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.  Continue Reading

PEMDAS Rules and Operations on Real Numbers

Now that you have already learned the four fundamental operations on real numbersaddition, subtraction, multiplication, division – it is time to combine these operations into a single problem. In the Philippine Civil Service Examination, most of the problems on operations on real numbers have at least two or more operations involved.  If you can recall, we call these operations MDAS in the elementary grades and later and PE making it PEMDAS. PEMDAS is the acronym for Parenthesis, Exponent, Multiplication, Division, Addition and Subtraction. This is basically the order of operations when you calculate an arithmetic problem involving two or more operations.


Calculate in the following order.

  1. the expressions inside the Parentheses.
  2. the expression with Exponents.
  3. If no operation separates Multiplication and Division, perform from left hand side to right whichever comes first.
  4. If no operation separates Addition and Subtraction, perform from left hand side to right whichever comes first.  Continue Reading

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.  Continue Reading

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. Continue Reading

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) Continue Reading

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  Continue Reading

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. Continue Reading

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 Continue Reading