What is BODMAS Rule in Mathematics and how to calculate?

BODMAS stands for: Brackets Orders Division Multiplication Addition and Subtraction.  In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is used, which is the synonym of BODMAS.

In BODMAS rule

1.    Brackets means "( )", "[ ]" and "{ }"

2.    Orders mean square roots and indices (which you may know as square numbers, powers or exponents). Hence, the second preference in BODMAS is given here to the orders or exponents (xⁿ).

3.    Later we perform the arithmetic operations (÷, ×, +, -).

When presented with a number sentence containing more than one operation (such as 9 - 10 + 6 x 15 = ?), the operations cannot be completed from left to right, but instead in their order of "importance", which is what BODMAS stands for.

Also Read: What is the Kardashev Scale?

Mathematical operations are what you do to the numbers given. The four main operations are:

·         Addition (+)

·         Subtraction (-)

·         Multiplication (x)

·         Division (÷)

Division and Multiplication must be represented alongside each other as they are of equal importance (so must be completed from left to right, whichever appears first) – this is the same for Addition and Subtraction.

 

We will solve examples based on this rule in the below sections.

 

Question A:   6 + 2 x 7 = A

 

Solution A:

    

In the given question, we have Addition and Multiplication.

So, according to BODMAS rule, the Multiplication must be completed first and then will complete Addition.

 

                        6 + 2 x 7 = A

                        6 + 14 = A          (In this step we calculated Multiplication of 2 x 7)

                        20 = A                (In this step we calculated Addition of 6 + 14)

 

The correct answer is: 20

 

 

 

Question B:   16 × (7 - 3) = A

 

Solution B:    

In the given question, we have Multiplication and Subtraction inside "Brackets".

So, according to BODMAS rule, we must complete operations inside "Brackets" and then Multiplication.

 

                        16 × (7 - 3) = A

                        16 × (4) = A                (calculated Subtraction inside Brackets 7-3)

                        64 = A                         (calculated Addition of 16 + 4)

 

The correct answer is: 64

 

 

 

Question C:   452 x 195 - 5432 = A + 656

Solution C:    

In the given question, we have Multiplication and Subtraction.

So, according to BODMAS rule, the Multiplication must be completed first and then will complete Subtraction.

 

                        452 x 195 - 5432 = A + 656

                        88140 - 5432 = A + 656       (calculated Multiplication of 452 x 195)

                        82708 = A + 656                  (calculated Subtraction of 88140 - 5432)

                        A = 82708 - 656                   

                        A = 82052                            (calculated Subtraction of 82708 - 656)

 

The correct answer is: 82052

 

 

 

Question D:   3 x (4 x 5²) ÷ 6 + 7 – 8 = A

 

Solution D:    

In the given question, we have all the Mathematical operations.

So, according to BODMAS rule, we will complete Brackets, Orders, Division, Multiplication, Addition and finally Subtraction.

 

                        3 x (4 x 5²) ÷ 6 + 7 – 8 = A

                        3 x (4 x 25) ÷ 6 + 7 – 8 = A              (calculated Orders of 5²)

                        3 x 100 ÷ 6 + 7 – 8 = A                    (calculated Multiplication of 4 x 25)

                        300 ÷ 6 + 7 – 8 = A                           (calculated Multiplication of 3 x 100)                                50 + 7 – 8 = A                                  (calculated Division of 300 ÷ 6)

                        57 – 8 = A                                          (calculated Addition of 50 + 7)

                        A = 49                                                 (calculated Subtraction of 57 - 8)

                       

The correct answer is: 49

 

Note: In step 2, we have Multiplication and Division both have equal importance, So we so must be completed from left to right.

 

 

 

Question E: [2 + (4(6 x 4) x 3 ÷ 8)] - 4 = A

 

Solution E:    

In the given question, we have all the Mathematical operations.

So, according to BODMAS rule, we will complete Brackets, Orders, Division, Multiplication, Addition and finally Subtraction.

 

                        [2 + (4(6 x 4) x 3 ÷ 8)] - 4 = A

                        [2 + (4(24) x 3 ÷ 8)] - 4 = A            (calculated Multiplication of 6 x 4)

                        [2 + (96 x 3 ÷ 8)] - 4 = A            

                        [2 + (288 ÷ 8)] - 4 = A                       (calculated Multiplication of 96 x 3)                                  [2 + 36] - 4 = A                                 (calculated Division of 288 ÷ 8)

                        38 - 4 = A                                           (calculated Addition of 2 + 36)

                        A = 34                                                 (calculated Subtraction of 38 - 4)

                       

The correct answer is: 34

 

 

 

Solve these 10 Examples from F to O:

 

Question F:   12 - 8 + 4 + 9 x (40 ÷ 4) = A

 

Question G:   5 x 2 + (12 + 6) - 28 ÷ 4 = A

 

Question H:   10 + 8 x 90 ÷ 9 - 4 = A

 

Question I:     8 x 3 + 70 ÷ 7 - 7 = A

 

Question J:    8 - 3 + 7 x 6 + 12 ÷ 3 = A

 

Question K:   45 ÷ 9 + 12 - 9 ÷ 3 = A

 

Question L:   [3 - (4 - 2(6 - 5) + 3)] + 2 = A

 

Question M: [5 - (3 - 6(4 - 2) + 7)] + 7 = A

 

Question N:   (12 ÷ 3 ) + 3 + ( 16 - 7 ) + 4 = A

 

Question O:   30 ÷ 5 + (5 x 6) x 19 + 4 = A