Order of Operation

Order of operations: Order of operation is the rules that we follows to apply operations on mathematical formula. When there more than one operation in any expression then we use order of operations.

What is DOMAS rule?

When there are multiple arithmetic operations in an equation we use DOMAS rule.

In BODMAS rule

  1. Always solve the Brackets first
  2. Then solve the Order of operations
  3. Division
  4. Multiplication
  5. Addition
  6. Subtraction




But in U.S we use PEMDAS:

  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction

If someone ask you to simplify equation like “3 – 2 × 4” then general question arises what can I do first. Should I first subtract then multiply “(3-2) × 4=1×4 = 4”?

Or first multiply then subtract “3 -2 × 4=3 – 8 = -5”?

Which is the correct answer?

It seems that answer depend on which angle you look at the problem. In mathematics one question have one exact answer and can’t multiple answer of one problem,so solve this problem we use “order of operation”. The order of operation are parentheses, exponents (root, power), Division, Multiplication, Addition & Subtraction. In equations where all the operation are present then correct order for solving the equations first expand the parentheses then solve exponents then you have to solve Division then you have to solve Multiplication, and then you have to solve the Addition and then subtraction.

Note: for multiplication or division (always solve questions from left to right).

Addition & Subtraction (always solve equations from left to right).




How to remember Order of Operation

A common technique to remember the order of operations PEMDAS is through abbreviations (“PLEASE EXCUSE MY DEAR AUNT SALLY”).

  1. Solve brackets first.

Always look for parentheses in an equation. If there is any parentheses in equation solve them first, because they have high priority than other order of operations.

  • Correct way:

The correct way to solve the equations is to first solve the parentheses then exponents, Multiplication, Division, Addition and Subtraction. You will always use DOMAS rule for solving algebra equations.

 

5 ×(8 + 4)(first solve the parentheses)

5 × 12 = 60   (then multiply the equation)

  • Wrong way:

If you don’t follow the DOMAS rule then your answeris wrong.

                             5× (8 + 4) = 40 + 4 =44

 

  1. Solve exponents (Power, root) before addition, Subtraction, Multiplication and division.

  • Correct way

The correct way to solve the equations is to first solve the parentheses then exponents, Multiplication, Division, Addition and Subtraction. You will always use DOMAS rule for solving algebra equations.

4 ×32  (first solve the exponents)

4 × 9 = 36 (then multiply the expression)

 

  • Wrong way

If you solve multiplication first and then solve exponent then the answer is wrong. If you don’t follow the DOMAS rule then your answeris wrong.

4 × 32 = 122= 144

Multiplication & Division

Now, look at any Division and multiplication operator in the equation. It is not necessary that division always come before the multiplication, these operators are solve from left to right. Look from left to right if any operator (multiplication or division) comes first solve them. They have low priority then exponent and parentheses.

  • Correct way

The correct way to solve the equations is to first solve the parentheses then exponents, Multiplication, Division, Addition and Subtraction. You will always use DOMAS rule for solving algebra equations.

20 ÷ 5× 2(look from left to right which operator comes first)

4 × 2 = 8

20 × 2÷ 5 (look from left to right which operator comes first)

40 ÷ 5 =8 (Answer is always same)

Addition & subtraction

Same is the case with addition and subtraction we will always go from left to right. Just look at below:

            10 + 4 – 6

Look from left to right first solve 10 + 4 then subtract it from 6.

10 + 4 – 6

14 – 6 = 8 (Answer)

 

Learn more about Trig identities .