Solutions to Practice Test on Multiplying Integers

Recall the rules on multiplying integers. Multiplying two with the like signs (negative and negative or positive and positive) gives a positive product. Multiplying two numbers with unlike signs gives a negative product.

1. -4 x -8 = 32

2. 3 x -7 = -21

3. -12 x -7 = 84

4. -8 x -1 x -4
Group any two first: -8 x -1 = 8. Then 8 x -4 = -32. » Read more

Practice Test on Multiplying Integers

In the previous post, we have learned the rules in multiplying integers.  Below is a 10-item practice test on multiplying integers. Note that in multiplication, we can use the x and () symbols in multiplying two numbers. This means that 3 x 4 is the same as 3 (4) and (3)(4). We will use both symbols in the practice test below to familiarize yourselves with them.  Any of the two symbols can be used in the Civil Service exams.

Practice Test on Multiplying Integers

1. -4 x -8

2. 3 x -7

3. -12 x -7

4.  -8 x -1 x -4 » Read more

How to Multiply Signed Numbers

In the two previous post in Mathematics, we have discussed how to add and subtract signed numbers. In this post, we are going to learn how to multiply signed numbers particularly integers. Signed means positive and negative.

Positive Integer x Positive Integer

Clearly, the product is positive. We had been multiplying positive integers since Grade school and we all know that the product is positive.

Positive Integer x Negative Integer

When you multiply, notice that you are actually adding repeated. When we say 2 x 3, we are actually saying twice three or 2 groups of 3 or 3 + 3. When we say, thrice 11, we are saying 11 + 11 + 11. With this in mind, 3 x – 5 = -5 + -5 + -5. Since we are adding integers which are negative, the sum is also negative or -15. This means that 3 x -5 = -15. If we generalize this, we can say that the product of a positive integer and a negative integer is negative. » Read more

Solutions to Subtracting Integers Practice Test

Blow are the solutions to the Civil Service Exam subtracting integers practice test.  As I have mentioned before, you do not have to memorize the rules of subtraction. All you have to do is convert it to addition. We can do this by converting a subtraction of integers problem  to addition of integers by changing the signs: minus “-: to plus negative “+ (-“  and minus negative “– –” or “– (-” to plus “+“. Observe how the subtraction problems are converted into addition problems in the solutions below. If you have any questions, please use the comment box below.

 1. 12 23 = 12 + (-23) = -11

2. -21 – (-4) = -21 + 4 = -17

3. 17 – (-36) = 17 + 36 = 53

4. -18 13 = -18 + (-13) =-31

5. 22 35 = 22 + (-35) = -13

6. -34 – (-21) = -34 + 21 = – 13

7. 29 – (-6) = 29 + 6 = 35

8. 98 – 14 = 84 (no need to change signs, this is ordinary subtraction since the minuend is larger than the subtrahend).

9. -87 53 = -87 + (-53) = -140

10. 63 92 = 63 + (-92) = -29

In the next post, we are going to discuss about multiplication and division of integers.

Civil Service Practice Test on Subtracting Integers

Three days ago, we have learned how to subtract positive and negative integers or signed numbers. In this post, I am going to give you a practice test on subtracting integers. For convenience, I have colored the negative signs blue instead of raising them to an exponent.

1. 12 – 23

2. 21 -(4)

3. 17 – (36)

4. 18 – 13

5. 22 – 35

6. 34 -( 21)

7. 29 -( 6)

8. 98 – 14

9.  87 – 53

10. 63 – 92

Click here to see the solutions and answers to the practice test given above.

The Scope of the Civil Service Examinations

The scope of the Civil Service examinations in the Philippines, both Professional and Subprofessional, are mainly  English and Mathematics proficiency. They comprise  about 80%  of the examination. Some of the questionnaires in grammar, correct usage, and paragraph organizations are in Filipino.  The remaining 20% are General Information questions, clerical operations in the Subprofessional examination and logical reasoning in the Professional examination.

Below are the scope of the Civil Service Examinations.

Professional Level

In mainly English and a small percentage in Filipino: vocabulary, grammar and correct usage, paragraph organization, reading comprehension, analogy, logical reasoning, and numerical reasoning.

Subprofessional Level

In mainly English and a small percentage in Filipino: vocabulary, grammar and correct usage, paragraph organization, reading comprehension, spelling, clerical operations, and numerical reasoning.

Both Professional and Subprofessional exams also include General Information on the following topics: Code of Conduct  and Ethical Standards for Public Officials and Employees (Republic Act 6713), Peace and Human Rights Issues and Concepts, and Environment Management and Protection.

For more information visit the Official Civil Service Commission website of the Philippines.


5 Effective Ways to Improve Your Vocabulary

English Proficiency makes up about 50% of the Philippine Civil Service Examinations both Professional and Subprofessional. Vocabulary test items such as word meaning and analogy are included in these exams. For a higher probability of passing, it is important that you have a wide vocabulary when taking these examinations. In this post, I am going to give you some tips on how to improve your vocabulary in English based on personal experience. I think these tips will not only improve your vocabulary, but also will improve your command of the English language in general. One thing to remember though: a wide vocabulary does not just develop overnight. It takes time.

1. Read, Read, and Read

Reading is one of the best ways to improve your vocabulary and you should do this everyday. In reading, you do not only meet new words, you see how they are used in sentences. Try reading an article or two a day and you will see your progress in a few months.


via Wikiepdia

Reading novels will introduce you to conversational English and reading news will introduce you to technical English. If you are observant with sentence structure, reading will also introduce you to correct grammar and usage. In effect, if you have not learned grammar formally, you’ll have an idea if a sentence is constructed correctly or not.

2. Play Word Games

Playing word games especially Scrabble against a computer will surely introduce you to new words. If you own a gadget, download a word game app and play against a computer. Download also a dictionary app so that you can look up the new words that you have learned.

In playing word games, you will not just enjoy, you will also learn.

3. Watch English Movies

Watching English movies can also help improve vocabulary. If you are not native English speaker (I assume that this is also read in other countries), I recommend that you watch movies with subtitles.  In so doing, you will most likely meet new words that are used in daily conversations especially in movies with modern settings. Be warned though that in order to make the movies more realistic, some dialogues may be grammatically incorrect. This is because it happens in reality.

4. Take Notes

Whether reading, playing word games, or watching movies, you might also want to take note of the new words that you encounter. Look up their meaning in a dictionary and use them in sentences. After writing a sentence using the new words, you might also want to look at online dictionaries. Most online dictionaries nowadays (such as have sample sentences on how to use words.

5. Write, Write, and Write

Writing a blog or a journal can also help improve your vocabulary. In writing your thoughts, you search for appropriate words to use. This will also help you better remember those words.

After all I said, you are probably asking the following questions in your mind.

How about memorizing?
What if I randomly look up a word at a dictionary and memorize them?

Well, picking some words and memorizing their meaning will help you a little. This strategy based on personal experience is not effective. Most word meanings that are memorized without context are easily forgotten.

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.


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