Question

Find the value of\[32 - [43 - \{ 51 - (20 - \overline {18 - 7} )\} ]\]

Answer 1

Hint: We need to solve this expression by performing all the given operations in an appropriate order. We have to use the BODMAS rule to solve the above equation. The BODMAS rule gives the priority order. Highest priority is to vinculum (bar), then next priority is brackets strictly in the order: (), {}, [].Then the next priority is order, then next priority is division, then next priority is multiplication, then next priority is addition and then finally performs subtraction.

Complete step by step answer:
We need to find the value of\[32 - [43 - \{ 51 - (20 - \overline {18 - 7} )\} ]\]
Let us solve the given equation,
\[32 - [43 - \{ 51 - (20 - \overline {18 - 7} )\} ]\]
We have to use the BODMAS rule to solve the above equation. According to BODMAS rule, the highest priority is to vinculum (bar).
Thus on performing the subtraction of the terms under the bar we get,
\[ = 32 - [43 - \{ 51 - (20 - 11)\} ]\]
According to BODMAS rule, the next priority is brackets strictly in the order: (), {}, [].
So, let us first remove the bracket (),
Thus on performing the subtraction in the innermost bracket we get,
\[ = 32 - [43 - \{ 51 - 9\} ]\]
Now, let us remove the bracket {},
Thus, on performing the subtraction in the innermost bracket we get,
\[ = 32 - [43 - 42]\]
Now, let us remove the bracket [],
Thus, on performing the subtraction in the innermost bracket we get,
\[ = 32 - 1\]
on performing the subtraction of both numbers we get,
\[ = 31\]
This is the required value.

Note: BODMAS rule is used to simplify the expression which involves multiple operations and multiple brackets. If this rule is not followed, we might end up getting the wrong answer as chances are high that we will solve expressions in the wrong order.