Question

-6/5,1/3,2/5 VERIFY ASSOCIATIVE PROPERTY AND DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER SUBTRACTION

Answer 1

Dear Student,

Assuming question is to verify associative property of subtraction and distributive property of multiplication over subtraction

$$\begin{gathered} Leta=-\frac{6}{5},b=\frac{1}{3},c=\frac{2}{5} \\ \left(i\right)Associativepropertyoversubtraction \\ Let(a-b)-c=a-(b-c) \\ \Rightarrow \left(\frac{\left(-6\right)}{5}-\frac{1}{3}\right)-\frac{2}{5}=\frac{\left(-6\right)}{5}-\left(\frac{1}{3}-\frac{2}{5}\right) \\ \Rightarrow \left(\frac{\left(-18\right)-5}{15}\right)-\frac{2}{5}=\frac{\left(-6\right)}{5}-\left(\frac{5-6}{15}\right) \\ \Rightarrow \left(\frac{-23}{15}\right)-\frac{2}{5}=\frac{\left(-6\right)}{5}-\left(\frac{-1}{15}\right) \\ \Rightarrow \frac{-23-6}{15}=\frac{-18+1}{15} \\ \Rightarrow \frac{-29}{15}\ne \frac{-17}{15} \\ Therefore,Subtractionisnotassociative \\ \left(ii\right)Distributivepropertyofmultiplicationoversubtraction \\ a\times (b-c)=a\times b-a\times c \\ \Rightarrow \frac{\left(-6\right)}{5}\times \left(\frac{1}{3}-\frac{2}{5}\right)=\frac{\left(-6\right)}{5}\times \frac{1}{3}-\frac{\left(-6\right)}{5}\times \frac{2}{5} \\ \Rightarrow \left(\frac{-6}{5}\right)\times \left(\frac{5-6}{15}\right)=\frac{\left(-2\right)}{5}-\frac{\left(-12\right)}{25} \\ \Rightarrow \left(\frac{-6}{5}\right)\times \left(\frac{-1}{15}\right)=\frac{-10+12}{25} \\ \Rightarrow \frac{2}{25}=\frac{2}{25} \\ Verified \\ Andifquestionistoverifyassociativepropertyovermultiplication \\ \left(a\times b\right)\times c=a\times \left(b\times c\right) \\ \Rightarrow \left(\frac{\left(-6\right)}{5}\times \frac{1}{3}\right)\times \frac{2}{5}=\frac{\left(-6\right)}{5}\times \left(\frac{1}{3}\times \frac{2}{5}\right) \\ \Rightarrow \left(\frac{-2}{5}\right)\times \frac{2}{5}=\frac{\left(-6\right)}{5}\times \left(\frac{2}{15}\right) \\ \Rightarrow \frac{-4}{25}=\frac{-4}{25} \\ Verified \end{gathered}$$

Regards,