Skill: Subtract integers

Explanation and Free Practice Resources

Subtracting integers means finding the difference between positive and negative whole numbers, including zero, by interpreting a−ba-b as adding the additive inverse of bb. A number line represents this as moving in the direction opposite to the subtracted number, clarifying why subtracting a negative increases a value and preventing the misconception that subtraction always makes a number smaller; this structure supports simplifying algebraic expressions.

Detailed Explanation: Subtract integers

To subtract integers, rewrite subtraction as adding the opposite:

a−b=a+(−b)a-b=a+(-b)

Then add the integers.

Example: Find (5−(−3))(5-(-3))

  1. Start with the expression:

5−(−3)5-(-3)
  1. The opposite of (−3)(-3) is (+3)(+3). Rewrite the subtraction:

5+35+3
  1. Add:

5+3=85+3=8

Therefore,

5−(−3)=8\boxed{5-(-3)=8}

On a number line, start at 55. Because you are subtracting (−3)(-3), move in the opposite direction of negative, which is 33 spaces to the right. You land on 88.

Subtracting a negative increases the value because it is the same as adding a positive.

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Negative Integer Subtraction


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