To solve the problem of dividing [tex]\(\frac{7}{15}\)[/tex] by [tex]\(\frac{3}{5}\)[/tex], we follow these steps:
1. Understand division by a fraction:
Dividing by a fraction is equivalent to multiplying by its reciprocal. So, [tex]\(\frac{a}{b} \div \frac{c}{d}\)[/tex] is the same as [tex]\(\frac{a}{b} \times \frac{d}{c}\)[/tex].
2. Find the reciprocal:
The reciprocal of [tex]\(\frac{3}{5}\)[/tex] is [tex]\(\frac{5}{3}\)[/tex].
3. Rewrite the division problem as a multiplication problem:
[tex]\[\frac{7}{15} \div \frac{3}{5} = \frac{7}{15} \times \frac{5}{3}\][/tex]
4. Multiply the fractions:
When multiplying fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{7}{15} \times \frac{5}{3} = \frac{7 \times 5}{15 \times 3}
\][/tex]
[tex]\[
= \frac{35}{45}
\][/tex]
5. Simplify the resulting fraction:
To simplify [tex]\(\frac{35}{45}\)[/tex], find the greatest common divisor (GCD) of 35 and 45. The GCD of 35 and 45 is 5.
Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{35 \div 5}{45 \div 5} = \frac{7}{9}
\][/tex]
Therefore, [tex]\(\frac{7}{15} \div \frac{3}{5} = \frac{7}{9}\)[/tex].
The correct answer is:
C. [tex]\(\frac{7}{9}\)[/tex]
