In addition and subtraction of signed numbers, the operation and the number sign of the number directly following will combine. This will be covered again in multiplication/division of signed numbers. If both signs are the same, the result is always positive. If the signs are different, the result is always negative.
Below is a more complete guide:
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When the signs of all numbers are the same, the sum will always be the same sign. |
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When the signs are different but the positive number is larger, subtract to get a positive result. |
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When the signs are different but the negative number is larger (smaller value), subtract to get a negative result. |
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When the signs are the same, the difference is positive so long as larger number is positive after combining signs. The opposite applies when the larger number is negative. |
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When the signs are different, a sum is formed so long as the negatives combine to make a positive. When the minus combines with a positive to make a negative, the difference is negative but appears as if the number were added. |
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Again, you’ll notice that there are certain interactions that occur with adjacent +/- where they combine. This has to do with multiplication of signs which can be checked out in the next section: Applications to Multiplication/Division.
You can think of adding a subtracting positive/negative numbers as movement along a number line. Any subtraction is movement to the left, and any addition is movement to right (after sign combining).