Adding integers using a number line or the rules for addition of integers

Adding integers is the process of getting the sum of two, three, or more integers. The sum of two or more integers could become smaller, bigger, or just equal to zero. 

The addition of integers could be performed using any of the following methods:

  • Using a number line
  • Using the rules for adding integers shown in the figure below
  • Using chips to model the integers
Rules for addition of integers

The first two methods will be covered here in this lesson. See our related topics below if you want to learn how to add integers using chips.

Adding integers using a number line

A number line is a good way to start when learning how to add integers. It will help you think through problems and approach them with intuition. As a result, the rules for addition of integers will make more sense and they will also be easier to remember.

Example #1

Add: 2 + 6

Start at 2 and move 6 units to the right. Since you stopped at 8, the answer is 8.

Adding 6 to 2

2 + 6 = 8

Notice that you will get the same answer if you start at 6 and move 2 units to the right.

Example #2

Add: -2 + 8:

Start at -2 and move 8 units to the right. Since you end up at 6, the answer is 6.

Adding 8 to -2

-2 + 8 = 6

Notice that you will get the same answer if you start at 8 and move 2 units to the left.

Example #3

Add: 4 + -7

Start at 4.

As already stated in example #2, the number you are adding to 4 is a negative number (-7 is negative), so you have to move 7 units to the left.

After you do that, you will end up at -3, so the answer is -3

4 + -7 = -3

Adding -7 to 4

Notice that you will get the same answer if you start at -7 and move 4 units to the right.

Example #4

Add: -2 + -6

Start at -2

Once again, the number you are adding is a negative number (-6 is negative), so you will move 6 units to the left.

You will end up at -8, so the answer is -8.

 -2 + -6 = -8

Adding -6 to -2

Notice that you will get the same answer if you start at -6 and move 2 units to the left.

Other examples showing how to add integers using a number line.

-1 + 8 = 7 ( Start at -1 and move 8 units to the right).

4 + -4 = 0 ( Start at 4 and move 4 units to the left).

7 + -9 = -2 ( Start at 7 and move 9 units to the left).

-5 + 3 = -2 ( Start at -5 and move 3 units to the right)

Problems than can arise when using a number line to add integers

What if you want to find the sum of the following integers?

-78 + 90

-520 + -144

-240 + 115

A couple of problems can come up

  • First, your number line may not fit in your notebook
  • Second, even if you could manage to fit the number line somewhere, since the numbers are so big, it will be very inconvenient or take a long time to count.

For example, starting from -78 and move 90 units to the right is very inconvenient. This is the reason that we need rules.

Rules for adding integers with the same sign

Rule #1

When adding integers with the same sign, add their absolute values. The sum has the same sign as the addends.

Example #4 revisited

Add: -2 + -6

Add the absolute value:

Absolute value of -2 = |-2| = 2

Absolute value of -6 = |-6| = 6

|-2| + |-6| = 2 + 6 = 8

The sum has the same sign as the addends.

Since the sign of the addends is -, the sign of the sum is -

-2 + -6 = -8

Rule #2

When adding integers with the different signs, find the difference of their absolute values. The sum has the same sign as the addend with the greater absolute value.

Example #3 revisited

Add: 4 + -7

Add the absolute value:

Absolute value of 4 = |4| = 4

Absolute value of -7 = |-7| = 7

|-7| - |4| = 7 - 4 = 3

The addend with the greater absolute value is -7. Therefore, the sign of the sum is -

4 + -7 = -3

Adding integers using the rules for addition of integers

Earlier, we mentioned that it will be hard to do the following additions using a number line.

1) -78 + 90

2) -520 + -144

3) -240 + 115

Let us use the rules to do them now!

1) -78 + 90

|-78| = 78

|90| = 90

90 - 78 =  12

The addend with the greater absolute value is 90. Therefore, the sign of the sum is +

-78 + 90 = 12

2) -520 + -144

|-520| = 520

|-144| = 144

520 + 144 = 664

The sum has the same sign as the addends.

Since the sign of the addends is -, the sign of the sum is -

-520 + -144 = -664

3) -240 + 115

|-240| = 240

|115| = 115

240 - 115 =  125

The addend with the greater absolute value is -240. Therefore, the sign of the sum is -

-240 + 115 = -125

Other related topics related to integers are modeling integers with chips, integers and inductive reasonings, and consecutive integers.

Adding integers quiz. Take this quiz to find out if you really understood this lesson.

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