Answer :
To divide the fractions
[tex]$$
\frac{13}{15} \div \frac{7}{10},
$$[/tex]
we start by rewriting the division as a multiplication by the reciprocal of the second fraction. This gives:
[tex]$$
\frac{13}{15} \times \frac{10}{7}.
$$[/tex]
Next, we multiply the numerators and the denominators separately:
[tex]$$
\text{Numerator: } 13 \times 10 = 130,
$$[/tex]
[tex]$$
\text{Denominator: } 15 \times 7 = 105.
$$[/tex]
Thus, the resulting fraction is:
[tex]$$
\frac{130}{105}.
$$[/tex]
To simplify the fraction, we look for the greatest common divisor (GCD) of 130 and 105. In this case, the GCD is 5. We then divide both the numerator and the denominator by 5:
[tex]$$
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}.
$$[/tex]
The fraction in simplest form is:
[tex]$$
\boxed{\frac{26}{21}}.
$$[/tex]
[tex]$$
\frac{13}{15} \div \frac{7}{10},
$$[/tex]
we start by rewriting the division as a multiplication by the reciprocal of the second fraction. This gives:
[tex]$$
\frac{13}{15} \times \frac{10}{7}.
$$[/tex]
Next, we multiply the numerators and the denominators separately:
[tex]$$
\text{Numerator: } 13 \times 10 = 130,
$$[/tex]
[tex]$$
\text{Denominator: } 15 \times 7 = 105.
$$[/tex]
Thus, the resulting fraction is:
[tex]$$
\frac{130}{105}.
$$[/tex]
To simplify the fraction, we look for the greatest common divisor (GCD) of 130 and 105. In this case, the GCD is 5. We then divide both the numerator and the denominator by 5:
[tex]$$
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}.
$$[/tex]
The fraction in simplest form is:
[tex]$$
\boxed{\frac{26}{21}}.
$$[/tex]
