Answer :

To solve

[tex]$$
\frac{13}{15} \div \frac{7}{10},
$$[/tex]

we follow these steps:

1. Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, we rewrite the division as a multiplication:

[tex]$$
\frac{13}{15} \div \frac{7}{10} = \frac{13}{15} \times \frac{10}{7}.
$$[/tex]

2. Multiply the numerators and the denominators:

[tex]$$
\frac{13}{15} \times \frac{10}{7} = \frac{13 \times 10}{15 \times 7} = \frac{130}{105}.
$$[/tex]

3. To simplify the fraction [tex]$\frac{130}{105}$[/tex], we find the greatest common divisor (GCD) of 130 and 105. The GCD of 130 and 105 is 5.

4. Divide both the numerator and the denominator by 5:

[tex]$$
\frac{130}{105} = \frac{130 \div 5}{105 \div 5} = \frac{26}{21}.
$$[/tex]

Thus, the simplified form of the expression is:

[tex]$$
\boxed{\frac{26}{21}}.
$$[/tex]

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Rewritten by : Barada