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**BODMAS Rule**

It illustrates the steps that need be taken in order to solve an expression.
The BODMAS rule states that if an expression involves brackets ((),, []), we must first solve or simplify the bracket before moving on to the left-to-right operations of division, multiplication, addition, and subtraction.
The incorrect solution will be obtained by resolving the issue in the incorrect order.
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**Important**: When referring to the numbers that contain powers, square roots, etc., the "O" in the BODMAS complete form is also referred to as "Order." For a better understanding of how to apply the BODMAS rule, look at the examples below.

**Full form of BODMAS rule**

Brackets, Orders, Division, Multiplication, Addition, and Subtraction are known as BODMAS, as we mentioned previously. When applying the BODMAS rule, we should carry out these procedures in the proper order.

B | Brackets | ( ), { }, [ ] |

O | Order of | Square roots, indices, exponents and powers |

D | Division | ÷, / |

M | Multiplication | ×, * |

A | Addition | + |

S | Subtraction | – |

**Conditions & Guidelines**

The following are a few prerequisites and guidelines for generic simplification:
Condition |
Rule |

x + (y + z) ⇒ x + y + z | Open the bracket and add the terms. |

x – (y + z) ⇒ x – y – z | To multiply the negative sign with each term inside a bracket, open the bracket. (All terms that are positive are also negative, and vice versa.) |

x(y + z) ⇒ xy + xz | Multiply each term inside the bracket by the outside term. |

**Tips for Recalling the BODMAS Rule:**

Following are the guidelines for utilising the BODMAS rule to simplify the expression:
- first, make the brackets simpler.
- Exponent or root term solutions
- Make a division or multiplication (from left to right)
- carry out the operation of addition or subtraction (from left to right)

**How to simply brackets ?**

The terms in the brackets can be immediately simplified.
Therefore, we can carry out the operations indicated by the brackets in the following order: multiplication, addition, subtraction, division.
**Question and answer**

**Question 1: 6 + 2 x 7**

The correct answer is 20.

The multiplication must be completed first (2 x 7 = 14) and then the addition (6 + 14 = 20).

This may be commonly miscalculated as 56 by working from left to right (6 + 2 = 8, 8 x 7 = 56).

**Question 2: 3 x (2 + 4) + 52**

The correct answer is 43.

The BODMAS rule states we should calculate the **B**rackets first (2 + 4 = 6), then the Orders (52 = 25), then any **D**ivision or **M**ultiplication (3 x 6 (the answer to the brackets) = 18), and finally any **A**ddition or **S**ubtraction (18 + 25 = 43).

Children can get the wrong answer of 35 by working from left to right.

**Question 3: 5 – 2 + 6 ÷ 3**

The correct answer is 5.

The division must be completed first (6 ÷ 3 = 2) which then leaves addition and subtraction; as both are of the same importance, we can then work from left to right. 5 – 2 + 2 (the answer to 6 ÷ 3) = 5.

This may be commonly miscalculated as either 3 by working from left to right, or as 1 by wrongly assuming that addition should be completed before subtraction.

**Question 4 : Solve (12+14) of 16**

**Solution- **

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

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

=34×16

=12

**Question 5 : 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]

= -30

**Question 6: 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

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### What purpose does the BODMAS rule serve?

The BODMAS rule assists in accurately simplifying the mathematical expression. This rule allows us to compute the supplied phrase in the proper manner, ensuring that the solution is accurate.## The BODMAS rule involves what arithmetic operations?

- Addition
- Subtraction
- Multiplication
- Division
- Square roots or surds and indices