order of operations

For calculations that have only one Mathematical Operation(+,  − ,  ×, ÷, Square root, Square etc.)  with one or two numbers is easy to derive the result. But think of a situation where there are several numbers and different operations together. For example: 4 × 3 + 6.

We can solve this in two ways:

1) 4 × 3 + 6 = 12 + 6 = 18

OR

2) 4 × 3 + 6 = 4 × 9 = 36

Out of these two solutions, which is the correct one? To determine this order of operation rule is applied. BODMAS and PEMDAS is an acronym that is used to remember the order of operations to be followed while solving expressions in mathematics.

BODMAS stands for Bracket, Orders, Division/Multiplication, Addition/Subtraction. BODMAS is also known as BIDMAS or PEMDAS.  

Follow the below rule to perform any mathematical calculation:

Step 1: Brackets Complete anything in the Brackets first

Step 2: Orders Next apply square, square root, indices etc.

Step 3: Division And/Or  Multiplication Next, complete any division or multiplication. If both exist in the problem then perform them in order from left to right.

Step 4: Addition And/Or  Subtraction Lastly, complete any addition or subtraction. If both exist in the problem then do them in order from left to right.

 

Let us try to solve a few problems by applying the order of operations rule.

---

Example 1: Take the above example and find out the correct solution.  The example that we discussed above is 4 × 3 + 6.
Solution: As per the rule we will perform multiplication first and then addition hence the solution 12 + 6 = 18 is correct. 

Example 2: Solve 4 × ( 3 + 6 )
Solution: Here the numbers are the same as example 1, but as priority is given to the brackets, therefore, calculation within the bracket will be done first and then the multiplication. So 4 × ( 9) = 36

Example 3: Solve 4² + 5
Solution: Calculate Powers first
16 + 5 = 21

Example 4: Solve 4 + 3 × 2
Solution: As per the rule, first multiply 3 times 2. Therefore, 4 + 6 = 10 is the answer.