Sunday, October 12, 2008

Order of Operations - BODMAS

As said here in this topic, when using Infix notation, we either need brackets or some rule to say the order in which we evaluate an expression. Say we have to evaluate 3 + 5 x 8, this thing possibly has two solutions depending on the priority we give to the addition and the multiplication operator, that is, 8 x8=65 or 3+40=43. When there isn't a particular standard followed, we will end up in wrong interpretation. Thus came the order or precedence of operators.

1) B or P - Brackets or Parenthesis
2) O or E or I - Orders or Exponents or Indices (square roots, powers, radix etc.)
3) D - Division
3) M - Multiplication
4) A - Addition
4) S - Subtraction

Since 5 x 8 / 4 will yield the same result when either one of multiplication or division is given the higher priority, either of it can be calculated first and thus they share a same level of precedence. Same is the case with the addition and the subtraction operators.

Let us have an example. (3 * (52 + 5) ) /5 + (3*15)/5

Here there are two (outer) brackets, hence we have to evaluate those two first. The expression in each bracket should be considered as a separate expression and should be evaluated separately by following BEDMAS separately. Two brackets that are not nested, can be evaluate them in parallel.

we have an exponent. 52 = 25. We don't have division. Then we have multiplication. 3* 25 = 75. Then we have addition 75+5=80. Now that the first bracket is evaluated. We can evaluate the other bracket in parallel to this. Here goes simple steps.

(3 * (52 + 5 )) /5 + (3*15)/5 - Outer Brackets - Ist and IInd
= (3 *( 25 + 5) )/5 + 15/5 - Inner bracket (power) of Ist, Multiplication of IInd
= (3 * 30)/5 + 15/5 - Addition in inner bracket of Ist - BEDMAS in Ist and IInd bracket over
= 90/5 + 15/5 - Multiplication in Ist outer bracket
= 18 + 3 - Division can be performed in parallel.
= 21 - BEDMAS for the expression is over - Final Result.

If the bracket operator is nested, like
(3 + (5*4)) , then the inner bracket should be evaluated first

When we come across something like this, 27/3/3, we need to know whether we evaluate from left to right, or right to left. Mostly we take it left to right. Hence we would evaluate this as (27/3)/3 = 9/3 = 3


alf said...

huh I always heard PEMDAS
"please excuse my dear aunt sally", anyone??
but since the abbreviation of mathematics used in this site is "maths" (commonly a European thing) instead of the american "math", I am inclined to think this is a cultural difference...

Trix said...

And that is why I have said, B or P
and O or E or I


Anonymous said...

ans is 27 not 21

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