Subtraction of 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, obey 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. Because we are subtracting a larger positive number from a smaller negative number, the result will be negative.
Result: The answer is always negative.
Example:
(− 1) − 5 = −1 + (− 5) = − 6

• Banking: Account at ₹250. Paying a bill of ₹400 
  250 − 400 = −150 (overdraft).

• Sea Level: Submarine from – 120 m to – 70 m 
  –70 − (– 120) = 50 m rise.

• Elevator: Basement –2 to 4th floor
  4 − (– 2) = 6 floors up