Question

for the following values of X,Y,Z find the product (X* Y)*Z and X (Y*X ) and observe the result (x*y ) Xz = x (y* Z)
X = 3/5 Y = -7/3 Z = 8/11​

Answer 1

Taking LHS

(X* Y)*Z

putting values of X , Y and Z

$( \frac{3}{5} \times \frac{ - 7}{3} ) \times \frac{8}{11}$

$( \frac{ \cancel3}{5} \times \frac{ - 7}{ \cancel3} ) \times \frac{8}{11}$

$\frac{ - 7}{5} \times \frac{8}{11}$

$\implies \frac{ - 56}{55}$

_______________________

Taking RHS

X*(Y*Z )

putting values of X , Y and Z

$\frac{3}{5} \times ( \frac{ - 7}{3} \times \frac{8}{11} )$

$\frac{3}{5} \times ( \frac{ - 56}{33} )$

$\frac{ \cancel3}{5} \times \frac{ - 56}{ \cancel{33}}$

$\frac{ 1}{5} \times \frac{ - 56}{ 11}$

$\implies \frac{ - 56}{55}$

LHS = RHS

This verifies Associative law for multiplication.