To find out how much more Jamal ate than his brother, we need to subtract the amount the 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.
First, we need to find a common denominator to subtract these fractions. The least common multiple of 3 and 4 is 12.
Now, we can convert the fractions:
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For Jamal: \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]
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For 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 \( \frac{5}{12} \) of a banana more than his brother.