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The value of (1+13)(1+14)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)(1+31)(1+41) is
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Simplifying inside the brackets first, (1+13)(1+14)=(43)(54)=2012=53(1+\frac{1}{3})(1+\frac{1}{4}) = (\frac{4}{3})(\frac{5}{4}) = \frac{20}{12} = \frac{5}{3}(1+31)(1+41)=(34)(45)=1220=35.
Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.