# Four Effective Techniques in Adding Integers

We have already discussed **addition of integers**. In this post, I am going to discuss four different techniques in adding integers.

**Adding Numbers with the Same Sign**

In adding integers with the same sign, we just add them and then copy the sign. For example, in adding 2 + 8, 2 and 8 are positive integers, so we just add them, and the answer will be positive. So, 2 + 8 = 10. On the other hand, if both integers are negative we also do the same: add them, then copy the sign. For example, -9 + -3 = -12 since both of them are negative integers.

Watch: **24 Taglish Math Videos about Integers in Youtube**

The techniques below are for adding integers with different signs. These strategies are important because you can visualize addition even without memorizing the rules.

**Techniques in Adding Integers with Different Signs**

* Technique 1: Using Positive and Negative Chip*s

You can imagine integers as positive and negative chips. Since +1 + -1 = 0, a pair of positive and negative chips will give a sum of 0. So, 3 means 3 positive chips and -4 means 4 negative chips. Since each pair of positive and negative chip cancels out each other (their sum is 0), then the remaining chips after the pairing will be the answer. So, 3 + (-4) as represented below is -1 since only one negative chip remains.

Another example is -4 + 6 = 2.

Watch: **How to Add Integers Using Chips in Youtube**

**Technique 2: Decomposing the Numbers**

This strategy uses the fact that **a + (-a) = 0**. Using this strategy, we can split one of the addends. For example, in 8 + (-5), we split 8 to 3 + 5 so that 5 and -5 will become 0. So,

8 + (-5) = 3 + 5 + (-5)

=3 + (5 + -5)= 3 + 0 = 3.

In -11 + 3, we can split -11 to -8 + -3. So,

-11 + 3 = -8 + (-3 + 3) = -8 + 0 = -8.

**Technique 3: Using the Number Line**

Integers can also be represented as movement on the number line. A positive integer is a movement to the right of 0 and a negative integer is a movement to the left. Positive 3 and -2 can be represented as shown below.

So, **3 **+ (**-5**) can be represented as a movement of 3 units to the right of **0**, then a movement of 5 units to the left. As we can see in the next diagarm, it the movement stopped at -2. So, 3 + (-5) = -2.

Also, -2 + 3 can be represented as a movement 2 units to the left of 0 and then a movement of 3 units to the right. The movement stopped at 1, so -2 + 3 = 1.

Watch: **How to Add Integers Using the Number Line in Youtube**

**Technique 4: Grouping Numbers with Similar Signs**

In adding more than 2 addends with different signs, group the numbers with the same signs. For example, 9 + (-2) + 4 + (-1), we can do the following:

(1) add the positive integers first: 9 + 4 = 13

(2) add the negative integers (-2 + -1 = -3)

(3): finally, add the two sums: 13 + (-3) = 10.

Try using the techniques above by answering the following and share to us which technique do you like most.

1.) 5 + (-10)

2.) -3 + 8

3.) 12 + – 10 + 7

4.) -10 + -3 + 4

1.) 5 + (-10) = -5

2.) -3 + 8 = 5

3.) 12 + – 10 + 7 = 9

4.) -10 + -3 + 4 = –

-9