To find the quotient of the fractions [tex]\(\frac{1}{3} \div \frac{5}{8}\)[/tex], follow these steps:
1. Identify the operation: We need to divide [tex]\(\frac{1}{3}\)[/tex] by [tex]\(\frac{5}{8}\)[/tex].
2. Division of fractions: Division by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of [tex]\(\frac{5}{8}\)[/tex] is [tex]\(\frac{8}{5}\)[/tex].
3. Set up the multiplication:
[tex]\[
\frac{1}{3} \div \frac{5}{8} = \frac{1}{3} \times \frac{8}{5}
\][/tex]
4. Multiply the numerators: Multiply the numerators of both fractions.
[tex]\[
1 \times 8 = 8
\][/tex]
5. Multiply the denominators: Multiply the denominators of both fractions.
[tex]\[
3 \times 5 = 15
\][/tex]
6. Resulting fraction: Combine the results from the numerators and the denominators into a fraction.
[tex]\[
\frac{8}{15}
\][/tex]
7. Simplify the fraction if possible: In this case, [tex]\(\frac{8}{15}\)[/tex] is already in its simplest form.
Thus, the quotient of [tex]\(\frac{1}{3} \div \frac{5}{8}\)[/tex] is [tex]\(\frac{8}{15}\)[/tex].
Therefore, the correct answer is:
A. [tex]\(\frac{8}{15}\)[/tex]
