Subtraction of Integers

Rules for Subtracting Integers:
1) Positive Integer – Positive Integer
Rule: The sign of the result depends on the order of the numbers.

• If the first number is larger, the result is positive.
  Examples:
• 8−1=7, 30−13=17
• If the first number is smaller, the result is negative.
  Examples:
• 4−7=−3, 1−5=−4

2) Negative Integer – Negative Integer
Rule: Change the subtraction into addition by changing the sign of the second number. Then, follow the rules for adding integers.

• Example:
• (−5) − (−1) = −5 + 1 = −4

3) Positive Integer – Negative Integer
Rule: Change the subtraction into addition. Subtracting a negative is the same as adding a positive.
Result: The answer is always positive.

• Example:
• 5−(−1) = 5 + 1 = 6
  

4) Negative Integer – Positive Integer
Rule: Change the subtraction into addition. The result will be negative because a larger positive number is being subtracted from a smaller negative number.
Result: The answer is always negative.

• Example:
• (−1) − 5 = −1 + (−5) = −6

  Signs of integers	What to do?	Sign of the answer	Examples
  (+) – (+)	Subtract	Sign of the larger integer	9-4=5, 4-7=-3
  (-) – (-)	Subtract	Sign of the larger integer	(-9) - (-5) = -9 + 5 = -4
  (+) – (-)	Add	+	(7) –  (-2) = 7 + 2 = 9
  (-) – (+)	Add	–	(-1) –(8) = (-1) + (-8) = -9