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How to Add and Subtract Integers with Parentheses?

Published in Integer Arithmetic 2 mins read

Adding and subtracting integers with parentheses requires careful attention to signs and order of operations. Here's a breakdown of the process:

Understanding the Basics

Before diving into parentheses, remember these fundamental rules for adding and subtracting integers:

  • Adding Integers with the Same Sign: Add their absolute values and keep the sign. Example: (-3) + (-5) = -8
  • Adding Integers with Different Signs: Subtract the smaller absolute value from the larger absolute value. Keep the sign of the integer with the larger absolute value. Example: (-7) + 4 = -3 (because 7-4=3, and 7 is the larger absolute value and is negative).

Dealing with Parentheses

Parentheses often indicate a multiplication of signs. Here's how to handle them:

  • Positive Sign Outside Parentheses: A "+" sign outside the parentheses doesn't change the sign of the term inside. Example: +(+5) = +5 and +(-3) = -3
  • Negative Sign Outside Parentheses: A "-" sign outside the parentheses does change the sign of the term inside. Example: -(+5) = -5 and -(-3) = +3

Steps for Adding and Subtracting Integers with Parentheses

  1. Simplify within Parentheses (if possible): If there are calculations to be done inside the parentheses, do those first.
  2. Remove Parentheses: Apply the sign rules above to remove the parentheses.
  3. Combine Integers: Add or subtract the integers from left to right, following the basic rules of integer addition and subtraction.

Examples

Let's illustrate with examples:

  • Example 1: 5 + (-3) - (-2)

    1. Remove Parentheses: 5 - 3 + 2
    2. Combine from left to right: 5 - 3 = 2, then 2 + 2 = 4
    3. Result: 4

  • Example 2: -7 - (+4) + (-1) - (-6)

    1. Remove Parentheses: -7 - 4 - 1 + 6
    2. Combine from left to right: -7 - 4 = -11, then -11 - 1 = -12, then -12 + 6 = -6
    3. Result: -6

  • Example 3: 10 - (-5 + 2)

    1. Simplify Inside Parentheses: -5 + 2 = -3
    2. Remove Parentheses: 10 - (-3) = 10 + 3
    3. Combine: 10 + 3 = 13
    4. Result: 13

Summary

Adding and subtracting integers with parentheses involves simplifying the expression by properly removing the parentheses, considering the signs, and then combining the integers according to the standard rules of addition and subtraction. Remember that a negative sign in front of a parenthesis changes the sign of the terms inside, while a positive sign does not.

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