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Order of Operations


What is Order of Operations

Order of Operations is the standard method in evaluating arithmetic expressions. Without the order of operations, students may obtain different answers to the same expression, depending on the student’s preference in order in evaluating, so correct order of operation is follows:

Basic order of operation

  1. Division
  2. Multiply
  3. Addition
  4. Subtraction

Note: If you calculate arithmetic expressions in the wrong order,  you will get a wrong answer !

How, Let’s See

Example:

Evaluate the arithmetic expression 4 + 6 x 3 . Below are the 2 students A and B, both Calculate in different order.

Student A Student B
4 + 6 x 3

= 4 + 18

4 + 6 x 3

= 10 x 3

= 22 = 30
Correct Wrong

As we can clearly see, both students got different answers to the same problem. Student A decided to multiply first before doing the addition whereas student B did the exact opposite. This is unacceptable as there can only be one correct answer in the evaluation of arithmetic expressions.

That is why mathematicians have come together to agreed on a set of rules to avoid confusion.

Basically, the order of operations tells of the order, in which the student should first approach operations such as parentheses, division, multiplication, subtraction and addition.

PEMDAS

  • P – Parentheses first
  • E – Exponents (ie Powers and Square Roots, etc.)
  • MD – Multiplication and Division (left-to-right)
  • AS – Addition and Subtraction (left-to-right)

Rules to follow when using the Order of Operations.

1. First, evaluate the operations within the parentheses.

2. Next, reduce the exponents and roots to its numerical form.

3. Afterwards, do all the multiplication and division from the left to right.

4. Finally, do the addition and subtraction to obtain the final answer.

Example

Let us look at how order of operation works.

3 x √25 – ( 4 +3 x 5)

According to the order of operations, we work out everything within the parentheses. In following rules (3) and (4) within the brackets, we have to multiply first before adding.

Now that the brackets have been removed, we can proceed on with the rest of the operations.

3 x √25  – 19

Next, we find the value of √25  .

3 x 5 – 19

Then, we multiply the terms and finally subtract to obtain the final answer of – 4.

Toppers Tips: Order of operations offer flexibility in writing mathematical expressions. Since addition and multiplication are commutative, it follows that 3 x 5 +2 can be written as 5 x 3 + 2 , 2 + 3 x 5 , 2 + 5 x 3 . It doesn’t change the mathematical concept behind the expression.

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