# Simplify each of the following and express the result as a rational number in standard form:

Question:

Simplify each of the following and express the result as a rational number in standard form:

(i) $\frac{-16}{21} \times \frac{14}{5}$

(ii) $\frac{7}{6} \times \frac{-3}{28}$

(iii) $\frac{-19}{36} \times 16$

(iv) $\frac{-13}{9} \times \frac{27}{-26}$

(v) $\frac{-9}{16} \times \frac{-64}{-27}$

(vi) $\frac{-50}{7} \times \frac{14}{3}$

(vii) $\frac{-11}{9} \times \frac{-81}{-88}$

(viii) $\frac{-5}{9} \times \frac{72}{-25}$

Solution:

(i) $\frac{-16}{21} \times \frac{14}{5}=\frac{-2 \times 2 \times 2 \times 2}{3 \times 7} \times \frac{2 \times 7}{5}=\frac{-32}{15}$

(ii) $\frac{7}{6} \times \frac{-3}{28}=\frac{7}{2 \times 3} \times \frac{-3}{2 \times 2 \times 7}=\frac{-1}{8}$

(iii) $\frac{-19}{36} \times 16=\frac{-19}{2 \times 2 \times 3 \times 3} \times 2 \times 2 \times 2 \times 2=\frac{-76}{9}$

$($ iv $) \frac{-13}{9} \times \frac{27}{-26}=\frac{-13}{3 \times 3} \times \frac{3 \times 3 \times 3}{-2 \times 13}=\frac{3}{2}$

$(\mathrm{v}) \frac{-9}{16} \times \frac{-64}{-27}=\frac{-9}{16} \times \frac{-4 \times 16}{-3 \times 9}=\frac{-4}{3}$

(vi) $\frac{-50}{7} \times \frac{14}{3}=\frac{-50}{7} \times \frac{2 \times 7}{3}=\frac{-100}{3}$

(vii) $\frac{-11}{9} \times \frac{-81}{-88}=\frac{-11}{9} \times \frac{-9 \times 9}{-8 \times 11}=\frac{-9}{8}$

(viii) $\frac{-5}{9} \times \frac{72}{-25}=\frac{-5}{9} \times \frac{8 \times 9}{-5 \times 5}=\frac{8}{5}$