Question

Verify the following and also name the property: $\frac{3}{5}\times \left(\frac{\left(-4\right)}{7}\times \frac{(-8)}{9}\right)=\left(\frac{3}{5}\times \frac{(-4)}{7}\right)\times \left(\frac{-8}{9}\right)$

Answer 1

Verifying $\frac{3}{5}\times \left(\frac{\left(-4\right)}{7}\times \frac{(-8)}{9}\right)=\left(\frac{3}{5}\times \frac{(-4)}{7}\right)\times \left(\frac{-8}{9}\right)$:

Taking L.H.S., we get

$\begin{array}{rcl}\frac{3}{5}\times \left(\frac{-4}{7}\times \frac{(-8)}{9}\right)& =& \frac{3}{5}\times \left(\frac{32}{63}\right)\\ & =& \frac{32}{105}\end{array}$.

Taking R.H.S , we get,

$\begin{array}{rcl}\left(\frac{3}{5}\times \frac{(-4)}{7}\right)\times \frac{(-8)}{9}& =& \left(\frac{-12}{35}\right)\times \left(\frac{-8}{9}\right)\\ & =& \frac{96}{315}\\ & =& \frac{32}{105}\end{array}$.

On comparing both L.HS. and R.H.S., we get,

$L.H.S=R.H.S.=\frac{32}{105}$

Hence, $\frac{3}{5}\times \left(\frac{\left(-4\right)}{7}\times \frac{(-8)}{9}\right)=\left(\frac{3}{5}\times \frac{(-4)}{7}\right)\times \left(\frac{-8}{9}\right)$ is verified.

Hence, The property involved in this verification is Associative Property of Multiplication which says that the grouping of numbers while performing an operation does not change the result of that operation, when operated on three or more numbers.