1. Which of the fractions $\frac{2}{3}, \frac{3}{4}, \frac{5}{6}, \frac{5}{8}$, and $\frac{11}{12}$ is the smallest?
1. Solution 1
We re-write each of the fractions using the common denominator 24 :
$$
\frac{2}{3}=\frac{16}{24} \quad \frac{3}{4}=\frac{18}{24} \quad \frac{5}{6}=\frac{20}{24} \quad \frac{5}{8}=\frac{15}{24} \quad \frac{11}{12}=\frac{22}{24}
$$

The smallest of these is $\frac{15}{24}=\frac{5}{8}$.
Solution 2
We note that $\frac{2}{3}=1-\frac{1}{3}$ and $\frac{3}{4}=1-\frac{1}{4}$ and $\frac{5}{6}=1-\frac{1}{6}$ and $\frac{11}{12}=1-\frac{1}{12}$.
The smallest of these four fractions is the one which is equal to 1 minus the largest of the unit fractions $\frac{1}{3}, \frac{1}{4}, \frac{1}{6}, \frac{1}{12}$. This is $\frac{2}{3}=1-\frac{1}{3}$.
So we need to compare $\frac{2}{3}$ and $\frac{5}{8}$, the smaller of which will be the smallest of the five fractions in the list.
Since $\frac{2}{3}=0 . \overline{6} \approx 0.667$ and $\frac{5}{8}=0.625$, then $\frac{5}{8}$ is the smallest of the five fractions.
ANSWER: $\frac{5}{8}$