Add and Express the sum as mixed fraction:
(i) $ \frac{-12}{5} $ and $ \frac{43}{10} $
(ii) $ \frac{24}{7} $ and $ \frac{-11}{4} $
(iii) $ \frac{-31}{6} $ and $ \frac{-27}{8} $
(iv) $ \frac{101}{6} $ and $ \frac{7}{8} $

To do:

We have to add and express the given sums as mixed fractions.

Solution:

(i) $\frac{-12}{5}+\frac{43}{10}=\frac{-12\times2}{5\times2}+\frac{43\times1}{10\times1}$           (LCM of 5 and 10 is 10)

$=\frac{-24}{10}+\frac{43}{10}$

$=\frac{-24+43}{10}$   

$=\frac{43-24}{10}$

$=\frac{19}{10}$

$=\frac{10+9}{10}$

$=\frac{10}{10}+\frac{9}{10}$

$=1+\frac{9}{10}$

$=1\frac{9}{10}$

Therefore, $\frac{-12}{5}+\frac{43}{10}=1\frac{9}{10}$.  

(ii) $\frac{24}{7}+\frac{-11}{4}=\frac{24\times4}{7\times4}+\frac{-11\times7}{4\times7}$           (LCM of 7 and 4 is 28)

$=\frac{96}{28}+\frac{-77}{28}$

$=\frac{96+(-77)}{28}$   

$=\frac{96-77}{28}$

$=\frac{19}{28}$

Therefore, $\frac{24}{7}+\frac{-11}{4}=\frac{19}{28}$.   

(iii) $\frac{-31}{6}+\frac{-27}{8}=\frac{-31\times4}{6\times4}+\frac{-27\times3}{8\times3}$           (LCM of 6 and 8 is 24)

$=\frac{-124}{24}+\frac{-81}{24}$

$=\frac{-124+(-81)}{24}$   

$=\frac{-(124+81)}{24}$

$=\frac{-205}{24}$

$=-(\frac{192+13}{24})$

$=-(\frac{192}{24}+\frac{13}{24})$

$=-(8+\frac{13}{24})$

$=-8\frac{13}{24}$

Therefore, $\frac{-31}{6}+\frac{-27}{8}=-8\frac{13}{24}$.    

(iv) $\frac{101}{6}+\frac{7}{8}=\frac{101\times4}{6\times4}+\frac{7\times3}{8\times3}$           (LCM of 6 and 8 is 24)

$=\frac{404}{24}+\frac{21}{24}$

$=\frac{404+21}{24}$   

$=\frac{425}{24}$

$=\frac{408+17}{24}$

$=\frac{408}{24}+\frac{17}{24}$

$=17+\frac{17}{24}$

$=17\frac{17}{24}$

Therefore, $\frac{101}{6}+\frac{7}{8}=17\frac{17}{24}$.     

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

24 Views

Kickstart Your Career

Get certified by completing the course

Get Started