## Answers to Practice Test on Dividing Integers

Below are the answers and the explanations of the Practice Test on Dividing Integers. Note that as mentioned in the post Dividing Positive and Negative Integers, the rules in dividing integers as well as real numbers are the following:

(1) positive number ÷ positive number = positive number

(2) positive number ÷ negative number = negative number

(3) negative number ÷ positive number = negative number

(4) negative number ÷ negative number = positive number.

1.) -35 ÷ 7 = -5 (by rule 3)

2.) 38 ÷ -19 = -2 (by rule 2) » Read more

## Practice Test on Dividing Integers

In the previous post we have discussed how to divide integers. Operations on real numbers, particularly integers, is one of the scopes of the Civil Service Examinations both Professional and Subprofessional.  You must master these operations because you will use them in solving equations and word problems in Algebra.

Test your skill by answering the exercises below. Recall that a divided by b is the same as a times reciprocal of b.

Practice Test on Dividing Integers

1.) -35 ÷ 7

2.) 38 ÷ -19  » Read more

## A Review on Operations on Real Numbers

We had just finished discussing the different operations on integers: addition, subtraction, multiplication and division. Since you are already familiar with these operations on integers, the operations on real numbers (integers, decimals, and fractions) will be very easy for you because the process is just the same. For example, positive a real number 0.4 is multiplied by a negative real number 0.1, the result is negative just like multiplying positive and negative integers.

Below are worked examples on the operations on real numbers. I made the examples easy so that you can recognize the pattern even if you forgot the rules on operating with decimals and fractions. Do not worry though if you have forgotten the rules because I will have separate posts about them. For now, try to solve and by compare your answer with the calculated results below. » Read more

## Dividing Positive and Negative Integers

In the previous post on integers, we have learned the rules in multiplying positive integers and negative integers. In this post, we are going to learn how to divide positive and negative integers.

If you have observed, in the post on subtracting integers, we have converted the “minus sign” to a “plus negative sign.” I think it is safe for us to say that subtraction is some sort of “disguised addition.” Similarly, we can also convert a division expression to multiplication. For example, we can turn

$\displaystyle \frac{5}{3}$ to $(5 \times \frac{1}{3})$.

In general, the division » Read more

## Answers to Grammar Practice Test 1

Below are the answers and the explanations to the Grammar and Correct Usage Practice Test 1. The incorrect word or phrase in the sentence is highlighted red, while the correct word or phrase is highlighted green.

1. The inventor stood to except the award.

Correct Sentence: The inventor stood to accept the award.
Explanation: Accept means “to receive”, except means “to exclude.”

2. Between the three of us, I think I am the slowest runner.

Correct Sentence: Among the three of us, I think I am the slowest runner.
Explanation: Among is used to refer to 3 or more members of the group, while between is used to refer to two member of the group. » Read more

## Grammar and Correct Usage Practice Test 1

One of the types of test in the Philippine Civil Service Examinations both Professional and Subprofessional is about grammar and correct usage. In the actual examinations, sentences are divided into phrases and numbered 1 through 5. You will be asked to identify the number of the phrase with incorrect grammar or usage.

In the practice test below, the sentences are shorter than the actual examinations, but the important thing is you should be able to identify the error. We will have compound and complex sentences in later practice tests.

Instructions Identify the word/phrase that makes the sentence incorrect if there are any. If no error is found, write NE. » Read more

## A Teaser on Answering Number Series Questions

First of all, I would like to point out the term series in the “Number Series” questions in the Civil Service Examinations is a bit incorrect. Technically, the list of numbers in the examinations is actually called a sequence.  A series is a sequence of sums — well, I will not go into details since it is not included in the examinations.  You can  click the link though if you want to know about it.

Second, this is quite a premature discussion since I have only written a few posts about integers. I planned to write about this later, but I thought that a teaser would be nice. In this post, I will show you that it is a must to master all the topics in mathematics because they are all connected. We will not discuss the strategies on how to answer the sequence problems here; I will have a separate post about them later. Don’t stop reading though because you are going to miss half of your life if you do (kidding). » Read more

## 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

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