Order of Operations (PEMDAS): Definition & Examples

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Order of operation is a basic concept in mathematics, especially in algebra. It has been studied in elementary school and continued in next level of education. It uses to solve multiple operation in mathematics.

Definition of Operation

Operation means doing something to solve mathematics’ problem. It contains addition, subtraction, division, multiplication, etc.

There are simple mathematics’ problem and also multiple mathematics’ problem. Simple mathematics problem consists of one or two operation. Multiple mathematics’ problem consists of three or more operations.

Multiple operation in mathematics can be a trap if it doesn’t be solved appropriate to the rule.

2 x (2 + 4) : 4 ≠ 2 x 2 + 4 : 4

Why?

It is because there is order of operation (PEMDAS).

Order of Operations (PEMDAS)

Order of operation is also called as PEMDAS. It organize which one operation that must be solved first if there are some operation in a mathematics’ problem. It is also having specific meaning based on each letter of PEMDAS.

  • Parenthesis

Parenthesis is first part that must be finished in mathematics operation’s problem. But not all of mathematics operation has it. It doesn’t matter if in the parenthesis is division or addition. The focus is only in parenthesis that must be solved first.   

  • Exponent

Exponent is not always written as ab. Sometimes it is also written as square-root. If mathematics’ problem has exponent part, it must be solved first before solving multiplication, division, addition, and subtraction.  

  • Multiplication and Division

Multiplication and division have same level in PEMDAS. But it is solved form left to right. It means which one in left side it is solved first.

  • Addition and Subtraction

Addition and subtraction have same level in PEMDAS. Which one in left side it is solved first.

In another words, based on PEMDAS, the rule of mathematics operation is Parenthesis → Exponent → Multiplication and Division → Addition and Subtraction.

Examples

1. Why 2 x (2 + 4) : 4  ≠ 2 x 2 + 4 : 4 ?

Answer

Because based on the PEMDAS it has different result.

  • 2 x (2 + 4) : 4 =  2 x 6 : 4

= 12 : 4

= 3

  • 2 x 2 + 4 : 4 = 4 + 1

= 5

2. 32 x 4 – 1 + 22 + 3 – √9 = …

Answer

32 x 4 – 1 + 22 + 3 – √9 = 9 x 4 – 1 + 4 + 3 – 3

= 36 – 1 + 4 + 3 – 3

= 35 + 4 + 3 – 3

= 39 + 3 – 3

= 42 – 3

= 39

3. [23 + 4 – 1] / [4 – 5 x √4] = …

Answer
[23 + 4 – 1] / [4 – 5 x √4] = [8 + 4 – 1] / [4 – 5 x 2]

= [12 – 1] / [4 – 10]

= 11 / -6

= -11/6

Note: be careful in denominator.