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

Question

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

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Allison 2 weeks 2021-09-08T21:21:23+00:00 1 Answer 0

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    2021-09-08T21:22:36+00:00

    Answer:

    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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45:7+7-4:2-5:5*4+35:2 =? ( )