In mathematics, in order to evaluate an arithmetic expression that involves multiple operators such as division, addition, multiplication, subtraction, operator precedence (order of operations) is required which is a collection of rules that reflect conventions about which procedures to perform first. This is known as the BODMAS Rule.
The full form of “BODMAS” is Brackets, of or order, Division, Multiplication, Addition, Subtraction. In the article below, we will find all details about the BODMAS Rule and some sample questions for understanding the concept better.
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BODMAS Rule:
According to the BODMAS rules,
(I) B: Brackets ((), {}, [])
If an expression contains brackets we have to first simplify all these brackets.
(II) O: of or order (power or roots)
Followed by brackets, we solve “of” or “power” (square or roots) in the given expression.
(III) D: Division (“/”, “÷”)
Then we solve division left to right in the given expression.
(IV) M: Multiplication (“*”, “x”)
After Division, we solve, multiplication from left to right in the given expression.
(V) A: Addition (“+”)
(VI) S: Subtraction (“-”)
After division and multiplication, we solve addition and subtraction from left to right in the given expression.
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Let’s understand the above concept with the following examples:
Example 1:
Simplify the given expression:
800 ÷ 10 [{12 * (18 – 7)} – 84]
Solution:
800 ÷ 10 [{12 * (18 – 7)} – 84]
= 800 ÷ 10 [{12 * 11} – 84] (to start with, we will first solve the innermost bracket)
= 800 ÷ 10 [132 – 84] (now, we took up the curly bracket and lastly we will simplify the expression in the outermost bracket)
= 800 ÷ 10 * 48 (here, we now have both multiplication and division signs; going by the rules, we will first solve the division part)
= 80 * 48 (after, division, we are only left with multiplication, which is the last step in order to solve this question)
= 3840
Example 2:
Simplify the given expression:
{(700 * 45) ÷ 350} + [(82 – 122) + 123]
(as we can see, the above question contains, 4 brackets, powers, division, multiplication, addition, and substraction)
Solution:
{(700 * 45) ÷ 350} + [(82 – 122) + 123] (let’s start by solving the inner round brackets on either side of the addition sign)
= {31500/350} + [(64 – 144) + 123]
= 90 + [-80 + 123]
(the above two steps are dedicated to solve the outer brackets on either side of the addition sign)
= 90 + 43
(we are only left with addition, which is the last step in order to solve this question)
= 133
Example 3:
Simplify the given expression:
125% of 56 + {(√324 + 72 – 3) ÷ 23} ÷ 2 + 62
(the above question needs to be solved using the BODMAS Rule applied from left to right)
Now, follow each step carefully to understand the procedure well.
Solution:
125% of 56 + {(√324 + 72 – 3) ÷ 23} ÷ 2 + 62
= 125/100 * 56 + {(18 + 49 – 3) ÷ 8} ÷ 2 + 36
=70 + {64 ÷ 8} ÷ 2 + 36
= 70 + 8 ÷ 2 + 36
= 70 + 4 + 36
= 74 + 36
= 110
Example 4:
Simplify the given expression:
[{6 of (320 – 43) ÷ 16} + 74 – 20 * (450 – 220) ÷ 23] + 82
Solution:
[{6 of (320 – 43) ÷ 16} + 74 – 20 * (450 – 220) ÷ 23] + 82
= [{6 of (320 – 64) ÷ 16} + 74 – 20 * 230 ÷ 23] + 64
= [{6 of 256 ÷ 16} + 74 – 4600 ÷ 23] + 64
= [{1536 ÷ 16} + 74 – 200] + 64
= [96 + 74 – 200] + 64
= [170 – 200] + 64
= -30 + 64
= 34
Example 5:
Simplify the given expression:
[{(564 + 634 – 562 – 345) ÷ 761 + 850 ÷ 17 of 5} – 132 * 48 ÷ 39]
Solution:
[{(564 + 634 – 562 – 345) ÷ 761 + 850 ÷ 17 of 5} – 132 * 48 ÷ 39]
= [{(564 + 634 – 3136 – 345) ÷ 761 + 850 ÷ 17 of 5} – 132 * 48 ÷ 39]
= [{(1198 – 3136 – 345)/761 + 850/(17 * 5)} – 169 * 48/39]
= [{(-1938 – 345)/761 + 850/85} – 8112/39]
= [{-2283/761 + 10} – 208]
= [{-3 + 10} – 208]
= [7 – 208]
= -201
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