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Adding Negative Numbers and Positive Numbers Calculator

Reviewed by Calculator Editorial Team

Adding negative numbers to positive numbers is a fundamental arithmetic operation. This guide explains the rules, provides examples, and includes a calculator to help you practice.

How to Add Negative and Positive Numbers

Adding numbers with different signs involves understanding the basic rules of arithmetic. When you add a negative number to a positive number, you subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.

If a > b, then a + (-b) = a - b

If b > a, then a + (-b) = -(b - a)

This means you always subtract the smaller number from the larger one, regardless of their signs. The result takes the sign of the number with the larger absolute value.

Rules for Adding Negative Numbers

Rule 1: Subtract the Smaller Absolute Value

When adding a negative number to a positive number, subtract the smaller absolute value from the larger one. For example, 5 + (-3) = 2 because 5 is larger than 3.

Rule 2: Keep the Sign of the Larger Number

The result will have the same sign as the number with the larger absolute value. In 5 + (-3), the result is positive because 5 has a larger absolute value than -3.

Special Case: Equal Absolute Values

If the absolute values are equal, the result is zero. For example, 4 + (-4) = 0.

Worked Examples

Example 1: Positive Number Larger

Calculate 8 + (-5):

  1. Identify the larger absolute value: 8 is larger than 5.
  2. Subtract the smaller from the larger: 8 - 5 = 3.
  3. Keep the sign of the larger number: the result is positive.
  4. Final result: 3.

Example 2: Negative Number Larger

Calculate -7 + 4:

  1. Identify the larger absolute value: 7 is larger than 4.
  2. Subtract the smaller from the larger: 7 - 4 = 3.
  3. Keep the sign of the larger number: the result is negative.
  4. Final result: -3.

Example 3: Equal Absolute Values

Calculate 6 + (-6):

  1. Identify the absolute values: both are 6.
  2. Subtract: 6 - 6 = 0.
  3. Final result: 0.

FAQ

What happens when you add a negative number to a positive number?
You subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.
Is adding a negative number the same as subtracting?
Yes, adding a negative number is equivalent to subtracting its absolute value. For example, 5 + (-3) is the same as 5 - 3.
What if the numbers have the same absolute value but different signs?
The result will be zero because the positive and negative values cancel each other out.
Can you add more than two numbers with different signs?
Yes, you can add any number of positive and negative numbers by following the same rules for each pair.