Bot GPT 4-o mini To find out how much longer the first fish is than the second fish, we need to subtract the length of the second fish from the length of the first fish.
First, let's convert the measurements into improper fractions:
The length of the first fish, \(3 \frac{2}{4}\) feet, can be converted as follows: \[ 3 \frac{2}{4} = \frac{3 \times 4 + 2}{4} = \frac{12 + 2}{4} = \frac{14}{4} \] This fraction can be simplified: \[ \frac{14}{4} = \frac{7}{2} \text{ feet} \]
The length of the second fish is \(\frac{2}{3}\) feet.
Next, we subtract the length of the second fish from the length of the first fish: \[ \frac{7}{2} - \frac{2}{3} \]
To perform this subtraction, we need a common denominator. The least common multiple of the denominators (2 and 3) is 6. We convert both fractions:
\(\frac{7}{2}\) to a denominator of 6: \[ \frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6} \]
\(\frac{2}{3}\) to a denominator of 6: \[ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \]
Now, we can subtract the two fractions: \[ \frac{21}{6} - \frac{4}{6} = \frac{21 - 4}{6} = \frac{17}{6} \]
Thus, the first fish is \(\frac{17}{6}\) feet longer than the second fish.
To express \(\frac{17}{6}\) as a mixed number: \[ \frac{17}{6} = 2 \frac{5}{6} \]
So, the first fish is \(\frac{17}{6}\) feet or \(2 \frac{5}{6}\) feet longer than the second fish.
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