A tailor has \(15\frac{3}{4}\) metres of fine silk. If making one kurta requires \(2\frac{1}{4}\) metres of silk, exactly how many kurtas can he make?

Total silk the tailor has = \(15\frac{3}{4}\) m
\(\begin{aligned} 15\frac{3}{4} &= \frac{15(4) + 3}{4} \\ &= \frac{60 + 3}{4} \\ &= \frac{63}{4} m\end{aligned}\)
Length of silk required to make one kurta = \(2\frac{1}{4}\) m
\(\begin{aligned} 2\frac{1}{4} &= \frac{2(4) + 1}{4} \\ &= \frac{8 + 1}{4} \\ &= \frac{9}{4} m\end{aligned}\)

\(\begin{aligned} Number\,of\,kurtas\,he\,can\,make &= \frac{Total\,length\,of\,silk}{Length\,required\,to\,make\,one\,kurta} \\ &= \frac{\frac{63}{4}}{\frac{9}{4}} \\ &= \frac{63}{4} × \frac{4}{9} \\ &= 7 \end{aligned}\)
Hence, he can make exactly 7 kurtas.