question_answer 2)

                If you subtract \[\frac{1}{2}\] from a number and multiply the result by \[\frac{1}{2}\], you get \[\frac{1}{8}\]. What is the number?

Answer:

                Let the number be \[x\]. According to the question, \[\frac{1}{2}\left( x-\frac{1}{2} \right)=\frac{1}{8}\] \[\Rightarrow \]               \[\frac{1}{2}\left( \frac{2x-1}{2} \right)=\frac{1}{8}\] \[\Rightarrow \]               \[\frac{2x-1}{4}=\frac{1}{8}\] \[\Rightarrow \]               \[\frac{2x-1}{4}\times 8=\frac{1}{8}\times 8\]    |Multiplying both sides by 8 \[\Rightarrow \]               \[(2x-1)\,2=1\] \[\Rightarrow \]               \[4x-2=1\] \[\Rightarrow \]               \[4x=1+2\]                          |Transposing ? 2 to RHS \[\Rightarrow \]               \[4x=3\] \[\Rightarrow \]               \[x=\frac{3}{4}\]                                               | Dividing both sides by 4 Hence, the desired number is \[\frac{3}{4}\].                 Check: \[\frac{1}{2}\left( \frac{3}{4}-\frac{1}{2} \right)\,=\frac{1}{2}\,\left( \frac{3-2}{4} \right)\] \[=\frac{1}{2}\,\left( \frac{1}{4} \right)\] \[=\frac{1}{8}\].                                                |as desired