What is the value of (1)/(2) + ( - (5)/(6)) + (1)/(4)

Question

What is the value of
`(1)/(2) + ( - (5)/(6)) + (1)/(4)`

Answer 1

-1/12

1) Evaluating that expression we can write

`(1)/(2)+(-(5)/(6))+(1)/(4)`

2) We need to find out a common denominator for those. Let's calculate the LCM by factoring by prime numbers:

`\begin{gathered} ((12\colon2*1)-(12\colon6*5)+(12\colon4*1))/(12) \\ (6-10+3)/(12)=-(1)/(12) \end{gathered}`

Note that when reducing to a common denominator, we have divided 12 by each original denominator and multiplied by its original numerator. In other words:

`\begin{gathered} \\ (1)/(2)+(-(5)/(6))+(1)/(4)=(6-10+3)/(12)=-(1)/(12) \end{gathered}`

3) Hence the answer is -1/12