To find the quotient of two fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex], follow these steps:
1. Understand the division of fractions:
Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus, the division of [tex]\(\frac{3}{5}\)[/tex] by [tex]\(\frac{1}{10}\)[/tex] can be expressed as:
[tex]\[
\frac{3}{5} \div \frac{1}{10} = \frac{3}{5} \times \frac{10}{1}
\][/tex]
2. Multiply the fractions:
To multiply two fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{3}{5} \times \frac{10}{1} = \frac{3 \times 10}{5 \times 1} = \frac{30}{5}
\][/tex]
3. Simplify the result:
Simplify the fraction [tex]\(\frac{30}{5}\)[/tex] by dividing the numerator by the denominator:
[tex]\[
\frac{30}{5} = 6
\][/tex]
Thus, the quotient of [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex] is [tex]\(6\)[/tex].
Therefore, the correct answer is:
D. 6
