Bot GPT 4-o mini To divide fractions, you multiply by the reciprocal of the divisor. Therefore, to divide \( \frac{10}{13} \) by \( \frac{4}{9} \), you can re-write the operation as:
\[ \frac{10}{13} \div \frac{4}{9} = \frac{10}{13} \times \frac{9}{4} \]
Now, multiply the fractions:
\[ \frac{10 \times 9}{13 \times 4} = \frac{90}{52} \]
Next, simplify \( \frac{90}{52} \). The greatest common divisor (GCD) of 90 and 52 is 2. So, divide both the numerator and the denominator by 2:
\[ \frac{90 \div 2}{52 \div 2} = \frac{45}{26} \]
Thus, the result of \( \frac{10}{13} \div \frac{4}{9} \) in simplest form is:
\[ \frac{45}{26} \]
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