Integer subtraction: Problem type 1
Integer subtraction can be written as integer addition as follows.
For any two integers a and b
a – b = a + (−b)
−a – b = (−a) + (−b)
a – (−b) = a + b
−a – (−b) = (−a) + b
After writing an integer subtraction as an integer addition, the rules of integer addition are applied and the results obtained.
The Rules of like signs and unlike signs
It can be put into two rules −
Rule 1 − Two like signs become a positive sign
+(+) = +
−(−) = +
Examples
3+(+4) = 3 + 4 = 7
6−(−5) = 6 + 5 = 11
Rule 2 − Two unlike signs become a negative sign
+(−) = −
−(+) = −
Examples
7+(−4) = 7 − 4 = 3
9−(+3) = 9 − 3 = 6
Formula
Two like signs become a positive sign
Two unlike signs become a negative sign
Subtract
3 − 7
Solution
Step 1:
3 – 7 = 3 + (−7)
The signs of the numbers are different. So, we subtract the absolute values of the integers.
|7| – |3| = 7 – 3 = 4
Step 2:
The sign of the number with larger absolute value (−7) is −.
We keep this sign with the difference obtained in above step
So, 3 − 7 = − 4
Subtract
−9 − 5
Solution
Step 1:
−9 – 5 = −9 + (− 5)
The signs of the number are same. So, we add the absolute values of the integers.
|−9| +| − 5| = 9 + 5 = 14
Step 2:
The sign of the numbers is −.
We keep this sign with the sum obtained in above step
So, −9 − 5= − 14
