## How to Subtract Positive and Negative Integers

This is the continuation of the series of Civil Service review in mathematics particularly on operations of integers. In this post, we are going to discuss the most complicated operation on integers. I have taught people of all ages about this topic and it seems that for many, this is the most difficult among the four operations. In this post, we are going to learn how to subtract positive and negative integers or signed numbers. Note that in subtracting integers, there are only  four forms. If a and b are positive, the subtraction are of the following forms.

Case 1: positive minus positive (ab)
Case 2: negative minus positive (ab)
Case 3: positive minus negative (ab)
Case 4: negative minus negative (ab)

##### How to Subtract Positive and Negative Integers

What most people don’t know that ab is the same as ab, or subtracting a number is the same as adding its negative. That means that you only have to memorize the steps in addition of integers. Given a subtraction sentence, you then transform it  into addition. Here are a few examples.

Case 1 Exampe 1: 5 – 8

Subtracting is the same as adding its negative, so 5 – 8 = 5 + 8. Note that 5 + 8 is already addition and 5 + 8 = 3.

Case 2 Example: 10 – 4

The expression 10 – 4 is the same as 10 + 4 = 14.

Remember also that if you see two consecutive – signs or a minus and a negative sign, you can transform it to +. That is, -(a) = + a and -(a) + a. In most exam, the negative signs are not usually superscript, so you will likely -(-a).

Case 3 Example: 5 – 6

The above expression might be written in 5- -6 or 5-(-6). In any case, two negative signs, a minus and a negative sign can be transformed into a plus sign so, 5 (6) = 5 + 6 = 11. Notice that the last equation is also an addition sentence.

Case 4 Example: 8 – 6

The expression 8 – 6 = 8 + 6 = 2.

Observe that the four forms are already completed in the examles. From the strategy above, we only remember two strategies: (1) transform any subtraction sentence to addition sentence and (2) replace two consecutive negatives or a minus and a negative with + sign.

## Solutions to Practice Exercises on Addition of Integers

We have learned how to add integers and in the previous post, I have given you practice exercises that you can use to evaluate your understanding of the topic. Below is the complete solutions to the practice exercises on adding integers. Share to me how many did you get right.

Solutions to Practice Exercises on Addition of Integers

1. 28 + 12 = 40.

2. 14 + 11 = 25

3. 24 + 15 = 9

Solution: We pair 15 and 15  to get 0. We have 9  left. So, the correct answer is 9.

4. –16 + 31 = 15

We pair 16  and 16 to get 0. We are left with positive 15.
5. 23 + 46 + 15 = 54

We add the two positive numbers first: 23 + 46 = 69. Next, we add 69 and 15. We get 15 from 69 and pair it with 15 resulting to 0, so we have 54 left.

6. 45 + 12 + 16 = 17

We add the negative numbers first: 12 + 16 = 28. We add the result to 45. We get 28 from 45 and pair it with  28 to get 0 leaving 17.

7. 12 +15 + 62 =  89

Explanation: They are negative, so we just added them. Of course negative added to negative is always negative.

8. 22 +  36 + 36 = 22

Explanation: 36 + 36 = 0, so we are left with 22.

9. 12 + 18 + 12 + 18 = 0

Explanation: 12 and 12 and 18 and 18 = 0.

10. 31 + 55 + 41 +  32 + 10 = 3

Explanation: Adding the positive integers, we have 31 + 55  = 86. Adding the negative integers, we have  41 +  32 + 10 =83. Now, 86 + 83 = 3

## April 2013 Civil Service Exam Top 10 and Results

Below are the lists of the national top 10 of  the 2013 Civil Service Exam. The paper-and-pencil test was held nationwide on April 14, 2013.  To view the official complete list of passers, please go to the official website of Civil Service Commission.

Professional National Topnotchers

1. Maravilla, Jan Angelique B – 86.21
2. Villaraza, Kristine C – 86.07
2. Baello, Joseph Alejandro M – 86.07
3. Mina, Rhinebert Kyle A – 85.95
3. Canoza, Bianca May O  – 85.95
4. Maravilla, Jan Abigail B – 85.94
5. Gapuz, Hazel Bernadette B – 85.93
6. Ganzon, Mina Angeles L  – 85.91
7. Guillen, Neil Daniel B – 85.75
8. Querubin, Emmanuel S – 85.7
8. Villar, Irene Marie F – 85.7
9. Palabay, Francis A – 85.67
10. Asur, Jodel LL – 85.63

SubProfessional Topnotchers

1. Gaite, Danielle JOanna C – 87.63
2. Ysulat, Andrea Claire C – 87.4
3. Tolentino, Ericko Paolo S – 87.35
4. Torres, Rosette Joy DF – 86.77
5. Quindoza, Mara Patricia D – 87.62
6. Durian, Noreen Rose A – 86.65
7. Briones, Glenn Ray B – 86.47
8. Marquez, Cielo Mae D – 86.39
9. Flores, Maria Kimmy I – 86.29
10. Villanueva, Acer M – 86.24

Source: Civil Service Commision

## Practice Exercises on Addition of Integers

In the previous post, we have learned about adding positive and negative integers particularly on how to add integers with different signs. In this post, I am going to give you 10 exercises on adding integers. I will give the answers below for you to be able to check if your answers are correct. Also, I am going to omit the + sign before the positive integers because this is not usually shown in the exam. This means that 3 will automatically mean +3 unless a – sign precedes it.

1. 28 + 12
2. 14 + 11
3. 24 + 15
4. 16 + 31
5. 23 + 46 + 15
6. 45 + 12 + 16
7.  12 + 15 + 62
8. 22 +  36 + 36
9. 12 + 18 + 12 + 18
10. 31 + 55 + 41 + 32 + 10

## How to Add Positive and Negative Integers

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

+138 = ++ +8 + 8+5 + (+88) = +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

+1720 = +17 + (173) =  (+17 + 17) + 3 = 0 + 33

Example 3: What is +16 + +37 + 20 + 3 +9 ?

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  +3232+21  + (+3232) = +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.

## What is the Philippine Civil Service Examination?

The Philippine Civil Service Examination is given by the Civil Service Commission (CSC) to aspirants who want to work in the Philippine government. All government employees aside from a few exceptions (like passing selected board exams) are required to take the CSC Examination to be granted tenure.

There are two levels of Civil Service Examinations: Subprofessional and Professional. The Subprofessional level is for those who have finished 2-year courses or below. Those who have graduated 4-year courses or beyond are advised to take the Professional level.

The CSC examination is mainly composed of English and Mathematics proficiency. The other areas include Filipino, office filing and ethics, and Philippine constitution particularly Republic Act 6713.  As of this writing, the passing score of the CSC Examination is 80%.

This blog will serve as a Civil Service Reviewer for those who want to take the examination. I will be discussing questions that are similar to the examination and provide answers, detailed explanations, and tips. I will also give online mock exercises and examinations. In addition, I will also provide updates, links, and examination results.

For now, I will be discussing Mathematics and English subjects. The other subjects such as Philippine constitution will be discussed later by more qualified persons.

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