BODMAS RULE:

We must remember the word VBODMAS in solving sums on simplification. These letters stand for vinculum, bracket, of, division, multiplication, addition and subtraction respectively.

The sums on simplification must be solved in that order i.e., first solve vinculum followed by bracket and so on until the sum is solved.

V | Vinculum means bar as (-) |

B | Bracket- () {} and then [ ] |

O | of |

D | Division [÷] |

M | Multiplication [x] |

A | Addition [+] |

S | Subtraction [-] |

In simplifying an expression first of all bar must be removed. After removing the bar, the brackets must be removed, strictly in the order ( ), { }and [ ].

After removing the brackets, we must use the following operations strictly in the order: (i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction

Example 1 | Example 2 | ||

B | Brackets | 5 × ( 7 – 3) = 5 × 4 = 20 | 24 ÷ ( 8 – 5 ) = 24 ÷ 3 = 8 |

O | Orders | 7 + 22 = 7 + 4 = 11 | 10 – 32 = 10 – 9 = 1 |

D | Divide | 9 + 12 ÷ 3 = 9 + 4 = 13 | 10 – 6 ÷ 2 = 10 – 3 = 7 |

M | Multiply | 10 ÷ 2× 3 = 10 + 6 = 16 | 9 – 4 × 2 = 9 – 8 = 1 |

A | Add | 4 × 3 + 5 = 12 + 5 = 17 | 2 × 7 + 8 = 14 + 8 = 22 |

S | Subtract | 10 ÷ 2 – 2 = 5 – 2 = 3 | 9 ÷ 3 – 1 = 3 – 1 = 2 |

Ordering Mathematical Operations

B | O | D | M | A | S |

Brackets [ ], { }, ( ) | Orders x2, √x | Divide ÷ | Multiply × | Addition + | Subtract × |

## BODMAS Rule Solved Examples

**Example 1:**

**Solution- **

**Step 1: **Solving the fraction inside the bracket first-

**Step 2:** Now the expression will be (3/4) of 16

### Simplification of Brackets

Simplification of terms inside the brackets can be done directly. That means we can perform the operations inside the bracket in the order of division, multiplication, addition and subtraction.

**Note:** The order of brackets to be simplified is (), {}, [].

**Example 2:**

Simplify: 14 + (8 – 2 × 3)

**Solution:**

14 + (8 – 2 × 3)

= 14 + (8 – 6)

= 14 + 2

= 16

Therefore, 14 + (8 – 2 × 3) = 16.

**Example 3:**

Simplify the following.

(i) 1800 ÷ [10{(12−6)+(24−12)}]

(ii) 1/2[{−2(1+2)}10]

**Solution:**

**(i) 1800 ÷ [10{(12−6)+(24−12)}]**

Step 1: Simplify the terms inside {}.

Step 2: Simplify {} and operate with terms outside the bracket.

1800 ÷ [10{(12−6)+(24−12)}]

= 1800 ÷ [10{6+12}]

= 1800 ÷ [10{18}]

Step 3: Simplify the terms inside [ ].

= 1800 ÷ 180

= 10

**(ii) 1/2[{−2(1+2)}10]**

Step 1: Simplify the terms inside () followed by {}, then [].

Step 2: Operate terms with the terms outside the bracket.

1/2[{−2(1+2)}10]

= 1/2 [{-2(3)} 10]

= 1/2 [{-6} 10]

= 1/2 [-60]

### BODMAS Rule without Brackets

The BODMAS rule can be applied to solve the mathematical expression without brackets too. Consider the following question to verify.

**Example 4:**

Simplify: 17 – 24 ÷ 6 × 4 + 8

**Solution:**

17 – 24 ÷ 6 × 4 + 8

As per the BODMAS rule, we should perform the division first.

17 – 4 × 4 + 8

Let’s perform the multiplication.

17 – 16 + 8

Finally, addition and subtraction.

25 – 16 = 9

**Example 5:**

Simplify the expression: 1/7 of 49 + 125 ÷ 25 – 12

**Solution:**

1/7 of 49 + 125 ÷ 25 – 12

= (1/7) × 49 + 125 ÷ 25 – 12

= 7 + 125 ÷ 25 – 12

= 7 + 5 – 12

= 12 – 12

= 0

### Solved Problems On Bodmas

**Question 1:** Solve 8 + 9 ÷ 9 + 5 × 2 − 7.

**Solution: **

The problem given is 8 + 9 ÷ 9 + 5 × 2 − 7.

The division operation is performed first.

9 ÷ 9 = 1

So, the expression reduces to 8 + 1 + 5 × 2 − 7

The multiplication operation is taken next,

5 × 2 = 10

So, the expression reduces to 8 + 1 + 10 − 7

The addition operation is

8 + 1 + 10 = 19

The final answer is 19 – 7 = 12.

**Question 2: **Simplify the expression [25 – 3 (6 + 1)] ÷ 4 + 9.

**Solution: **

The problem given is [25 – 3 (6 + 1)] ÷ 4 + 9.

The round bracket is (6 + 1) = 7.

The next bracket is 3 (7) = 21

Take [25 – 21] ÷ 4 + 9

(25 – 21) = 4

Then division operation is performed,

4 ÷ 4 = 1

Then 1 + 9 = 10

The final answer is 10.

**Question 3: **Solve (1 / 4 + 1 / 8) of 64.

**Solution: **

In the first step, consider (1 / 4 + 1 / 8) = (2 + 1) / 8 = 3 / 8

Take (3 / 8) of 64

Here the term “of” refers to the operation of multiplication.

(3 / 8) of 64 = (3 / 8) * 64

= 24

**Question 4: **Simplify the given expression: 180 ÷ 15 {(12 – 6) – (14 – 12)}.

**Solution: **

Initially, the first ( ) brackets are simplified,

180 ÷ 15 {(12 – 6) – (14 – 12)}

= 180 ÷ 15 (6 − 2) (solve round bracket)

= 180 ÷ 15 (4) (solve curly bracket)

= 12 (4) (divide 180 by 15 = 12)

= 12 × 4 (if no operator is mentioned behind any given bracket, multiplication operation can be performed)

= 48

The final answer is 48.

**Question 5: **Simplify the following expression 3 + 24 × (15 ÷ 3) using the BODMAS rule.

**Solution: **

The expression given is 3 + 24 × (15 ÷ 3).

The bracket is taken first.

(15 ÷ 3) = 5

Then 3 + 24 × 5

The calculation is done in order 24 = 2 × 2 × 2 × 2 = 16

16 × 5 = 80

The addition operation is performed next.

3 + 80 = 83

The final answer is 83.

**Question 6:**

**Solution:**

First consider the vinculum or line bracket 16 [8 – {5 – 2 (1 + 1)}] = 16 [8 – {5 – 2 * 2}] ( solve the curved bracket)

= 16 [8 – {5 – 4}]( multiply the curly bracket )

= 16 [8 – 1] ( solve the curly bracket)

= 16 * 7 ( solve the inner part of the square bracket)

= 112

Hence, the final answer is 112.

**Question 7: **Solve the expression using BODMAS rule{50 – (2 + 3) + 15}.

**Solution: **

Input Equation:

= {50 – (2 + 3) + 15}

= {50 – (5) + 15}

= {50 – 5 + 15}

= {45 + 15}

= {60}

= 60

**Question 8: **Simplify the expression using the BODMAS rule [18 – 2 (5 + 1)] ÷ 3 + 7.

**Solution: **

Input Equation can be rewritten:

= [18 – 2 * (5 + 1)] / 3 + 7

= [18 – 2 * (6)] / 3 + 7

= [18 – 2 * 6] / 3 + 7

= [18 – 12] / 3 + 7

= [6] / 3 + 7

= (6 / 3) + 7

= 2 + 7

= 9

### BODMAS Rule Problems

Try to solve the BODMAS Rule Questions given below to understand the application of the rule in simplifications.

- What is the value of 28 – [26 – {2 + 5 × (6 – 3)}]?
- Simplify: 2 + 5(4 + 2) + 32 – (1 + 6 × 3)
- Find the value of 7 + {8 – 3 of (√4 + 2)}.

### What is the BODMAS Rule of Maths?

BODMAS is an acronym for the sequence of operations to be performed while simplifying the mathematical expressions. Thus, BODMAS stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction.

### Can we use the BODMAS rule when there are no brackets?

Yes, we can use the BODMAS rule when there are no brackets also.

### What does S represent in the BODMAS rule?

The letter S denotes the subtraction in the BODMAS rule of mathematics.

### Which arithmetic operations are involved in the BODMAS rule?

The main arithmetic operations involved in the BODMAS rule are:

Addition

Subtraction

Multiplication

Division

Square roots or surds and indices

Addition

Subtraction

Multiplication

Division

Square roots or surds and indices

### What is the use of the BODMAS rule?

The BODMAS rule helps in simplifying the mathematical expression accurately. Using this rule, we can compute the given expression in the right way so that the answer is correct.

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