National and Regional Contests USA Contests MAA AMC AMC 8 2022 AMC 8 - 8 Product of Fractions Problem Statement What is the value of 1 3 ⋅ 2 4 ⋅ 3 5 ⋯ 18 20 ⋅ 19 21 ⋅ 20 22 ? \displaystyle\frac{1}{3}\cdot\displaystyle\frac{2}{4}\cdot\displaystyle\frac{3}{5}\cdots\displaystyle\frac{18}{20}\cdot\displaystyle\frac{19}{21}\cdot\displaystyle\frac{20}{22}? 3 1 ⋅ 4 2 ⋅ 5 3 ⋯ 20 18 ⋅ 21 19 ⋅ 22 20 ? < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( A ) < / s p a n > 1 462 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( B ) < / s p a n > 1 231 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( C ) < / s p a n > 1 132 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( D ) < / s p a n > 2 213 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( E ) < / s p a n > 1 22 <span class='latex-bold'>(A)</span> ~\displaystyle\frac{1}{462}\qquad<span class='latex-bold'>(B)</span> ~\displaystyle\frac{1}{231}\qquad<span class='latex-bold'>(C)</span> ~\displaystyle\frac{1}{132}\qquad<span class='latex-bold'>(D)</span> ~\displaystyle\frac{2}{213}\qquad<span class='latex-bold'>(E)</span> ~\displaystyle\frac{1}{22}\qquad < s p an c l a ss = ′ l a t e x − b o l d ′ > ( A ) < / s p an > 462 1 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( B ) < / s p an > 231 1 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( C ) < / s p an > 132 1 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( D ) < / s p an > 213 2 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( E ) < / s p an > 22 1