These questions ask you to compare a pair, choose a comparison symbol, arrange several integers, or identify values inside an interval. Treat the number line as the final judge of order.
Order from left to right
For a pair, imagine both marks on the same line: the right-hand mark is greater and the left-hand mark is less. A positive always stands to the right of a negative, and zero stands between the two groups. For example, 2 is greater than -30 without any need to compare 2 with 30.
| Values being compared | Reliable decision |
|---|---|
| Two positives | The larger magnitude is farther right and therefore greater; 11 is greater than 6. |
| Two negatives | The smaller magnitude is nearer zero and therefore greater; -4 is greater than -9. |
| Different signs or zero | Place negatives first, then zero, then positives when reading least to greatest. |
| Opposites | Their gap is twice their shared magnitude; the distance between -7 and 7 is 14 units. |
To order a mixed list, sort the negative group first, place zero next if present, and finish with the positive group. Within the negative group, larger magnitudes come earlier in least-to-greatest order. For integers strictly between endpoints, leave out both endpoints before sorting what remains.
Traps that reverse the order
| Tempting route | How to reject it |
|---|---|
| Compare only the magnitudes when signs differ | Magnitude measures distance from zero, not order. Any positive mark remains to the right of every negative mark. |
| Call the negative with larger digits the greater value | A larger negative magnitude lies farther left. On the negative side, closeness to zero wins a greatest-value question. |
| Sort negative values by increasing magnitude | That produces greatest to least within the negative group. For least to greatest, begin with the negative of largest magnitude. |
| Treat zero as the smallest integer | Zero is only the boundary between signs. Every negative integer lies to its left and is therefore smaller. |
| Include an endpoint in a strict interval | Strictly between means the boundary marks do not count. Test each candidate against both boundaries before ordering it. |
Try it
Which symbol makes the comparison -3 ... 0 true?
- <
- >
- =
- either < or >, depending on which value is read first
Arrange 3, -2, 5, -6 and 0 from least to greatest.
- 0, -2, -6, 3, 5
- -2, -6, 0, 3, 5
- -6, -2, 0, 3, 5
- -6, -2, 3, 5, 0
By how many units do 6 and -6 differ? Enter the difference in units.