What is BODMAS ? : Check here Order of Operations with examples

When compared to procedures involving just two numbers, solving an arithmetic expression that includes numerous operations like addition, subtraction, multiplication, and division is more difficult. A two-number operation is simple, but how do you work out an expression with brackets and several operations, as well as how to make a bracket simpler? Let's review the BODMAS rule and discover how brackets might be made simpler. The Bodmas rule is arranged according to the letters in the acronym BODMAS, which stand for brackets, order of powers or roots, division, and multiplication. A stands for addition and S for subtraction. According to the BODMAS rule, multi-operator mathematical equations must be resolved in the BODMAS order from left to right.The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction, is also known as BODMAS in some areas.

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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. When an expression has many operators, the BODMAS rule can be used. In this instance, we must first simplify the words inside the brackets, from the innermost to the outermost brackets [()], as well as any roots or exponents that may be present. then carry out the division or multiplication operation going from left to right.

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 Brackets first (2 + 4 = 6), then the Orders (52 = 25), then any Division or Multiplication (3 x 6 (the answer to the brackets) = 18), and finally any Addition or Subtraction (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- 

Given: (12+14) of 16

Step 1: Solving the fraction inside the bracket first-

12+14=34

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

=34×16
=12

Question 5: 

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

 

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.