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Why does (3y/4) = (3/4)y?

1 Answer

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  • ?
    Lv 7
    4 years ago
    Favorite Answer

     

    Because dividing by 4 is the same as multiplying by 1/4

    and multiplication is associative and commutative, i.e.

    (a * b) * c = a * (b * c) = a * (c * b) = (a * c) * b

    (a * b) * c = (a * c) * b

    Let a = 3, b = y, c = 1/4

    (3 * y) * 1/4 = (3 * 1/4) * y

    (3y)/4 = (3/4)y

    You can always check with a numeric example (although this is not a proof):

    y = 20

    (3y)/4 = (3*20)/4 = 60/4 = 15

    (3/4)y = (3/4)*20 = 0.75*20 = 15

    Pick any number for y. (3y)/4 will always be equal to (3/4)y

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