Add integers symbolically

Adding integers symbolically means determining the sum of positive integers, negative integers, and zero by interpreting signs and comparing absolute values: same-sign integers combine their magnitudes and retain the sign, while opposite-sign integers produce the sign of the greater absolute value with the difference of the magnitudes. This understanding prevents treating a minus sign as automatically making every sum negative and supports evaluating algebraic expressions involving signed quantities; it is limited to integers, not addition of noninteger rational numbers or more advanced abstract generalizations.

Detailed Explanation: Add integers symbolically

To add integers, first look at their signs.

Same signs: Add the absolute values, then keep the common sign.
Different signs: Subtract the smaller absolute value from the larger absolute value. Keep the sign of the integer with the greater absolute value.
Remember: the absolute value is the distance from zero, so $\vert -8 \vert =8$ and $\vert 13 \vert =13$ .

Example: Find

-8+13

The integers have different signs: $-8$ is negative and $13$ is positive.
Compare their absolute values: $8$ and $13$ . Since $13$ is greater, the answer will be positive.
Subtract the smaller absolute value from the larger:

13-8=5

Therefore,

-8+13=5

The positive integer has the greater absolute value, so the sum is positive.

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Negative Integer Addition

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Add integers symbolically

Detailed Explanation: Add integers symbolically

Learn by doing: Add integers symbolically

Practice with unlimited practice problems

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Negative Integer Addition