Questions: Divide. Write your answer in simplest form. 13/15 ÷ 7/10

Solution Steps

To divide two fractions, you multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction if possible.

To divide the fractions \( \frac{13}{15} \) and \( \frac{7}{10} \), we multiply the first fraction by the reciprocal of the second fraction: \[ \frac{13}{15} \div \frac{7}{10} = \frac{13}{15} \times \frac{10}{7} \]

Now, we perform the multiplication: \[ \frac{13 \times 10}{15 \times 7} = \frac{130}{105} \]

Next, we simplify \( \frac{130}{105} \). The greatest common divisor (GCD) of 130 and 105 is 5. Thus, we divide both the numerator and the denominator by 5: \[ \frac{130 \div 5}{105 \div 5} = \frac{26}{21} \]

Final Answer