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

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