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10 March, 02:57

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

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  1. 10 March, 03:09
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    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
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