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} $

To do:

We have to simplify the given expressions and express  them as rational numbers in standard form.

Solution:

(i) $\frac{-16}{21}\times\frac{14}{5}=\frac{(-)\times(+)\times16\times14}{(21)\times(5)}$ 

$=\frac{-16\times2}{3\times5}$

$=\frac{-32}{15}$ 

(ii) $\frac{7}{6}\times\frac{-3}{28}=\frac{(+)\times(-)\times7\times3}{(6)\times(28)}$ 

$=\frac{-1\times1}{2\times4}$

$=\frac{-1}{8}$  

(iii) $\frac{-19}{36}\times16=\frac{(-)\times(+)\times19\times16}{36}$ 

$=\frac{-19\times4}{9}$

$=\frac{-76}{9}$   

(iv) $\frac{-13}{9}\times\frac{27}{-26}=\frac{(-)\times(-)\times13\times27}{(9)\times(26)}$ 

$=\frac{1\times3}{1\times2}$

$=\frac{3}{2}$  

(v) $\frac{-9}{16}\times\frac{-64}{-27}=\frac{(-)\times(+)\times9\times64}{(16)\times(27)}$ 

$=\frac{-1\times4}{1\times3}$

$=\frac{-4}{3}$   

(vi) $\frac{-50}{7}\times\frac{14}{3}=\frac{(-)\times(+)\times50\times14}{(7)\times(3)}$ 

$=\frac{-50\times2}{1\times3}$

$=\frac{-100}{3}$    

(vii) $\frac{-11}{9}\times\frac{-81}{-88}=\frac{(-)\times(+)\times11\times81}{(9)\times(88)}$ 

$=\frac{-1\times9}{1\times8}$

$=\frac{-9}{8}$ 

(viii) $\frac{-5}{9}\times\frac{72}{-25}=\frac{(-)\times(-)\times5\times72}{(9)\times(25)}$ 

$=\frac{1\times8}{1\times5}$

$=\frac{8}{5}$

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Updated on: 10-Oct-2022

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