Overview
Summary of integers: what they are, how to show them on a number line, real-life uses, and how to compare them.
What Are Integers?
- Integers are whole numbers: positive, negative, or zero.
- Fractions and decimals are not integers.
- Zero is an integer that is neither positive nor negative.
- On the number line, zero separates negatives (left) and positives (right).
Number Line and Direction
- Right of zero: positive integers; can be written with or without a plus sign.
- Left of zero: negative integers; always use a minus sign.
- Moving right increases value; moving left decreases value.
- Example: 3 plus 2 moves two spaces right to 5; 0 minus 5 moves five left to −5.
Real-World Contexts for Integers
- Sea level is zero; above is positive, below is negative.
- “Above” or “up” means positive; “backwards,” “decrease,” or “below” means negative.
Keywords and Integer Representation
| Phrase | Keyword | Integer |
|---|
| 15 feet above ground | above | +15 |
| Ten floors up | up | +10 |
| Five steps backwards | backwards | −5 |
| Decrease of nine points | decrease | −9 |
| 40 feet above sea level | above | +40 |
| 40 feet below sea level | below | −40 |
Comparing Integers
- Numbers right of zero are greater; left are smaller.
- Zero is greater than any negative, but less than any positive.
- Positives are always more than negatives.
- Among negatives, the one closer to zero is greater.
| Comparison | Reason | Conclusion |
|---|
| 0 vs −5 | Zero is right of −5 | 0 > −5 |
| 0 vs +5 | +5 is right of zero | 0 < +5 |
| +3 vs −5 | Positives > negatives | +3 > −5 |
| −4 vs +1 | Negatives < positives | −4 < +1 |
| +18 vs −25 | Positives > negatives | +18 > −25 |
| −3 vs −5 | −3 closer to zero | −3 > −5 |
| −4 vs −2 | −4 farther left than −2 | −4 < −2 |
| −40 vs −21 | −40 farther left than −21 | −40 < −21 |
Key Terms
- Integer: Any whole number, positive, negative, or zero.
- Number Line: A way to show how numbers increase right and decrease left.
Next Steps
- Practice matching key words (“above,” “decrease”) to integer signs.
- Use the number line to visualize adding and subtracting.
- Compare pairs by where they are in relation to zero.