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Mathematics

By what number should 1217\dfrac{12}{17} be divided to get 47-\dfrac{4}{7}?

Rational Numbers

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Answer

Let the number be xx

1217÷x=471217×1x=47x=1217×74x=12×717×4x=8468x=2117x=1417\dfrac{12}{17} ÷ x = -\dfrac{4}{7}\\[1em] \Rightarrow \dfrac{12}{17} \times \dfrac{1}{x} = -\dfrac{4}{7} \\[1em] \Rightarrow x = \dfrac{12}{17} \times -\dfrac{7}{4}\\[1em] \Rightarrow x = -\dfrac{12 \times 7}{17 \times 4}\\[1em] \Rightarrow x = -\dfrac{84}{68}\\[1em] \Rightarrow x = -\dfrac{21}{17}\\[1em] \Rightarrow x = -1\dfrac{4}{17}

1417-1\dfrac{4}{17} must be divided by 1217\dfrac{12}{17} so that the product is 47-\dfrac{4}{7}.

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