askvity

How to Subtract Integers?

Published in Integer Operations 2 mins read

Subtracting integers involves understanding how to handle positive and negative numbers. The core concept is to change subtraction into addition by using the additive inverse (opposite) of the second number.

Understanding Integer Subtraction

Here’s a breakdown of the rules for subtracting integers:

  • Subtracting a positive integer: This is equivalent to adding a negative integer. For example, 5 - 3 is the same as 5 + (-3).
  • Subtracting a negative integer: This is equivalent to adding a positive integer. For example, 5 - (-3) is the same as 5 + 3.

Steps to Subtract Integers

  1. Rewrite the subtraction as addition: Change the subtraction sign to an addition sign. Then, change the sign of the number being subtracted to its opposite.
    • If you have a - b, rewrite it as a + (-b).
    • If you have a - (-b), rewrite it as a + b.
  2. Add the integers: Now that you have an addition problem, follow the rules for adding integers:
    • Same signs: If both numbers are positive or both are negative, add their absolute values and keep the original sign. For instance, -3 + (-5) is -8 and 3 + 5 is 8 (as also mentioned in the video "Subtracting Integers - YouTube", at 0:46 and 6:30 where they discuss about the signs).
    • Different signs: If the signs are different, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. For example, 7 + (-3) is 4, and -7 + 3 is -4.

Examples

Here are a few examples to illustrate:

  • Example 1: 7 - 4
    • Rewrite as: 7 + (-4)
    • Solve: 7 + (-4) = 3
  • Example 2: 5 - (-2)
    • Rewrite as: 5 + 2
    • Solve: 5 + 2 = 7
  • Example 3: -3 - 6
    • Rewrite as: -3 + (-6)
    • Solve: -3 + (-6) = -9
  • Example 4: -8 - (-4)
    • Rewrite as: -8 + 4
    • Solve: -8 + 4 = -4

Key Points to Remember

  • Subtracting a number is the same as adding its opposite.
  • When adding integers with different signs, find the difference of their absolute values and use the sign of the number with the greater absolute value.
  • When adding integers with the same signs, add their absolute values and use the same sign.

Related Articles