Curriculum

Addition and Subtraction of Integers

Working with integers requires following specific rules based on the “signs” (positive or negative) of the numbers involved.

Core Rules for Calculation

To determine the result of an integer operation, follow these two primary notes:

Note 1: Same Signs

If both integers are positive (+) or both are negative (-), find the sum of their numerical values and assign the sign of the integer with the greater magnitude.

Note 2: Different Signs

If one integer is positive (+) and the other is negative (-), find the difference between their numerical values and assign the sign of the integer with the greater magnitude.

Basic Examples

Here is how the rules apply to the number 3 and 5:

Both Positive: $3 + 5 = 8$

Both Negative: $-3 - 5 = -(3 + 5) = -8$

Negative & Positive: $-3 + 5 = +(5 - 3) = 2$

Positive & Negative: $3 - 5 = -(5 - 3) = -2$

Practice Examples

Applying the rules to the numbers 12 and 13:

Operation	Thinking Process	Result
$12 + 13$	Same signs: Add $12$ and $13$	$25$
$-12 - 13$	Same signs: Add $12$ and $13$ , keep negative	$-25$
$-12 + 13$	Different signs: $13 - 12 = 1$ . $13$ is larger (+).	$1$
$12 - 13$	Different signs: $13 - 12 = 1$ . $13$ is larger (-).	$-1$