Answer :
To solve the division
[tex]$$
\frac{13}{15} \div \frac{7}{10},
$$[/tex]
follow these steps:
1. Write the division as a multiplication by the reciprocal of the second fraction:
[tex]$$
\frac{13}{15} \div \frac{7}{10} = \frac{13}{15} \times \frac{10}{7}.
$$[/tex]
2. Multiply the numerators and the denominators:
[tex]$$
\text{Numerator: } 13 \times 10 = 130, \quad \text{Denominator: } 15 \times 7 = 105.
$$[/tex]
So, the product is
[tex]$$
\frac{130}{105}.
$$[/tex]
3. Simplify the fraction by finding the greatest common divisor (GCD) of 130 and 105. The GCD is 5.
4. Divide both the numerator and the denominator by 5:
[tex]$$
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}.
$$[/tex]
Thus, the simplified form of the given expression is
[tex]$$
\frac{26}{21}.
$$[/tex]
[tex]$$
\frac{13}{15} \div \frac{7}{10},
$$[/tex]
follow these steps:
1. Write the division as a multiplication by the reciprocal of the second fraction:
[tex]$$
\frac{13}{15} \div \frac{7}{10} = \frac{13}{15} \times \frac{10}{7}.
$$[/tex]
2. Multiply the numerators and the denominators:
[tex]$$
\text{Numerator: } 13 \times 10 = 130, \quad \text{Denominator: } 15 \times 7 = 105.
$$[/tex]
So, the product is
[tex]$$
\frac{130}{105}.
$$[/tex]
3. Simplify the fraction by finding the greatest common divisor (GCD) of 130 and 105. The GCD is 5.
4. Divide both the numerator and the denominator by 5:
[tex]$$
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}.
$$[/tex]
Thus, the simplified form of the given expression is
[tex]$$
\frac{26}{21}.
$$[/tex]
