These questions ask you to add two or more integers, compare reordered sums, or find a missing addend. Read each addend as a move: positive goes right and negative goes left.
Choose the rule from the signs
| Sign pattern | Decision method |
|---|---|
| Both positive | Add the magnitudes and keep the positive direction; 4 plus 7 gives 11. |
| Both negative | Add the magnitudes and keep the negative direction; -3 plus -8 gives -11. |
| Different signs | Subtract magnitudes and use the sign of the larger magnitude; -12 plus 5 gives -7. |
| Equal magnitudes with different signs | The moves cancel completely; 15 plus -15 gives zero. |
| One addend is zero | Make no move, so the other integer stays unchanged. |
For a long sum, either work from left to right or group positive addends together and negative addends together. Both routes are valid because swapping or regrouping addends does not change a sum. Keep each sign attached while grouping: 11 plus -3 plus -5 becomes 11 plus -8, then 3.
For a missing addend, look at the move from the known start to the target. A move from -6 to 1 goes seven units right, so the missing addend is positive 7. Substitute it back to check that the stated target is reached.
Traps that lose the direction
| Tempting route | How to reject it |
|---|---|
| Read every plus sign as permission to combine magnitudes | The signs on the addends determine whether the moves join or oppose each other. Different signs require a magnitude difference. |
| Give zero the power to erase the other addend | Adding zero means taking no extra step. It leaves both the magnitude and sign of the starting value intact. |
| Keep the sign of the first addend or the smaller magnitude | For different signs, compare magnitudes after subtracting them. The larger magnitude controls the side of zero where the total lands. |
| Drop signs while grouping a long sum | Carry each sign into its group, total the positive and negative groups separately, and only then combine those two signed totals. |
Try it
What is the value of 8 + 5?
- 3
- -3
- -13
- 13
Select all true statements about the sum -7 + 12 + (-9) + 4.
- The negative addends together contribute -16.
- The positive addends together contribute 16.
- The sum is 0.
- The sum is 32, since all four magnitudes combine.
- The sum is -32, because the negative addends are written first.
Which integer must be added to -13 to reach -4? Enter that integer.