Question

Simplify:
\[ - 48 - \left[ {18 - \left\{ {\left( { - 16} \right) - \left( {5 - \overline {4 - 7} } \right)} \right\}} \right]\]

Answer 1

Hint: In the above question, we will use bodmas rule to get the solution. This rule says that whenever we are simplifying any expression, we should follow the order to solve it, to get a correct answer. In this rule B stands for bracket, which means , we have to firstly solve all the brackets present in the expression, and then this is followed by order, which means power and roots, etc. Now, the D stands for division which is followed by M which stands for multiplication, A stands for addition and S stands for subtraction. Now, we will follow the order of the BODMAS rule to simplify the above equation.

Complete step-by-step answer:
In the above question we have to simplify an expression \[ - 48 - \left[ {18 - \left\{ {\left( { - 16} \right) - \left( {5 - \overline {4 - 7} } \right)} \right\}} \right]\]
Now, to simplify this, we will use BODMAS rule here,
We can also see that the horizontal line present on the $\overline {4 - 7} $ is known as vinculum. And this vinculum is used to show that the numbers given below this line are considered as grouped together.
Now, according to this we will do the calculation of the values present in the brackets.
Firstly we will solve the vinculum value
\[
   \Rightarrow - 48 - \left[ {18 - \left\{ {\left( { - 16} \right) - \left( {5 - \overline {4 - 7} } \right)} \right\}} \right] \\
   \Rightarrow - 48 - \left[ {18 - \left\{ {\left( { - 16} \right) - \left( {5 - \left( { - 3} \right)} \right)} \right\}} \right] \\
   \Rightarrow - 48 - \left[ {18 - \left\{ {\left( { - 16} \right) - \left( 8 \right)} \right\}} \right] \\
 \]
Thus, we have solved the vinculum. Now, we will solve the brackets
\[
   \Rightarrow - 48 - \left[ {18 - \left\{ {\left( { - 16} \right) - \left( 8 \right)} \right\}} \right] \\
   \Rightarrow - 48 - \left[ {18 - \left\{ { - 24} \right\}} \right] \\
   \Rightarrow - 48 - \left[ {18 + 24} \right] \\
   \Rightarrow - 48 - \left[ {42} \right] \\
   \Rightarrow - 90 \\
 \]

Hence, the answer is $ - 90$

Note:
In the above question, BODMAS rule is used along with vinculum and this vinculum is very important to solve because the correct answer is behind this. Now, $\overline {4 - 7} $ is the expression given under vinculum. So, we have to solve $4 - 7$ in the very beginning. Now, we will solve the brackets and simplify the expression to get a final answer.