Question

Solve: I have 7 in denominator I am equivalent to 27/63. What fraction am I ?
i have 30 in the numerator I am equivalent to 6 elevenths what fraction am I
I have 5 in the denominator I am equivalent to 8/20 what fraction am I
I have twenty eight in the numerator I am equivalent to four fifths what fraction am i
i have 6 in the denominator I am equivalent to 15/18

Answer 1

$$\begin{gathered} 1. \\ \mathrm{Let}\mathrm{the}\mathrm{fraction}\mathrm{be}\frac{\mathrm{x}}{7} \\ \mathrm{Then},\frac{\mathrm{x}}{7}=\frac{27}{63} \\ \mathrm{Multiplying}\mathrm{by}7\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ \frac{\mathrm{x}}{7}\times 7=\frac{27}{63}\times 7 \\ \Rightarrow \mathrm{x}=\frac{27}{9}=3 \\ \mathrm{Therefore}\mathrm{the}\mathrm{fraction}\mathrm{is}\frac{3}{7}. \\ 2. \\ \mathrm{Let}\mathrm{the}\mathrm{fraction}\mathrm{be}\frac{30}{\mathrm{y}} \\ \mathrm{Then},\frac{30}{\mathrm{y}}=\frac{6}{11} \\ \mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}\frac{1}{30},\mathrm{we}\mathrm{g} \\ \frac{30}{\mathrm{y}}\times \frac{1}{30}=\frac{6}{11}\times \frac{1}{30} \\ \Rightarrow \frac{1}{\mathrm{y}}=\frac{1}{55}\Rightarrow \mathrm{y}=55. \\ \mathrm{The}\mathrm{required}\mathrm{fraction}\mathrm{is}\frac{30}{55}. \\ 3. \\ \mathrm{Let}\mathrm{the}\mathrm{fraction}\mathrm{be}\frac{\mathrm{z}}{5}.\mathrm{Then} \\ \frac{\mathrm{z}}{5}=\frac{8}{20} \\ \mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}20,\mathrm{we}\mathrm{get} \\ \frac{\mathrm{z}}{5}\times 20=\frac{8}{20}\times 20 \\ \Rightarrow \mathrm{z}\times 4=8 \\ \mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}4,\mathrm{we}\mathrm{get} \\ \mathrm{z}=\frac{8}{4}=2. \\ \mathrm{The}\mathrm{required}\mathrm{fraction}\mathrm{is}\frac{2}{5}. \\ 4. \\ \mathrm{Let}\mathrm{the}\mathrm{fraction}\mathrm{be}\frac{28}{\mathrm{x}}.\mathrm{Then} \\ \frac{28}{\mathrm{x}}=\frac{4}{5} \\ \mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}\frac{1}{28},\mathrm{we}\mathrm{get} \\ \frac{28}{\mathrm{x}}\times \frac{1}{28}=\frac{4}{5}\times \frac{1}{28} \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{1}{5}\times \frac{1}{7}=\frac{1}{35} \\ \Rightarrow \mathrm{x}=35. \\ \mathrm{The}\mathrm{required}\mathrm{fraction}\mathrm{is}\frac{28}{35} \end{gathered}$$