Answer :

To solve the problem

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

follow these steps:

1. First, rewrite division as multiplication by the reciprocal. That is,

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

2. Multiply the fractions by multiplying the numerators together and the denominators together:

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

3. Now, simplify the fraction [tex]$\frac{130}{105}$[/tex]. To do this, factor out the greatest common divisor (GCD) of [tex]$130$[/tex] and [tex]$105$[/tex]. The GCD of [tex]$130$[/tex] and [tex]$105$[/tex] is [tex]$5$[/tex]. Divide both the numerator and the denominator by [tex]$5$[/tex]:

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

Thus, the simplest form of the given expression is

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

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Rewritten by : Barada