Real Number Operations and PEMDAS Practice Test 1

In the previous post, you have learned the PEMDAS rules or the rules in performing arithmetic operations namely addition, subtraction, multiplication and division. In this post, you will practice to see if you have mastered these rules. I have mixed the notations so that you will be familiarized with all of them. For example, 4 \times 8 + 3 \times -2 can also be written as 4(8) + 3(-2) or (4)(8) + (3)(-2).

You should also be familiar with division where in the expression

\displaystyle \frac{(3 + 2) \times 3}{3 + 5}

the operation in both the numerator and numerator are simplified first before dividing the expressions. This is equivalent to (3 + 2)(3) \div (3 + 5). Do not worry though regarding the use of parentheses, we will discuss them in the next topic. For now, answer the questions to the best of your abilities.  » Read more

Subject-Verb Agreement Practice Test 1 Answers

Below are the answers to the Subject-Verb Agreement Practice Test 1. The incorrect verb in each sentence is highlighted red and the correct verb in the corrected sentence is highlighted green. An explanation follows every correction. 

Subject-Verb Agreement Practice Test 1 Answers

1. My brother or my sister are arriving tomorrow.

Correct sentence:  My brother or my sister is arriving tomorrow

Explanation: Two singular subjects connected by or require a singular verb. In this sentence, there brother and sister are both singular, so the sentence should use the singular verb is.

2. Neither Ella nor her friends is available to assist you.  » Read more

Subject-Verb Agreement Practice Test 1

The subject-verb agreement is one of the basic rules in grammar and correct usage. It is important that you master this rule if you want to pass the Civil Service Examination. 

The basic rule in the subject-verb agreement is that a singular subject requires a singular verb and a plural subject requires a plural verb. Of course, to be able to answer correctly, you must be able to identify the subject of the sentence and the verb. As a review, a subject is the noun or pronoun that performs the verb. A verb on the other hand, is a word that shows action. We will have a separate discussion on these topics. For now, just answer the practice test below and see how much do you remember of the subject-verb agreement.

Subject-Verb Agreement Practice Test 1

1. My brother or my sister are arriving tomorrow.

2. Neither Ella nor her friends is available to assist you.

3. Armand, together with his friends, are going on a camping trip tomorrow. » Read more

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.

Answers and Explanation

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

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

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.

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