**Addition of Integers**

**Addition of Integers Rule 1 – While adding two integers with the same sign, we add their values regardless of their signs, and give the sum, their common sign.**

**Adding two numbers with positive sign**

For example, to add 15 and 30, both of which have positive sign, we would add the values

15 + 30 = 45.

The sum 45, would be given their common sign, + and the number would be +45

**Adding two negative numbers**

For example, to add -5 and -20, both of which have negative sign, we would add the values 5 and 20, ignoring their signs

5 + 20 = 25.

The sum 25, would be given their common sign, – and the number would be -25

**Addition of Integers Rule 2 – When we have to add two integers with different signs ( one is positive and other is negative), we find their difference, regardless of their signs, and give the sign of the integer with the greater value to such difference.**

**Adding two integers with different signs – Positive number greater than negative number**

For example, to add -5 and +20, two integers with different signs ( one is positive and other is negative), we find their difference,

20 – 5 = 15.

The difference 15, would be given the sign of the integer with the greater value, which is 20 with a positive sign, and the answer would be +15.

**Adding two integers with different signs – Negative number greater than Positive number**

For example, to add -35 and +20, two integers with different signs ( one is positive and other is negative), we find their difference,

35-20 = 15.

The difference 15, would be given the sign of the integer with the greater value, which is 35 with a negative sign, and the answer would be – 15.

**Addition of Integers Examples **

**Addition of Integers Example 1**

Find the sum of 25 and 27?

**Explanation**

While adding two integers with the same sign, we add their values regardless of their signs, and give the sum, their common sign.

In present case,

First, we add the values of the two integers, regardless of the negative sign:

25 + 27 = 52

Now we would assign the common sign to the answer,

In present case the common sign is ( + )

So, the sum of 25 and 27 is +52 or 52

**Addition of Integers Example 2 – Adding two negative numbers**

Find the sum of (-47) and (-52) ?

**Explanation**

While adding two integers with the same sign, we add their values regardless of their signs, and give the sum, their common sign.

In present case,

First, we add the values of the two integers, regardless of the negative sign:

47 + 52 = 99

Now we would assign the common sign to the answer,

In present case the common sign is ( – )

So, the sum of (-47) and (-52) is -99

**Addition of Integers Example 3**

Find the sum of 68 and -32?

**Explanation**

When we have to add two integers with different signs ( one is positive and other is negative), we find their difference, regardless of their signs, and give the sign of the integer with the greater value to such difference.

In present case,

First we find the difference to the given integers i.e, 68 – 32 = 36

Now, we would assign the sign of the greater integer to the result.

In this case, 68 > 32

and the sign of 68 is ( + )

Hence, the sum of 68 and -32 is +36 or, 36

**Addition of Integers Example 4**

Find the sum of -17 and 25?

**Explanation**

When we have to add two integers with different signs ( one is positive and other is negative), we find their difference, regardless of their signs, and give the sign of the integer with the greater value to such difference.

In present case,

First, we find the difference to the given integers i.e, 25 – 17 = 8

Now, we would assign the sign of the greater integer to the result.

In this case, 25 > 17

and the sign of 25 is ( + )

Hence, the sum of -17 and 25 is +8 or, 8

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**Subtracting Integers****Multiplication of Integers****Dividing Integers****Properties of Integers – Closure, Commutative, Associative, Distributive**