Question

If P=-8/27,Q=3/4 and R=-12/15,then verify that P*(Q*R)=(P*Q)*R

Answer 1

Given that : P = -8/27, Q = 3/4 and R = -12/15

We need to prove that: P * ( Q * R ) = ( P * Q ) * R

Which is associative property of multiplication , the multiplication of three or more numbers remains the same regardless of how the numbers are grouped

The left hand side = P * ( Q * R )

So, we will find Q * R first then multiply the result by P

P * ( Q * R ) = -8/27 * ( 3/4 * -12/15) = -8/27 * -3/5 = 8/45 ⇒ (1)

The right hand side = ( P * Q ) * R

So, we will find P * Q first then multiply the result by R

( P * Q ) * R = ( -8/27 * 3/4 ) * -12/15 = -2/9 * -12/15 = 8/45 ⇒ (2)

From (1) and (2)

So, P * ( Q * R ) = ( P * Q ) * R