Question

Find the value of \[36 \div \left[ {3 \div \left( {48 \div 8} \right)} \right]\]

Answer 1

Hint: This question involves the arithmetic operations like addition/ subtraction/ multiplication/ division. We need to know how to find the common factor between the two terms. Also, we need to know which type of bracket has the most priority in the given question to make the easy calculation of these types of questions.

Complete step by step solution:
The given expression is shown below,
\[36 \div \left[ {3 \div \left( {48 \div 8} \right)} \right] = ? \to \left( 1 \right)\]
In this type of question, we would solve the operation inside the parentheses at first, the operation which is inside the next bracket given in the question.
Let’s solve the function inside the parenthesis,
We have
\[\left( {48 \div 8} \right)\]
It can also be written as,
\[\left( {48 \div 8} \right) = \dfrac{{48}}{8}\]
For this the common factor is\[8\], so let’s divide the numerator and denominator by\[8\]. So, we get
\[\dfrac{{\left( {\dfrac{{48}}{8}} \right)}}{{\dfrac{8}{8}}} = 6\]
So, we have
\[\left( {48 \div 8} \right) = 6\]
Let’s substitute the above-mentioned value in the equation\[\left( 1 \right)\], we get
\[\left( 1 \right) \to 36 \div \left[ {3 \div \left( {48 \div 8} \right)} \right] = ?\]
\[36 \div \left[ {3 \div \left( {48 \div 8} \right)} \right] = 36 \div \left[ {3 \div 6} \right] \to \left( 2 \right)\]
Let’s solve the function inside the closed bracket
We have\[\left[ {3 \div 6} \right]\]
It also can be written as,
\[\left[ {3 \div 6} \right] = \dfrac{3}{6} = \dfrac{1}{2} = 0.5\]
So, we get
\[\left[ {3 \div 6} \right] = 0.5\]
Let’s substitute this value in the equation\[\left( 2 \right)\], we get
\[\left( 2 \right) \to 36 \div \left[ {3 \div \left( {48 \div 8} \right)} \right] = 36 \div \left[ {3 \div 6} \right]\]
\[36 \div \left[ {3 \div 6} \right] = 36 \div 0.5 \to \left( 3 \right)\]
Let’s solve the above expression.
We have,
\[36 \div 0.5\]
It also can be written as,
\[\dfrac{{36}}{{0.5}} = \dfrac{{36}}{{\left( {\dfrac{1}{2}} \right)}}\]
So, we get
\[36 \times \dfrac{2}{1} = 72\]
Finally, we get\[36 \div 0.5 = 72\]
So, the final answer is,
\[36 \div \left[ {3 \div \left( {48 \div 8} \right)} \right] = 72\]

Note: This question describes the arithmetic operations like addition/ subtraction/ multiplication/ division. In this type of question first, we would solve the expression in the innermost bracket functions, secondly, we would solve the second innermost bracket functions given in the question. By using this method we can easily find the final answer for the given question.