How do you add integers with different signs?

To add integers with different signs, you subtract the numbers and keep the sign of the larger number (absolute value).

Understanding Integer Addition with Different Signs

Adding integers with different signs is a fundamental concept in mathematics. Let's break down the process with examples and explanations:

• The Rule: Subtract the absolute values of the two numbers. Then, keep the sign of the number with the larger absolute value.

  • Absolute value refers to the distance of a number from zero, regardless of its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.

• Example 1: -3 + 2

  1. Find the absolute values: |-3| = 3 and |2| = 2.
  2. Subtract the smaller absolute value from the larger: 3 - 2 = 1.
  3. The larger absolute value belongs to -3, which has a negative sign.
  4. Therefore, -3 + 2 = -1.

• Example 2: 3 + -2

  1. Find the absolute values: |3| = 3 and |-2| = 2.
  2. Subtract the smaller absolute value from the larger: 3 - 2 = 1.
  3. The larger absolute value belongs to 3, which has a positive sign.
  4. Therefore, 3 + -2 = 1.

Summary Table

Expression	Absolute Values	Subtraction	Sign of Larger Absolute Value	Result
-3 + 2		-3	= 3,	2
3 + -2		3	= 3,	-2

Comparison with Adding Integers with the Same Sign

It's important to distinguish this from adding integers with the same sign. As stated in the reference, when integers have the same sign, you add the numbers and keep that same sign. For example:

• 3 + 2 = 5
• -3 + -2 = -5