Find the value and express as a rational number in standard form:
Question:

Find the value and express as a rational number in standard form:

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

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

(iii) $-6 \div\left(\frac{-8}{17}\right)$

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

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

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

Solution:

(i) $\frac{2}{5} \div \frac{26}{15}=\frac{2}{5} \times \frac{15}{26}=\frac{3}{13}$

(ii) $\frac{10}{3} \div \frac{-35}{12}=\frac{10}{3} \times \frac{12}{-35}=\frac{-8}{7}$

(iii) $-6 \div \frac{-8}{17}=-6 \times \frac{17}{-8}=\frac{51}{4}$

(iv) $\frac{-40}{99} \div(-20)=\frac{-40}{99} \times \frac{1}{-20}=\frac{2}{99}$

(v) $\frac{-22}{27} \div \frac{-110}{18}=\frac{-22}{27} \times \frac{18}{-110}=\frac{2}{15}$

(vi) $\frac{-36}{125} \div \frac{-3}{75}=\frac{-36}{125} \times \frac{75}{-3}=\frac{36}{5}$