which of the following is largest
3/5,7/9,4/7,5/13
plz exolain in detail

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Given}, \\ 1. \frac{3}{5}, \frac{7}{9},\frac{4}{7},\frac{5}{13} \\ \Rightarrow \mathrm{take} \mathrm{lcm} \mathrm{of} 5,9,7,13 \mathrm{and} \mathrm{convert} \mathrm{the} \mathrm{denominator} \mathrm{to} \mathrm{the} \mathrm{same} \mathrm{number} \mathrm{as} \mathrm{lcm} \\ \mathrm{lcm} \mathrm{of} 5,9,7,13 \mathrm{will} \mathrm{be} 4095 \\ \frac{3\times 819}{5\times 819}=\frac{2457}{4095} \\ \frac{7\times 455}{9\times 455}=\frac{3185}{4095} \\ \frac{4\times 585}{7\times 585}=\frac{2340}{4095} \\ \frac{5\times 315}{13\times 315}=\frac{1575}{4095} \\ \mathrm{since} \mathrm{denominator} \mathrm{is} \mathrm{same} \mathrm{we} \mathrm{can} \mathrm{equate} \mathrm{numerators}, \mathrm{comparing} \mathrm{we} \mathrm{get} \\ \frac{3185}{4095} \mathrm{is} \mathrm{greatest} \\ \mathrm{hence}, \\ \frac{7}{9} \mathrm{is} \mathrm{greatest} \end{gathered}$$

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