Answer

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**Hint**: First we solve the given equations $ \left( 81\div 9 \right)\div 3=a $ and $ 81\div \left( 9\div 3 \right)=b $ separately and find the value of $ a $ and $ b $ by simplifying the given operation i.e. division. Then, we compare the values of $ a $ and $ b $ to obtain a desired result.

**:**

__Complete step-by-step answer__We have given that $ \left( 81\div 9 \right)\div 3=a $ and $ 81\div \left( 9\div 3 \right)=b $ .

We have to find that from given options, which is correct.

To compare the values of $ a $ and $ b $ , first we have to solve the given equations.

Let us consider equation $ \left( 81\div 9 \right)\div 3=a $

We will use the BODMAS rule to solve the given equations, according to the BODMAS rule first we have to solve the brackets.

So, we solve $ \left( 81\div 9 \right) $ , we get

$ \left( 81\div 9 \right)=9 $

Now, we have

$ \begin{align}

& 9\div 3=a \\

& a=3 \\

\end{align} $

Now, let us consider equation $ 81\div \left( 9\div 3 \right)=b $

First we solve $ \left( 9\div 3 \right) $ , we get

$ \left( 9\div 3 \right)=3 $

Now, we have

$ \begin{align}

& 81\div 3=b \\

& b=27 \\

\end{align} $

So, we get the values $ a=3 $ and $ b=27 $ , when we compare both, we get

$ \begin{align}

& 27>3 \\

& b>a \\

\end{align} $

**So, the correct answer is “Option C”.**

**Note**: To solve such types of questions, we have to follow BODMAS rule. This rule explains the order of operations to solve an expression. According to this rule in an expression, we must first solve the brackets, followed by powers or roots, then division, multiplication, addition and subtraction from left to right. When we solve an expression without using the BODMAS rule, we will get a wrong answer.

For example- the given equations are $ \left( 81\div 9 \right)\div 3=a $ and

When we solve the given equations without using BODMAS rule, we get

$ \begin{align}

& \left( 81\div 9 \right)\div 3=a \\

& 9\div 3=a \\

& a=3 \\

\end{align} $

$ \begin{align}

& 81\div \left( 9\div 3 \right)=b \\

& 9\div 3=b \\

& b=3 \\

\end{align} $

We will get $ a=b $ and we choose option A as the correct answer but it is incorrect. So, be careful while solving such types of questions.

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