Order of Operations

In every walk of life we are met with a set of orders or patterns without which everything falls apart. Just like when we get up in the morning we brush our teeth, finish our morning ablutions, eat breakfast, pack our stuff and leave for school. We cannot afford to mess the order because then it gets absurd.

In the same way in Mathematics a principle for order of operations is followed.Operations means to add, subtract, multiply, divide, squaring, etc. If it isn’t a number it is probably an operation.

But if we came across: 3 + (8 × 32 + 9) how should we calculate?

  • Will left to right solution get us the answer?
  • Will right to left lead to the right answer?
  • Will solving the exponents first and then the rest get us to the end?

All across the globe mathematicians were completely confused with the respected results.

Hence, they came up with a conclusion to follow an order to operate a set of parameters.

Order of operations

The order of operations is the order which is followed to add, subtract, multiply or divide to solve a problem in mathematics.

Order of operations is the method which operations should be performed in a particular order. It gives us a procedure as to which operations to do first.

To remember the conventional order of operations, you can think of –

PEMDAS (“Please excuse my dear Aunt Sally” is an easy way to memorize this)


  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

This means that first we should do what data is within parentheses, then exponents,  followed by multiplication and division always from left to right), and then addition and subtraction (from left to right). If parentheses are within other parentheses, solve it from the inside out.

Coming back to the above example and why is it necessary to follow the order PEDMAS.




Now try to answer the following:

  1. 29 – 23 × 0 ÷ 1
  2. 65 ÷ 5 × 7 × 3
  3. 19 – 12 + 4 × 3
  4. 4 × 4 ÷ 1 + 9
  5. 20 – 10 × 3 ÷ 1
Answer key
  1. 0
  2. 273
  3. 19
  4. 25
  5. 30