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Question-124390




Question Number 124390 by ELIZAR last updated on 03/Dec/20
Answered by benjo_mathlover last updated on 03/Dec/20
((31)/9)= 3+(4/9)= 4−(5/9) = 4−(1/(9/5))=4−(1/(3−(6/5)))  = 4−(1/(3−(1/(5/6)))) = 4−(1/(3−(1/(1−(1/6)))))
$$\frac{\mathrm{31}}{\mathrm{9}}=\:\mathrm{3}+\frac{\mathrm{4}}{\mathrm{9}}=\:\mathrm{4}−\frac{\mathrm{5}}{\mathrm{9}}\:=\:\mathrm{4}−\frac{\mathrm{1}}{\frac{\mathrm{9}}{\mathrm{5}}}=\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}−\frac{\mathrm{6}}{\mathrm{5}}} \\ $$$$=\:\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}−\frac{\mathrm{1}}{\frac{\mathrm{5}}{\mathrm{6}}}}\:=\:\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}−\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{6}}}} \\ $$

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