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CEMC Cayley

Algebra Difficulty 2.0 Junior Find the answer

The product (1−13)(1−14)(1−15) \left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right) is equal to what?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Simplifying, (1−13)(1−14)(1−15)=(23)(34)(45) \left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)=\left(\frac{2}{3}\right)\left(\frac{3}{4}\right)\left(\frac{4}{5}\right) . We can simplify further by dividing equal numerators and denominators to obtain a final value of 25 \frac{2}{5} .

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