Question

1] The product of a fraction and the difference of 3 5/6 {mixed fraction} and 2 1/3{mixed fraction} is 1.Find the fraction.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{required}\mathrm{fraction}\mathrm{be}\mathrm{x} \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{that}\mathrm{the}\mathrm{product}\mathrm{of}\mathrm{x}\mathrm{and}\mathrm{the}\mathrm{difference}\mathrm{of}3\frac{5}{6}\mathrm{and}2\frac{1}{3}\mathrm{is}1 \\ \mathrm{This}\mathrm{implies}\mathrm{that}, \\ \mathrm{x}\left(3\frac{5}{6}-2\frac{1}{3}\right)=1 \\ \mathrm{x}\left(\frac{23}{6}-\frac{7}{3}\right)=1(\mathrm{change}\mathrm{mixed}\mathrm{fraction}\mathrm{to}\mathrm{improper}\mathrm{fraction}) \\ \mathrm{x}\left(\frac{23-14}{6}\right)=1 \\ \mathrm{x}\left(\frac{9}{6}\right)=1 \\ \mathrm{x}\left(\frac{3}{2}\right)=1 \\ \mathrm{This}\mathrm{further}\mathrm{implies}\mathrm{that}, \\ \mathrm{x}=1\times \frac{2}{3} \\ \mathrm{x}=\frac{2}{3} \end{gathered}$$