One of the topics in basic mathematics that will likely be included in the the Philippine Civil Service Exam both professional and subprofessional are operations on integers. Although a few Civil Service test items may be given from this topic, it is important that you master it because a lot of calculation in other topics will need knowledge of integers and its operations (addition, subtraction, multiplication, division). For example, solving some word problems in mathematics and solving equations will need knowledge on operations of integers.

Integers are whole numbers that are either positive or negative. Examples of integers are -5, 6, 0, and 10. If we place this on the number line, negative integers are the integers that are below 0 (left of 0), while the positive integers are the integers above 0 (right of 0).

##### Adding Integers that Are Both Positive

When you add integers that are both positive, it is just like adding whole numbers. Below are the examples.

Example 1: ^{+}2 + ^{+}4 = ^{+}6

Example 2: ^{+}9 + ^{+}41 + ^{+}6 + = ^{+}56

Example 3: ^{+}120 + ^{+}13 + ^{+}12 + = ^{+}145

Although we have created a small + before the number to indicate that it is positive, in reality, only negative numbers have signs. This means that ^{+}2 + ^{+}4 = ^{+}6 is just written as 2 + 4 = 6.

##### Adding Integers that Are Both Negative

Adding number that are both negative is just the same as adding numbers that are both positive. The only difference is that if you add two negative numbers, the result is negative.

Example 1: ^{–}5 + ^{–}8 = ^{–}13

Example 2: ^{–}10 + ^{–}18 + ^{–}32 + = ^{–}60

Example 3: ^{–}220 + ^{–}11 + ^{–}16 + = ^{–}247

##### How to Add Positive and Negative Integers

Before adding, you should always remember that ^{+}1 and ^{–}1 cancel out each other, or ^{+}1 + ^{–}1 is 0. So the strategy is to pair the positive and negative numbers and take out what’s left.

*Example 1:* What is ^{+}13 + ^{–}8?

Solution:

We pair 8 positives and 8 negatives to cancel out. Then what’s left is of ^{+}13 is ^{+}5. In equation form, we have

^{+}13 + ^{–}8 = ^{+}5 + ^{+}8 + ^{–}8 = ^{+}5 + (^{+}8 + ^{–}8) = ^{+}5 + (0) = ^{+}5

*Example 2:* What is ^{+}17 + ^{–}20?

Solution:

We pair 17 negatives and 17 positives. What’s left of ^{–}20 is ^{–}3. In equation form, we have

^{+}17 + ^{–}20 = ^{+}17 + (^{–}17 + ^{–}3) = (^{+}17 + ^{–}17) + ^{–}3 = 0 + ^{–}3 = ^{–}3

*Example 3*: What is ^{+}16 + ^{+}37 + ^{–}20 + ^{–}3 +^{–}9 ?

In answering questions with multiple addends, combine all the positives and the negatives then add.

That is ^{+}16 + ^{+}37 = ^{+}53 and ^{–}20 + ^{–}3 +^{–}9 = ^{–}32.

So, the final equation is ^{+}53 + ^{–}32. We pair 32 positives and 32 negatives leaving 21 positives.

In equation form, we have

^{+}53 + ^{–}32 = ^{+}21 + ^{+}32 + ^{–}32 = ^{+}21 + (^{+}32 + ^{–}32) = ^{+}21 + 0 = ^{+}21

By now, you will have realized, that adding integers is pretty easy. If you have questions, please fill out the comment box below.