Addition of Integers

Adding Integers

Below is a quick summary of the rules for adding integers.

rules for adding integers or rules for addition of integers when signs are the same add their absolute values then copy the common sign if the signs are different subtract their absolute values then use the sign of the integer with the bigger absolute value

Integer addition is a very straightforward process. Just follow the basic steps provided below and you’ll get the correct answers every time. There are two cases when adding integers. The first scenario is when we add integers having the same sign. These are the steps:

Case 1: Steps when Adding Integers with the Same Sign

Step 1: Take the absolute value of each number.

Step 2: Add the absolute values of the numbers.

Step 3: Keep the same sign.

For more practice, click the link below:

Adding Integers Practice Problems with Answers

Examples of Integer Additions with Like Sign

Example 1: Add the integers below that have the same sign.

the sum of positive 5 and positive 6, in symbol, 5+6
  • Step 1: Take the absolute values of the numbers.
The absolute value of positive 5 is equal to 5 while the absolute value of positive 6 is positive 6. In math symbols we have, |+5|=5 and |+6|=6.
  • Step 2: Add the absolute values.
The sum of 5 and 6 is equal to 11. In equation form, 5+6=11.
  • Step 3: Keep the same sign which is positive.
Positive 5 plus positive 6 equals positive 11.

Example 2: Add the integers below that have the same sign.

Negative 10 plus negative 3.
  • Step 1: Find the absolute values of negative 10 and negative 3.
|-10|=10 and |-3|=3
  • Step 2: Find the sum of their absolute values.
The sum of 10 and 3 is 13. That is 10+3=13.
  • Step 3: Keep the same sign which is negative.
Negative 10 added to negative 3 is equal to negative 13. You can also write this as (-10)+(-3)=-13.

Now here’s the little twist. We are now going to add integers that have different signs.

Case 2: Steps when Adding Integers with Different Signs

Step 1: Take the absolute value of each number.

Step 2: Subtract the number with a smaller absolute value from the number with bigger or larger absolute value.

Step 3: Copy the sign of the number with the bigger or larger absolute value.

Examples of Integer Additions with Unlike Signs

Example 1: Add the integers below that have different signs.

what is the sum of negative 15 and 7, or -15+7 = ?
  • Step 1: Take the absolute values of the numbers.
the absolute value of negative 15 equals 15 and the absolute value of positive 7 equals 7
  • Step 2: Since the absolute value of positive 7 is less than the absolute value of negative 15, subtract 7 from 15.
15 minus 7 equals 8, or 15 - 7 = 8
  • Step 3: The absolute value of negative 15 is greater than the absolute value of positive 7. Therefore, the final answer will have a negative sign because we copy the sign the sign of the number that has a bigger absolute value.
negative 15 plus positive 7 is negative 8. in an equation, -15 + (+7) = -8

Example 2: Add the integers below that have different signs.

positive 23 plus negative 18 is equal to positive 5, that is, 23 + (-18) = 5
  • Step 1: Find the absolute value of each number.
the absolute value of positive 23 is 23 while the absolute value of negative 18 is 18. in symbols, we have |+23|=23 and |-18|=18
  • Step 2: Since the absolute value of negative 18 is less than the absolute value of positive 23, we will subtract 18 from 23.
twenty-three minus 18 equals 5, or 23 - 18 = 5
  • Step 3: The final answer will have a positive sign because we will get it from positive 23 which has a larger absolute value than negative 18.
positive 23 plus negative 18 is equal to positive. in an equation, we can express this as 23 +(-18)=5

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Adding Integers Practice Problems with Answers

Subtracting Integers

Multiplying Integers

Dividing Integers