Divide the sum of $-\frac{13}{5}$ and $\frac{12}{7}$ by the product of $\frac{-31}{7}$ and $\frac{-1}{2}$.

To do:

We have to divide the sum of $-\frac{13}{5}$ and $\frac{12}{7}$ by the product of $\frac{-31}{7}$ and $\frac{-1}{2}$.

Solution:

Sum of $-\frac{13}{5}$ and $\frac{12}{7}$ is,

$-\frac{13}{5}+\frac{12}{7}=\frac{-13\times7+12\times5}{35}$         (LCM of 5 and 7 is 35)

$=\frac{-91+60}{35}$

$=\frac{-31}{35}$

Product of $\frac{-31}{7}$ and $\frac{-1}{2}$ is,

$\frac{-31}{7}\times\frac{-1}{2}=\frac{-31\times-1}{7\times2}$

$=\frac{31}{14}$

Therefore,

$\frac{-31}{35}\div\frac{31}{14}=\frac{-31}{35}\times\frac{14}{31}$

$=\frac{-31\times14}{35\times31}$

$=\frac{-2}{5}$

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Updated on: 10-Oct-2022

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