Compare Fractions to 2/5: Determining Extra Credit Eligibility

To solve this problem, we'll compare each student's share of work against $\frac{2}{5}$ to determine who receives extra points.

Let's perform these comparisons:

• Daniel: He completed $\frac{1}{2}$ of the work.
  Compare $\frac{1}{2}$ with $\frac{2}{5}$:
  Cross-multiply: $1 \times 5$ vs $2 \times 2$ -> $5 > 4$.
  This shows $\frac{1}{2} > \frac{2}{5}$.
• Andy: He completed $\frac{1}{6}$ of the work.
  Compare $\frac{1}{6}$ with $\frac{2}{5}$:
  Cross-multiply: $1 \times 5$ vs $6 \times 2$ -> $5 < 12$.
  This shows $\frac{1}{6} < \frac{2}{5}$.
• Sara: She completed $\frac{2}{7}$ of the work.
  Compare $\frac{2}{7}$ with $\frac{2}{5}$:
  Cross-multiply: $2 \times 5$ vs $7 \times 2$ -> $10 < 14$.
  This shows $\frac{2}{7} < \frac{2}{5}$.

Only Daniel completed more than $\frac{2}{5}$ of the work. Thus, he receives extra points.

The teacher gives extra points to Daniel.