Discussion
Amongst the following fractions, the largest and second largest fractions, respectively are
\(\frac{5}{6}, \frac{3}{4}, \frac{1}{2}, \frac{2}{3}, \frac{3}{5}\)
Answer: A
The largest and second largest are 5/6 and 3/4.
Write all five fractions over a common denominator; the LCM of 6, 4, 2, 3 and 5 is 60:
\[ \begin{aligned} \tfrac{5}{6} &= \tfrac{50}{60} \\ \tfrac{3}{4} &= \tfrac{45}{60} \\ \tfrac{2}{3} &= \tfrac{40}{60} \\ \tfrac{3}{5} &= \tfrac{36}{60} \\ \tfrac{1}{2} &= \tfrac{30}{60} \end{aligned} \]
In order, \( \tfrac{5}{6} \gt \tfrac{3}{4} \gt \tfrac{2}{3} \gt \tfrac{3}{5} \gt \tfrac{1}{2} \). Option 5/6 and 3/5 skips 3/4 and 2/3; 3/5 and 2/3 are the fourth and third; 3/4 and 1/2 are the second and the smallest.
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