To divide the fractions \(\frac{8}{5}\) by \(\frac{24}{25}\), we multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of \(\frac{24}{25}\) is \(\frac{25}{24}\).
So, we can rewrite the division as:
\[ \frac{8}{5} \div \frac{24}{25} = \frac{8}{5} \times \frac{25}{24} \]
Now, we multiply the fractions:
\[ \frac{8 \times 25}{5 \times 24} \]
Calculating the numerator and denominator:
\[ 8 \times 25 = 200 \] and \[ 5 \times 24 = 120 \]
Thus, we have:
\[ \frac{200}{120} \]
Next, we simplify \(\frac{200}{120}\). The greatest common divisor (GCD) of 200 and 120 is 40. We divide the numerator and the denominator by 40:
\[ \frac{200 \div 40}{120 \div 40} = \frac{5}{3} \]
Therefore, the answer is:
\[ \frac{5}{3} \]
This improper fraction can also be expressed as a mixed number:
\[ 1 \frac{2}{3} \]
So, the final answer in simplest form is:
\[ \frac{5}{3} \] or \(1 \frac{2}{3}\).
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