Multiplying and Dividing Integers
| Signs | Result |
|---|---|
| Positive × Positive | Positive |
| Negative × Negative | Positive |
| Positive × Negative | Negative |
| Negative × Positive | Negative |
Rule: Same signs → positive result. Different signs → negative result.
Absolute Value & Key Tips
The absolute value of a number is its distance from zero (always positive).
|−7| = 7 |4| = 4
- Temperature problems are a common real-world context for integers
- Watch out for double negatives: − (−x) = +x
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What is −5 − (−2)?
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Answer: −3
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Which is the largest: −8, −1, −5, −12?
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Answer: −1
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On a number line, which point is 4 units to the left of −2?
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Answer: −6
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What is (−7) + 10?
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Answer: 3
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