These questions ask you to subtract positive or negative integers, recognize equivalent forms, evaluate chains, or recover a missing subtracted value. One consistent rewrite turns every case into integer addition.
Keep, change, take the opposite
Keep the first integer unchanged, change the subtraction sign to addition, and take the opposite of the integer being subtracted. For example, 6 minus -4 becomes 6 plus 4 and gives 10. The same method makes -9 minus 3 become -9 plus -3, which gives -12.
| Subtraction pattern | Resulting move |
|---|---|
| Subtract a positive | Add a negative, so move left. The path may cross zero. |
| Subtract a negative | Add a positive, so move right. A negative start may remain negative or cross zero. |
| Subtract zero | Add zero and stay at the starting integer. |
| Several subtractions | Rewrite each subtracted term with care, then evaluate the resulting sum or work from left to right. |
Subtraction cannot usually be swapped: 9 minus 3 gives 6, while 3 minus 9 gives -6. For a missing subtracted value, write a simple equation and test the direction. In 4 minus an unknown equals 10, the result must rise by six, so the unknown is -6; substituting confirms the result.
Traps in the rewrite
| Tempting route | How to reject it |
|---|---|
| Always take the smaller magnitude from the larger | Subtraction fixes a starting value and a direction. Preserve the written order before doing any magnitude work. |
| Let subtracting zero erase the starting value or its sign | Zero has no size to remove. Rewriting as addition of zero shows that the original integer is unchanged. |
| Read subtraction of a negative as one ordinary minus | Take the opposite of the entire subtracted integer. Its negative sign reverses, turning the move into addition of a positive amount. |
| Assume subtraction gives the same result in either order | Swapping the terms reverses the direction between the same two marks. The two results are opposites unless both terms are equal. |
Try it
Select all expressions and values that are equal to 9 - 4.
- 9 + (-4)
- 5
- 9 + 4
- 4 - 9
- 13
What is the value of -5 - (-2) - (-8)?
- -15
- -11
- 5
- 15
Which integer must be subtracted from -3 to give 4? Enter that integer.