​ Find the value and express as a rational number in standard from: (i) 2/5÷26/15 (ii) 10/3÷ -35/12 (iii) -6÷(-8/17)

Question

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 1

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

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

= \(\frac{36}{5}\times \frac{3}{3}\)

= \(\frac{36}{5}\)