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