Question

find the product and verify the associative property for multiplication of rational numbers
(i). 1/5×(-7/1×6/11)​

Answer 1

GIVEN :

The product of the associative property for multiplication of rational numbers

$\frac{1}{5}\times (-\frac{7}{1}\times \frac{6}{11})$

TO FIND :

​The product  and verify the associative property for multiplication of given rational numbers

$\frac{1}{5}\times (-\frac{7}{1}\times \frac{6}{11})=(-\frac{7}{1}\times \frac{6}{11})\times \frac{1}{5}$

SOLUTION:

Given that the product of the associative property for multiplication of rational numbers  $\frac{1}{5}\times (-\frac{7}{1}\times \frac{6}{11})$

Now verify the Associative property for multiplication of rational numbers

$\frac{1}{5}\times (-\frac{7}{1}\times \frac{6}{11})=(-\frac{7}{1}\times \frac{6}{11})\times \frac{1}{5}$

Now we have that $\frac{1}{5}\times (-\frac{7}{1}\times \frac{6}{11})$

$=\frac{1}{5}\times (-\frac{42}{11})$

$=-\frac{42}{55}$

$\frac{1}{5}\times (-\frac{7}{1}\times \frac{6}{11})=-\frac{42}{11}\hfill (1)$

Now we have that $(-\frac{7}{1}\times \frac{6}{11})\times \frac{1}{5}$

$=(-\frac{42}{11})\times \frac{1}{5}$

$=-\frac{42}{55}$

$(-\frac{7}{1}\times \frac{6}{11})\times \frac{1}{5}=-\frac{42}{55}\hfill (2)$

∴ equations (1) and (2) are equal

Hence the product and verified of Associative property for multiplication of given rational numbers is  $\frac{1}{5}\times (-\frac{7}{1}\times \frac{6}{11})=(-\frac{7}{1}\times \frac{6}{11})\times \frac{1}{5}$