Compare Fractions 4/7 and 6/9: A Cake-Sharing Problem

To solve this problem, we'll compare the fractions representative of the cake portions that Benjamin and George ate.

• Step 1: Simplify Fractions
  George ate $\frac{6}{9}$ of the cake. Simplifying this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 3. Thus, $\frac{6}{9} = \frac{2}{3}$.
• Step 2: Find Common Denominator
  The denominators of the two fractions we are comparing are 7 and 3. The least common multiple (LCM) of 7 and 3 is 21.
• Step 3: Convert to Common Denominator
  Convert $\frac{4}{7}$ and $\frac{2}{3}$ to fractions with a common denominator of 21:
  - For $\frac{4}{7}$, multiply the numerator and the denominator by 3: $\frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21}$.
  - For $\frac{2}{3}$, multiply the numerator and the denominator by 7: $\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}$.
• Step 4: Compare the Fractions
  Now, compare the numerators: 12 and 14. Since 14 is greater than 12, we can conclude that $\frac{14}{21}$ (or $\frac{2}{3}$) is greater than $\frac{12}{21}$ (or $\frac{4}{7}$).

Therefore, George ate more of the cake.

The correct answer is George.