Find the value and express as a rational number in standard from:(i)

1.	Find the value and express as a rational number in standard from:(i) \(\frac{2}{5}÷\frac{26}{15}\)(ii) \(\frac{10}{3}÷\frac{-35}{12}\)(iii) \(-6÷(\frac{-8}{17})\)(iv) \(\frac{-40}{99}÷(-20)\)(v) \(27÷\frac{-110}{18}\)(vi) \(\frac{-36}{125}÷\frac{-3}{75}\)
Answer» (i) \(\frac{\frac{2}{5}}{\frac{26}{15}}\) = \(\frac{\frac{2}{1}}{\frac{26}{3}}\) = \(\frac{2}{26}\times \frac{3}{1}\) = \(\frac{3}{13}\) (ii) \(\frac{\frac{10}{3}}{\frac{-35}{12}}\) = \(\frac{\frac{10}{1}}{\frac{-35}{4}}\) = \(\frac{10}{1}\times \frac{-35}{4}\) = \(\frac{-8}{7}\) (iii) \(\frac{-6}{\frac{-8}{17}}\) = \(\frac{\frac{-6}{1}}{\frac{-8}{17}}\) = \(-6\times \frac{17}{-8}\) = \(\frac{51}{4}\) (iv) \(\frac{\frac{-40}{99}}{-20}\) = \(\frac{\frac{2}{99}}{\frac{1}{1}}\) = \(\frac{2}{99}\times \frac{1}{1}\) = \(\frac{2}{99}\) (v) \(\frac{\frac{-22}{27}}{\frac{-110}{18}}\) = \(\frac{\frac{22}{3}}{\frac{110}{2}}\) = \(\frac{22}{3}\times \frac{2}{110}\) = \(\frac{2}{15}\) (vi) \(\frac{\frac{-36}{125}}{\frac{-3}{75}}\) = \(\frac{\frac{36}{5}}{\frac{3}{3}}\) = \(\frac{36}{5}\times \frac{3}{3}\) = \(\frac{36}{5}\)

Find the value and express as a rational number in standard from:(i) \(\frac{2}{5}÷\frac{26}{15}\)(ii) \(\frac{10}{3}÷\frac{-35}{12}\)(iii) \(-6÷(\frac{-8}{17})\)(iv) \(\frac{-40}{99}÷(-20)\)(v) \(27÷\frac{-110}{18}\)(vi) \(\frac{-36}{125}÷\frac{-3}{75}\)

Answer»

(i) \(\frac{\frac{2}{5}}{\frac{26}{15}}\)

= \(\frac{\frac{2}{1}}{\frac{26}{3}}\)

= \(\frac{2}{26}\times \frac{3}{1}\)

= \(\frac{3}{13}\)

(ii) \(\frac{\frac{10}{3}}{\frac{-35}{12}}\)

= \(\frac{\frac{10}{1}}{\frac{-35}{4}}\)

= \(\frac{10}{1}\times \frac{-35}{4}\)

= \(\frac{-8}{7}\)

(iii) \(\frac{-6}{\frac{-8}{17}}\)

= \(\frac{\frac{-6}{1}}{\frac{-8}{17}}\)

= \(-6\times \frac{17}{-8}\)

= \(\frac{51}{4}\)

(iv) \(\frac{\frac{-40}{99}}{-20}\)

= \(\frac{\frac{2}{99}}{\frac{1}{1}}\)

= \(\frac{2}{99}\times \frac{1}{1}\)

= \(\frac{2}{99}\)

(v) \(\frac{\frac{-22}{27}}{\frac{-110}{18}}\)

= \(\frac{\frac{22}{3}}{\frac{110}{2}}\)

= \(\frac{22}{3}\times \frac{2}{110}\)

= \(\frac{2}{15}\)

(vi) \(\frac{\frac{-36}{125}}{\frac{-3}{75}}\)

= \(\frac{\frac{36}{5}}{\frac{3}{3}}\)

= \(\frac{36}{5}\times \frac{3}{3}\)

= \(\frac{36}{5}\)