Question

How do you simplify $ \left[ {\dfrac{3}{4} \times \dfrac{2}{3} - \left( {\dfrac{1}{2} - \dfrac{1}{3}} \right)} \right]12 $ using PEMDAS ?

Answer 1

Hint: In order to solve this question we need to know about PEMDAS . It is the acronym which helps in remembering the order of operations need to be performed while simplifying a question . As we read PEMDAS , letter by letter from left to right we get to know that the preference or the priorities of the operators start getting lesser. We solve the operator of higher priority first , taking the operands from either of two sides of the operator and then calculating it terms by terms as per their precedence .

Complete step-by-step answer:
 Rewriting the question , $ \left[ {\dfrac{3}{4} \times \dfrac{2}{3} - \left( {\dfrac{1}{2} - \dfrac{1}{3}} \right)} \right]12 $ , we can see here are many terms to be solved step by step .
And we are supposed to simplify each term to get a single answer of each term and again simplify in the same manner until we get the single answer.
Using the PEMDAS , it suggests that P stands for Parentheses , E stands for Exponents , M stands for Multiplication , D stands for Division , A stands for Addition , S stands for Subtraction .
So as per our given question parentheses should be performed first and thereafter multiplication .
 $ \left[ {\dfrac{3}{4} \times \dfrac{2}{3} - \left( {\dfrac{1}{2} - \dfrac{1}{3}} \right)} \right]12 $ , we now know that parentheses under parentheses will be solved and take out LCM of the numbers inside parentheses , as –
 $
\Rightarrow \left[ {\dfrac{3}{4} \times \dfrac{2}{3} - \left( {\dfrac{1}{2} - \dfrac{1}{3}} \right)} \right]12 \\
\Rightarrow \left[ {\dfrac{3}{4} \times \dfrac{2}{3} - \left( {\dfrac{{3 - 2}}{6}} \right)} \right]12 \\
\Rightarrow \left[ {\dfrac{3}{4} \times \dfrac{2}{3} - \dfrac{1}{6}} \right]12 \;
  $
 Now , we are going to perform the multiplication inside the parentheses , we get -
 $
\Rightarrow \left[ {\dfrac{3}{4} \times \dfrac{2}{3} - \dfrac{1}{6}} \right]12 \\
\Rightarrow \left[ {\dfrac{6}{{12}} - \dfrac{1}{6}} \right]12 \;
  $
And now we should apply operation of subtraction in order to simplify further ,
 $
\Rightarrow \left[ {\dfrac{6}{{12}} - \dfrac{1}{6}} \right]12 \\
\Rightarrow \left[ {\dfrac{{6 - 2}}{{12}}} \right]12 \\
\Rightarrow \dfrac{4}{{12}} \times 12 \;
  $
Now we will finally do multiplication and cancel out the common factors for the purpose of simplifying , here 12 is cancelled and we get –
  $
   = \dfrac{4}{{12}} \times 12 \\
   = 4 \;
  $
here as no operator left to be performed also the answer to the original question has ended in a single answer “ 4 ”.
So, the correct answer is “4”.

Note: While performing the simplification using PEMDAS also accepts to solve by the rule of PEDMSA .
Parentheses is not an operation but can be considered as a container for operations.
It's Easier but needs to be simplified carefully as the variations in the priorities can result in obtaining wrong answers .
Multiplication and Division have the same equal powers in computing .
Also Addition and subtraction have equal powers in computing .