Add integers

Adding integers means combining signed quantities according to their direction and magnitude: integers with the same sign combine their absolute values and retain that sign, while integers with opposite signs produce the sign of the greater absolute value and the difference of the absolute values. Number-line movement and the relationships between opposites, zero, and additive inverses clarify why adding zero preserves a value and why addition is commutative and associative; this scope concerns integers rather than rational-number or symbolic-expression addition.

Detailed Explanation: Add integers

To add integers:

Check the signs.
- If the signs are the same, add the absolute values and keep the common sign.
- If the signs are different, subtract the smaller absolute value from the larger absolute value. Keep the sign of the number with the greater absolute value.

Example: Find $-8+13$

The integers have different signs, so subtract their absolute values:

13-8=5

The absolute value of $13$ is greater than the absolute value of $-8$ , so the answer keeps the positive sign:

-8+13=\boxed{5}

On a number line, start at $-8$ and move $13$ units to the right because you are adding a positive number. You land on $5$ .

Remember, adding $0$ does not change a number, and switching the order of the addends does not change the sum: $a+b=b+a$ .

Learn by doing: Add integers

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Negative Integer Addition

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