Question

verify associatative property of multiplication of 3/5×( -4/7× -8/9) =(3/5× -4/7)×-8/9​

Answer 1

Question :-

Verify associative property of multiplication.

Given Equation :-

LHS -

$\frac{3}{5} \times ( \frac{ - 4}{7} \times \frac{ - 8}{9} )$

RHS -

$(\frac{3}{5} \times \frac{ - 4}{7} ) \times \frac{ - 8}{9}$

Answer :-

$\frac{32}{105} = \frac{32}{105}$

How To Get It :-

LHS -

$\frac{3}{5} \times ( \frac{ - 4}{7} \times \frac{ - 8}{9} )$

$= > \frac{3}{5} \times \frac{32}{63}$

$= > \frac{32}{105}$

RHS -

$(\frac{3}{5} \times \frac{ - 4}{7} ) \times \frac{ - 8}{9}$

$= > \frac{ - 12}{35} \times \frac{ - 8}{9}$

$= > \frac{32}{105}$

Since,

$\frac{32}{105} = \frac{32}{105}$

Therefore,

LHS = RHS

Hence Proved!

Points To Be Noted :-

In LHS -

• In the first step, no cross-multiplication was done.
• On multiplying numerators negative 4 and negative 8, we get positive 32 because negative( - ) integer multiplied by a negative( - ) integer is always a positive ( + ) integer.
• In the second step, on during cross-multiplication, we finally get the answer as 32/105.

In RHS -

• In the first step, no cross-multiplication was done.
• On multiplying numerators positive 3 and negative 4, we get negative 12 because positive( + ) integer multiplied by a negative( - ) integer is always a negative ( - ) integer.
• In the second step, by doing cross-multiplication and negative multiplied negative that is positive we finally get the answer as 32/105.

________________________________________