- Operations with Integers
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- Integer subtraction: Problem type 1
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# 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