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Bodmas Rule
When a single expression contains many mathematical operations then BODMAS rules are used for the simplification of the expression. The word BODMAS has been arranged according to the priority of the operations.
The letters of BODMAS express the following operations:
B Stands for Bracket
O Stands for of
D Stands for Division
M Stands for Multiplication
A Stands for Addition and
S Stands for Subtraction
Brackets
There are three types of Brackets, small, middle or medium and big.
Small Bracket is denoted by ()
Middle Bracket is denoted by {}
Big Bracket is denoted by [ ]
Brackets are used according to the placement of operations. First we use small bracket then middle Bracket and Big bracket is used at last in an expression. i.e. \[\left[ \left\{ \left( 4+5 \right)\times 6 \right\}+7 \right].\]
Elimination of Brackets
The solution of the expression is obtained by eliminating the brackets. The first priority of eliminating the bracket is small bracket then middle bracket and finally big bracket.
The following steps are used to simplify the expression, \[\left[ \left\{ (4+5)\times 6 \right\}+7 \right]:\]
I st: Eliminate the small bracket by adding 4 and 5, in small bracket, \[[\{(4+5)\times 6\}+7][\{9\times 6\}+7].\]
\[\text{I}{{\text{I}}^{\text{nd}}}\] : Eliminate the middle bracket by multiplying 9 and 6, in middle bracket, \[[\{9\times 6\}+7]=[54+7].\]
\[\text{II}{{\text{I}}^{\text{rd}}}\]: Add 54 and 7 to eliminate big bracket [54 + 7] = 61. The solution of the above given expression is 61.
Simplify: \[[\{(34+17)-20\}+21]-20\]?
(a) 31
(b) 32
(c) 36
(d) Both (a) and (c)
(e) None of these
Answer: (b)
Explanation
\[[\{(34+17)-20\}+21]-20\] \[=[\{51-20\}+21]-20=[31+21]-20=52-20=32.\]
How many different three digit numbers can be obtained by using the digits 0,1,3 without repeating any digit in the number?
(a) 4
(b) 5
(c) 3
(d) 2
(e) None of these
Answer: (a)
Which one of the following is the smallest seven digit number having four different digits?
(a) 1230000
(b) 0000123
(c) 1000023
(d) 1000032
(e) None of these
Answer: (c)
Simplify:\[~45+3\times 2\]of \[5-\text{(}16+4\text{)}-8\div 4.\]
(a) 55
(b) 43
(c) 53
(d) Both (a) and (c)
(e) None of these
Answer: (c)
Explanation
\[45+3\times 2\]of \[5-(6+4)-8\div 4\] \[=~45+3\times 2\]of\[5-20-8\div 4\] [Bracket removed] \[=~~45+3\times 2\]of 5 ?20 ? 2 [Operation of division \[8\div 4=2]\] = 45 + 30 - 20 - 2 [Operation of multiplication \[3\times 2\times 5=30]\] = 75 - 20 - 2 [Operation of addition 45 + 30 = 75] = 75 - 22 = 53 [Operation of subtraction]
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