Question

Perform the indicated operation. 5/8-[1/2-(-1/4)]

Answer 1

`(5)/(8)-[(1)/(2)-(-(1)/(4))] = (-1)/(8)`

Solution:

Given that, we have to perform the indicated operation

`(5)/(8)-[(1)/(2)-(-(1)/(4))]`

We can use BODMAS rule to perform the operation

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right

So, in the given expression, we have to solve for brackets first

Solve the innermost bracket

`(5)/(8)-[(1)/(2)+(1)/(4)]`

Now solve the bracket again

`(5)/(8)-[(1)/(2)+(1)/(4)] = (5)/(8)-[(4+2)/(8)] = (5)/(8)-[(6)/(8)]`

Now remove the parenthesis

`\rightarrow (5)/(8) - (6)/(8)`

Now perform subtraction operation

`\rightarrow (5)/(8) - (6)/(8) = (5-6)/(8) = (-1)/(8)`

Thus we got,

`(5)/(8)-[(1)/(2)-(-(1)/(4))] = (-1)/(8)`

Thus the indicated operation is performed