BODMAS Full Form

The full form of BODMAS in maths is Bracket Order Division Multiplication Addition and Subtraction. There are several signs in mathematics against every numerical calculation. This rule is followed to avoid any confusion while calculation and to reach the same result, when solved by anyone.

History

BODMAS was invented by the mathematician Achilles Reselfelt. 

It is a mnemonic that helps us remember how to evaluate mathematical operators in a statement involving more than one operation.

Explanation

As a rule, BODMAS is self-explanatory from its full form; it tells us the priority order of the mathematical operation.

Example: \((2 + 5)^1 \div 7 + 5\times 3 – 9\)

1. The highest priority is given to Bracket.
   Any function inside the bracket will be the evaluated first.
   • Here, the operation inside the bracket is an addition, so we will add 5 & 2
     \((2 + 5)^1 \div 7 + 5\times 3 – 9 = (7)^1 \div 7 + 5\times 3 – 9\) 

2. Order is the Power that is raised on a number such as square, cube, etc.
   • Here, power is one on 7
     \((7)^1 \div 7 + 5\times 3 – 9 = 7 \div 7 + 5 \times 3 – 9\)

3. The next priority is given to the Division.
   • Divide 7 by 7, we get,
     \(7 \div 7 + 5 \times 3 – 9 = 1 + 5 \times 3 – 9\)

4. Multiplication Comes third,
   • Multiplying 5 & 3
     \(1 + 5 \times 3 – 9 = 1 + 15 – 9\)

5. Addition comes fourth (or) second last,
   • Adding 1 to 15
     \(1 + 15 – 9 = 16 – 9\)

6. Finally, the last operation priority is given to Subtraction.
   • Subtracting 9 from 16
     \(16 – 9 = 7\).

NOTE: In addition to BODMAS, there is another Rule known as PEMDAS having the full form as Parentheses(bracket), Exponential, Multiplication, Division, Addition, Subtraction.

Solved Examples

Question 1. \(3 \times (4 \times 5^2) \div 6 + 7 – 8 = ?\)

Solution.

\(
3 \times ( 4 \times 25) \div 6 + 7 – 8 \\
= 3 \times (100) \div 6 + 7 – 8 \\ = 3 \times \frac{50}{3} + 7 -8 \\
=> 50 + 7 – 8 \\ = 49 \\
\)

Question 2. \(42 \div 2 + a \times 3 − 22 = 8\)
Find value of \(a\).

Solution.

\(
42 \div 2 + 3a – 22 = 8 \\
21 + 3a – 22 = 8 \\
3a – 1 = 8 \\
3a = 9 \\
a = 3 \\
\)

Hence, the value of \(a\) is 3.

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