To find out how much more Jamal ate than his brother, we need to subtract the amount his brother ate from the amount Jamal ate.
Jamal ate \( \frac{2}{3} \) of his banana and his brother ate \( \frac{1}{4} \) of his banana.
We can solve this by finding a common denominator for the fractions. The least common denominator (LCD) for \( 3 \) and \( 4 \) is \( 12 \).
Now we convert the fractions to have the denominator of \( 12 \):
- Jamal: \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]
- His brother: \[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \]
Now, we can subtract the two amounts: \[ \frac{8}{12} - \frac{3}{12} = \frac{8 - 3}{12} = \frac{5}{12} \]
So, Jamal ate \( \frac{5}{12} \) more than his brother.
The answer is \( \frac{5}{12} \).