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} $

To do:

We have to find the values and express them in standard form.

Solution:

We know that,

$a \div b = a \times \frac{1}{b}$

Therefore,

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

$=\frac{2\times15}{5\times26}$

$=\frac{1\times3}{1\times13}$

$=\frac{3}{13}$     

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

$=\frac{10\times12}{3\times(-35)}$

$=\frac{2\times4}{1\times(-7)}$

$=\frac{-8}{7}$      

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

$=\frac{-6\times17}{-8}$

$=\frac{3\times17}{4}$

$=\frac{51}{4}$       

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

$=\frac{-40\times1}{99\times(-20)}$

$=\frac{2\times1}{99\times1}$

$=\frac{2}{99}$       

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

$=\frac{-22\times18}{27\times(-110)}$

$=\frac{1\times2}{3\times5}$

$=\frac{2}{15}$   

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

$=\frac{-36\times75}{125\times(-3)}$

$=\frac{12\times3}{5\times1}$

$=\frac{36}{5}$    

Tutorialspoint

Updated on: 10-Oct-2022

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