Number Comparison Problem: Determining Which Value is Larger

To solve this problem, we will compare the given fractions to determine which is largest:

• Compare $\frac{2}{3}$ and $\frac{7}{11}$:

  • Cross multiply: $2 \times 11 = 22$ and $3 \times 7 = 21$.
    Since $22 > 21$, $\frac{2}{3}$ is larger than $\frac{7}{11}$.

• Compare $\frac{2}{3}$ and $\frac{6}{10}$:

  • Simplify $\frac{6}{10} = \frac{3}{5}$.
    Cross multiply: $2 \times 5 = 10$ and $3 \times 3 = 9$.
    Since $10 > 9$, $\frac{2}{3}$ is larger than $\frac{3}{5}$ (same as $\frac{6}{10}$).

• To confirm, compare $\frac{2}{3}$ and $\frac{3}{5}$ again directly:

  • Cross multiply: $2 \times 5 = 10$ and $3 \times 3 = 9$.
    Since $10 > 9$, $\frac{2}{3}$ is also larger than $\frac{3}{5}$.

Therefore, the largest fraction of all given choices is indeed $\frac{2}{3}$.