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By what percent will a fraction change if its numerator is decreased by 10% and its denominator is decreased by 50%?

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  1. Fraction = n.
    n*0.9/0.5 = 1.8n.
    1.8n/n = 1.8 = 180%,
    Change = 180% - 100% = 80%.

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  2. let the original fraction be n/d
    new fraction is .9n/.5d or 9n/5d

    change = 9n/5d - n/d
    = 9n/5d - 5m/5d
    = 4n/5d

    percentage change = (4n/5d) / n/d
    = 4/5 = 80%

    illustration:
    suppose our original fraction was 5/8
    new fraction = .9(5)/4 = 45/40 or 9/8
    change = 9/8-5/8 = 1/2
    percentage change = (1/2) / (5/8) = 4/5 = .8 = 80%

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