Answer:
We conclude that
[tex]a\times \left(b-c\right)=\:a\times b-a\times c[/tex]
[tex]-\frac{7}{3}=-\frac{7}{3}[/tex]
L.H.S = R.H.S
Step-by-step explanation:
Given the property expression
[tex]a\times \left(b-c\right)=\:a\times b-a\times c[/tex]
Given that:
Determining the LEFT-HAND SIDE
[tex]a\times \left(b-c\right)[/tex]
substituting a= -3/5, b= 5/9 and c= -10/3
[tex]a\times \left(b-c\right)\:=\:\:-\frac{3}{5}\times \left(\frac{5}{9}-\left(-\frac{10}{3}\right)\right)\:\:\:\:\:\:\:\:\:\:\:\:[/tex]
[tex]=-\frac{3}{5}\times \:\left(\frac{5}{9}+\frac{10}{3}\right)\:\:\:[/tex]
[tex]=-\frac{3}{5}\times \frac{35}{9}[/tex]
[tex]=-\frac{7}{3}[/tex]
Determining the RIGHT-HAND SIDE
[tex]\:a\times \:b-a\times \:c[/tex]
substituting a= -3/5, b= 5/9 and c= -10/3
[tex]\:a\times \:b-a\times \:c=ab-ac[/tex]
[tex]=-\frac{3}{5}\left(\frac{5}{9}\right)-\left(-\frac{3}{5}\right)\left(-\frac{10}{3}\right)[/tex]
[tex]=-\frac{3}{5}\cdot \frac{5}{9}-\frac{3}{5}\cdot \frac{10}{3}[/tex]
[tex]=-\frac{15}{45}-\frac{30}{15}[/tex]
[tex]=-\frac{1}{3}-2[/tex]
[tex]=\frac{-7}{3}[/tex]
Apply the fraction rule: [tex]\frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]=-\frac{7}{3}[/tex]
Therefore, we conclude that
[tex]a\times \left(b-c\right)=\:a\times b-a\times c[/tex]
[tex]-\frac{7}{3}=-\frac{7}{3}[/tex]
L.H.S = R.H.S
