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]
[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]
