CSE PEMDAS Tutorial and Mock Test

In this CSE PEMDAS reviewer, we’ll read all about the guidelines that help us obtain only one correct answer. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete. If there are grouping symbols in the expression, PEMDAS tells you to calculate within the grouping symbols first. Without these guidelines given in PEMDAS, the accurate and objective nature of mathematical calculation could not exist.

So what exactly is PEMDAS? The word PEMDAS stands for parenthesis, exponents, multiplication, division, addition, subtraction. It is mandatory that you learn and remember this process if you want to have a higher chance of passing the Civil Service examination. Don’t worry as I will do my best to explain to you how this works so that you could easily understand it. So now, let’s have an example. Let’s try to solve an equation without using PEMDAS.

3 × 5 + 8 = ?

If the PEMDAS rule does not exist, I could multiply first, and then add to get 23. I also have the option to add first, then multiply and get 16. So which answer is correct? Using PEMDAS, the only correct answer is 23, because the order of the letters in PEMDAS tells us that M, multiplication, should be performed before A, addition.

Here’s an explanation of the rules given in PEMDAS:

Step 1: At the top of the list, remember to ALWAYS simplify everything inside the grouping symbols. Examples of grouping symbols are parentheses (  ), brackets, and braces {  }. For nested grouping symbols, work it out from the inside and out.

Step 2: Exponential expressions are calculated or evaluated first before performing any of the four fundamental arithmetic operations, namely: addition, subtraction, multiplication, and division.

Step 3: Next, multiply and/or divide whichever comes first from left to right before performing addition and subtraction. This tells us that multiplication and division have a higher level of importance than addition and subtraction.

Step 4: Lastly, add and/or subtract whichever comes first from left to right.

One important thing:

This CSE PEMDAS reviewer would like you to remember that the operations of multiplication and division have the same level of priority. To decide when to multiply or divide, always perform the one which appears first from left to right. If the division comes first before the multiplication, divide first then multiply and vice versa.

Gusto ng reviewer na ito na alalahanin nyo na pagdating sa PEMDAS, pantay lamang ang multiplication at division. Kapag nauna sa kaliwa ang division, unahin ninyo mag-divide. Kapag nauna naman ang multiplication, unahin mag-multiply.

In the same manner, addition and subtraction are co-equal in terms of importance. Even if ADDITION (letter A) comes first before SUBTRACTION (letter S) in the PEMDAS acronym, you should always perform the operation that comes first as you work it out from left to right. If subtraction comes first before addition, subtract first before adding and vice versa.

Sa parehong paraan, ang addition at subtraction ay magkaparehas din ng importansya. Kahit na nauuna ang ADDITION (letter A) bago ang SUBTRACTION (letter S) sa acronym na PEMDAS, unahin nyo pa rin ang operation na nauuna sa kaliwa. Kung nauuna ang subtraction bago ang addition, then mag-subtract muna. Ganun din ang gawin kapag nauna naman ang addition.

Another important note:

If you encounter an equation without any parenthesis and/or exponents, then proceed with MDAS. I bet you already know what it means.

CSE PEMDAS Example

Before we head onto some PEMDAS test questions, we’ll solve one sample equation first:

Simplify the following expression using the PEMDAS order of operation.

2 × 4² + 5² ÷ (26 – 1)

First, simplify the expression inside the parenthesis. 26 minus 1 is 25.

2 × 4² + 5² ÷ (26-1) becomes 2 × 4² + 5² ÷ 25

 

After that, evaluate the powers (terms with exponents). 4 raised to the power of 2 is 16 and 5 raised to the power of 2 is 25. I told you this CSE PEMDAS reviewer is a great help.

2 × 4² + 5² ÷ 25 will become 2 × 16 + 25 ÷ 25

 

After doing so, we will have a simpler expression that involves addition, multiplication, and division. Looking at the current equation from left to right, we see that we should multiply first, then divide. 2 multiply by 16 is 32 and 25 divided by 25 is 1.

2 × 16 + 25 ÷ 25 will now look like 32 +1

 

All that is left to do is perform the remaining process.

32 +1 = 33

 

Civil Service PEMDAS Test Exercise

Now that you understand how to follow the PEMDAS rule, let’s head onto some test exercises. This will be easy for you if you always remember what process to do first. Don’t forget to write your answers so you can check them later.

1. 3 − (2³ ÷ 1) + 5 = ___?

2. (5 + 7³) ÷ 7 × 7 = ___?

3. (6 + 7²) + 1 = ___?

4. (6³ − 9 − 1) × 4 = ___?

5. (2 − 7) − 8 − 3 = ___?

6. 4³ − (2 + 2³) × 5 = ___?

7. (6 − 1 + 7) = ___?

8. (3² − 3⁴) + 5 = ___?

9. (7 + 8 − 4²) × 2 + 1 = ___?

10. 6 − (8 + 3³) − 4 = ___?

11. (7 + 3 × 6 + 3² – 4) = ___?

12. (7 + 2³) × 9 = ___?

13. (3 × 6) − 5 = ___?

14. 6 × (2⁴ ÷ 4) ÷ 2 = ___?

15. (2³ − 9 − 8) ÷ 3 × 3  ___?

16. 2³ ÷ (7 ÷ 7 ÷ 8) = ___?

17. (6 + 6²) × 3 = ___?

18. (3 + 1) × 8 × 4 = ___?

19. (7³ × 4) + 7 = ___?

20. 6² − 3 × (3² × 2) + 5 = ___?

After you have answered all the questions, click on any of the social media buttons below so you can see the correct answers.

So did you do well in this CSE Pemdas reviewer and mock test? You should have gotten at least 17 correct answers. If you did, good job. If you got less, then you should practice more. I’ll be adding more practice questions in the future regarding PEMDAS equations. For now, you can review more about Math by checking out these CSE Numerical Reasoning reviewers.