Simplification : BODMAS

Simplification : BODMAS
Order of Operations to Solve Expression
We have already studied four basic fundamental operations ie., addition, subtraction, multiplication and division. Sometimes, we face many problems to simplify an expression which involves two or more than two basic operations. In such cases, we use the given order of operations :

Division → Multiplication → Addition → Subtraction

The above order is known as ‘DMAS’, where “D’ stands for ‘division’, ‘M’ stands for ‘multiplication’, ‘A’ stands for ‘addition’ and ‘S’ stands for ‘subtraction’.

Example :

Simplify: (a) 30 ÷ 6 + 10 - 2 × 5         (b) 48 ÷ 16 × 2 + 17 – 9

Solution : (a) 30 ÷ 6 + 10 - 2 × 5

Solution : (b) 48 ÷ 16 × 2 + 17 - 9

= 48 ÷ 16 × 2 + 17 - 9 (Division)

= 3 × 2 + 17 - 9 (Multiplication)

= 6 + 17 - 9 (Addition)

= 23 - 9 (Subtraction)

=14

Simplification : BODMAS

Use of Brackets

If some expressions are enclosed within a pair of brackets, it means that they have to be simplified first before the other operations. To simplify such expressions involving brackets, we must proceed the order of the letters of the word ‘BODMAS’, where ‘B’, ‘O”, ‘D’, ‘M’’, ‘A’ and ‘S’ stand for ‘bracket’, ‘of, ‘division’, ‘multiplication’, ‘addition’ and ‘subtraction’ respectively. Brackets are used to separate the various parts of an expression. There are four kinds of brackets which are solved in the following order :

1. Bar or vinculum —

2. Circular brackets ( )

3. Curly brackets or braces { }

4. Square brackets or big brackets [ ]

Example 1 : Simplify:\(\left[ 15\times \left\{ 10+\left( 20\div \overline{20-18} \right) \right\} \right]\)

Solution :\(\left[ 15\times \left\{ 10+\left( 20\div \overline{20-18} \right) \right\} \right]\)

= [15 × {10 + (20 ÷ 2)}]

= [15 × {10 + 10}]

= [15 × 20]

= 300

Example 2 : Simplify: [100 ÷ {30 - (20 - 0)}]

Solution : [100 ÷ {30 - (20 - 0)}]

 = [100 ÷ {30 - 20}]

 = [100 ÷ 10]

 = 10

Example 3 : Simplify: [42 × {30 ÷ (10 - 4)}]

Solution : [42 × {30 ÷ (10 - 4)}]

 = [42 × {30 ÷ 6}]

= 42 × 5

 = 210

Example 4 : Simplify:\(\left[ 2\times \left\{ \left( 20\div \overline{20-18} \right)+\left( 34\times \overline{4+68} \right) \right\} \right]\)

Solution : \(\left[ 2\times \left\{ \left( 20\div \overline{20-18} \right)+\left( 34\times \overline{4+68} \right) \right\} \right]\)

= [2 × {(20 ÷ 2) + (34 × 72)}]

= [2 × {10 + 2448}]

 = [2 × 2458]

 = 4916