Answer :
To solve
$$\frac{13}{15} \div \frac{7}{10},$$
follow these steps:
1. Remember that dividing by a fraction is equivalent to multiplying by its reciprocal. That is,
$$\frac{13}{15} \div \frac{7}{10} = \frac{13}{15} \times \frac{10}{7}.$$
2. Multiply the two fractions by multiplying their numerators together and their denominators together:
$$\frac{13 \times 10}{15 \times 7} = \frac{130}{105}.$$
3. Next, simplify the fraction $\frac{130}{105}$. To do this, find the greatest common divisor (gcd) of 130 and 105. The gcd is 5.
4. Divide both the numerator and the denominator by 5:
$$\text{Numerator: } \frac{130}{5} = 26,$$
$$\text{Denominator: } \frac{105}{5} = 21.$$
5. Thus, the simplified form of the fraction is:
$$\frac{26}{21}.$$
So, the answer in simplest form is
$$\boxed{\frac{26}{21}}.$$
$$\frac{13}{15} \div \frac{7}{10},$$
follow these steps:
1. Remember that dividing by a fraction is equivalent to multiplying by its reciprocal. That is,
$$\frac{13}{15} \div \frac{7}{10} = \frac{13}{15} \times \frac{10}{7}.$$
2. Multiply the two fractions by multiplying their numerators together and their denominators together:
$$\frac{13 \times 10}{15 \times 7} = \frac{130}{105}.$$
3. Next, simplify the fraction $\frac{130}{105}$. To do this, find the greatest common divisor (gcd) of 130 and 105. The gcd is 5.
4. Divide both the numerator and the denominator by 5:
$$\text{Numerator: } \frac{130}{5} = 26,$$
$$\text{Denominator: } \frac{105}{5} = 21.$$
5. Thus, the simplified form of the fraction is:
$$\frac{26}{21}.$$
So, the answer in simplest form is
$$\boxed{\frac{26}{21}}.$$
