Integers are positive, negative numbers including zero and do not include any fractional part. This topic will cover the rules for adding integers. There are certain rules which will help us in understanding how:

• Two positive integers are added
• Two negative integers are added
• One positive and another negative integers are added

First Rule:

When two positive integers are added then the final answer is assigned with a positive (+) sign

For Example:

(i) 8 + 9 = 17

Here 8 and 9 both are positive integers and they are added to get 17.

(ii) 25 + 30 = 55

Here 25 and 30 both are positive integers and they are added to get 55

(iii) 80 + 10 = 90

Here 80 and 10 both are positive integers and they are added to get 90

(iv) 30 + 10 = 40

Here 30 and 10 both are positive integers and they are added to get 40

Second Rule:

When two integers are negative integers (-) then we will add the absolute value of two integers and the final answer will be assigned a negative (-) sign.

For example:

(i) (-8) + (-5) = -13

Here both the integers are negative i.e. – 8 and – 5. So we will add their absolute value that is 8 and 5 which adds to 13. Now since both the numbers are negative so the answer will also carry a negative sign.

(ii) (-6) + (-6) = - 12

Here both the integers are negative i.e. – 6 and – 6. So we will add their absolute value that is 6 and 6 which adds to 12. Now since both the numbers are negative so the answer will also carry a negative sign.

(iii) (-5) + (-2) = -7

Here both the integers are negative i.e. – 5 and – 2. So we will add their absolute value that is 5 and 2 which adds to 7. Now since both the numbers are negative so the answer will also carry a negative sign.

(iv) (-7) + (-3) = -10

Here both the integers are negative i.e. – 7 and – 3. So we will add their absolute value that is 7 and 3 which adds to 10. Now since both the numbers are negative so the answer will also carry a negative sign.

Third Rule:

When one integer is positive and another integer is negative then we will find the difference of the two integers by considering their absolute value and then will assign the result with a sign of integer with the higher absolute value.

For Example:

(i) 4 + (-7) = -3

Here the first number is positive i.e. 4 and the second number is negative i.e. – 3. We know from the rule that when one integer is positive and another negative then we have to find the difference between those two integers by considering their absolute value. Hence 7 – 4 = 3, but the integer with higher absolute value is 7. Hence the result 3 will have negative (-) sign i.e. – 3.

(ii) (-8) + 2 = -6

Here the first number is negative i.e. – 8 and the second number is positive i.e. +2. We know from the rule that when one integer is positive and another negative then we have to find the difference between those two integers by considering their absolute value. Hence 8 – 2 = 6, but the integer with higher absolute value is 8. Hence the result 6 will have negative (-) sign i.e. – 6.

(iii) (-5) + 10 = + 5

Here the first number is negative i.e. – 5 and the second number is positive i.e. +10. We know from the rule that when one integer is positive and another negative then we have to find the difference between those two integers by considering their absolute value. Hence 10 – 5 = 5, but the integer with higher absolute value is 10. Hence the result 5 will have positive (+) sign i.e. + 5.

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