Order of Operations and PEMDAS Rule

Math is present in every aspect of our lives. All of our daily lives are built on it, including mobile devices, ancient and modern architecture, art, wealth, engineering, and even sports. Did you know that the word Math is derived from the Greek word máthema, which means “study, intelligence, or learning”? In this blog, we will be learning about one powerful trick on the rule of operation that can make your calculations easy- PEMDAS. So if you are interested to learn this rule of operation of PEMDAS, then do read this blog till the end. 

What Are Operations?

Before actually digging deep into what is meant by the order of operations and the PEMDAS rule, let us first get our basics clear and revise the definition or meaning of the term operations. In simple words of mathematics, operations mean when something can be added, subtracted, divided etc. Some of the main types of operations in mathematics are as follows:

• Addition 
• Subtraction 
• Division 
• Multiplication 
• Squaring 
• Square root, etc. 

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What is Order of Operations?

Now by the definition of operations, you must be wondering that it is always easy to add, subtract, multiply, divide and perhaps, there is no need for an order of operations. But what will you do when you will witness something like this: 

12 + (16 * 15² – 33) 

Which part would you calculate first? From where you will begin from? Will you start from the left and then go right or vice-versa? Will you solve the bracket first? To clear up this ambiguity, we have a set of precedence rules known as the “order of operations,” which have been in place since at least the 1500s.

Note: If you calculate them in the wrong order, you’ll get an incorrect answer! People decided to obey laws while doing calculations a long time ago, which came to be known as the order of operations. 

Example: 
30 / 5 * 5 = 30 / 25 = 1.2 (Wrong)
30 / 5 * 5 = 6 * 5 = 30 (Right)

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The PEMDAS Rule 

So far you must have learnt through this blog on PEMDAS that all the mathematical operations are performed with certain rules that can be also quoted as the order of operation. Having said that, PEMDAS is one such rule or the order of operations that mathematics has to offer. It is somewhat similar to the BODMAS rule. Let us know how they are related to each other in the next section of this blog on PEMDAS. 

PEMDAS vs BODMAS 

BODMAS	PEMDAS
B = Brackets  O = Orders  D = Division M = Multiplication  A = Addition  S = Subtraction	P = Parentheses (Simply means brackets) E = Exponents (same as orders or powers and roots) M = Multiplication  D = Division A = Addition  S = Subtraction

Seeing the above table on BODMAS and PEMDAS, you must be wondering that there are hardly any differences in these two order of operations. You guessed it right! You will come to know the differences after reading the below mentioned points: 

• Instead of “PEMDAS,” British English speakers often use the word “BODMAS.” 
• The two acronyms mean the same thing because “brackets” is the same as parentheses and “orders” is the same as exponents. 
• In the British-English edition, you can also see that the “M” and “D” are reversed; this confirms that multiplication and division have the same “rank” or “class.” 
• BEDMAS is a method used by Canadian English speakers to divide the gap.

How To Remember PEMDAS?

The abbreviation or acronym PEMDAS, which is converted into the mnemonic phrase ‘Please Excuse My Dear Aunt Sally,’ is a popular technique for remembering the order of operations. This term stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, and it aids in remembering their order.

Always note that the complete form of PEMDAS indicates the operation’s rank: Parentheses rank higher than exponents, which rank higher than multiplication and division (multiplication and division are on the same level), and multiplication and division rank higher than addition and subtraction (which are together on the bottom rank). In other words, the precedence is:

1. Parentheses (simplify inside them)
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

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When to Use PEMDAS?

The PEMDAS approach is used when a mathematical expression or question has more than one operation. PEMDAS in Math provides you with a structured approach to generating a specific answer for each mathematical expression. When using the PEMDAS system, there is a set of rules that must be followed in order. When you’ve mastered these laws, you’ll be able to perform several tasks at once.

Points to Remember When Using PEMDAS

• The operations in brackets should be solved first.
• Solve the exponents in the expression after that.
• Carry out multiplication or division from left to right, whichever comes first.
• Carry out addition or subtraction from left to right, whichever comes first.

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PEMDAS Examples with Answers

1. 9 + (12 + 1)²
   Ans: 9 + (12 + 1)² = 9 + (13)² = 9 + 169 = 178

2. 7 + [–5(–10 – 1)]³
   Ans: 7 + [–5(–10 – 1)]³ = 7 + [–5(–11)]³ = 7 + [55]³⁺ = 7 + 166375 = 166382

3. 12 / 6 × 3 / 2
   Ans: 12 / 6 × 3 / 2 = 2 × 3 / 2 = 6 / 2 = 3

4. 8 + (16 × 5² – 10)
   Ans: 8 + (16 × 5² – 10) = 8 + (16 × 25 – 10) = 8 + (16 × 25 – 10) = 8 + (400 – 10) = 8 + (390) = 398 

5. 7 x 3 + 10 x (25 ÷ 5)
   Ans: 7 x 3 + 10 x (25 ÷ 5) = 7 x 3 + 10 x (5) = 21 + 50 = 71 

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This was all about the order of operations and PEMDAS rule. We hope this blog helped you in understanding this concept better. Let us know your feedback in the comments section below. Stay tuned with Leverage Edu for more such educational content!