Question

Verify a(b-c)=ab-ac for a=1.6;b=1/-2;& c=-5/-7​

Answer 1

Given:

$a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}$

To verify:

$a(b-c)=ab-ac$ for the given values.

Solution:

We have,

$a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}$

We need to verify $a(b-c)=ab-ac$.

Taking left hand side, we get

$a(b-c)=1.6\left(\dfrac{1}{-2}-\dfrac{-5}{-7}\right)$

$a(b-c)=1.6\left(-\dfrac{1}{2}-\dfrac{5}{7}\right)$

Taking LCM, we get

$a(b-c)=1.6\left(\dfrac{-7-10}{14}\right)$

$a(b-c)=\dfrac{16}{10}\left(\dfrac{-17}{14}\right)$

$a(b-c)=\dfrac{8}{5}\left(\dfrac{-17}{14}\right)$

$a(b-c)=-\dfrac{68}{35}\right)$

Taking right hand side, we get

$ab-ac=1.6\times \dfrac{1}{-2}-1.6\times \dfrac{-5}{-7}$

$ab-ac=-\dfrac{16}{20}-\dfrac{8}{7}$

$ab-ac=-\dfrac{4}{5}-\dfrac{8}{7}$

Taking LCM, we get

$ab-ac=\dfrac{-28-40}{35}$

$ab-ac=\dfrac{-68}{35}$

Now,

$LHS=RHS$

Hence proved.