Question

5. Verify the property a× (b-c)= a×b-a×c for each of the following:a= -3\5; b= 5\9; c= -10\3​

Answer 1

Answer:

We conclude that

$a\times \left(b-c\right)=\:a\times b-a\times c$

           $-\frac{7}{3}=-\frac{7}{3}$

        L.H.S = R.H.S    

Step-by-step explanation:

Given the property expression

$a\times \left(b-c\right)=\:a\times b-a\times c$

Given that:

• a = -3/5

• b = 5/9

• c = -10/3

Determining the LEFT-HAND SIDE

$a\times \left(b-c\right)$

substituting a= -3/5, b= 5/9 and c= -10/3​

$a\times \left(b-c\right)\:=\:\:-\frac{3}{5}\times \left(\frac{5}{9}-\left(-\frac{10}{3}\right)\right)\:\:\:\:\:\:\:\:\:\:\:\:$

                  $=-\frac{3}{5}\times \:\left(\frac{5}{9}+\frac{10}{3}\right)\:\:\:$

                  $=-\frac{3}{5}\times \frac{35}{9}$

                   $=-\frac{7}{3}$

Determining the RIGHT-HAND SIDE              

$\:a\times \:b-a\times \:c$

substituting a= -3/5, b= 5/9 and c= -10/3​

$\:a\times \:b-a\times \:c=ab-ac$

                      $=-\frac{3}{5}\left(\frac{5}{9}\right)-\left(-\frac{3}{5}\right)\left(-\frac{10}{3}\right)$

                      $=-\frac{3}{5}\cdot \frac{5}{9}-\frac{3}{5}\cdot \frac{10}{3}$

                      $=-\frac{15}{45}-\frac{30}{15}$

                      $=-\frac{1}{3}-2$

                      $=\frac{-7}{3}$

Apply the fraction rule:  $\frac{-a}{b}=-\frac{a}{b}$

                      $=-\frac{7}{3}$

Therefore, we conclude that

$a\times \left(b-c\right)=\:a\times b-a\times c$

           $-\frac{7}{3}=-\frac{7}{3}$

        L.H.S = R.H.S