To determine the quotient of the fractions [tex]\(\frac{3}{5} \div \frac{5}{11}\)[/tex], we will follow a step-by-step process for dividing fractions:
1. Understand the operation:
- Dividing by a fraction is the same as multiplying by its reciprocal. So, we need to find the reciprocal of [tex]\(\frac{5}{11}\)[/tex].
2. Find the reciprocal:
- The reciprocal of [tex]\(\frac{5}{11}\)[/tex] is [tex]\(\frac{11}{5}\)[/tex].
3. Rewrite the division as multiplication:
- Now, we rewrite the original problem [tex]\(\frac{3}{5} \div \frac{5}{11}\)[/tex] as [tex]\(\frac{3}{5} \times \frac{11}{5}\)[/tex].
4. Multiply the fractions:
- To multiply the fractions, we multiply the numerators together and the denominators together.
- Numerator: [tex]\(3 \times 11 = 33\)[/tex]
- Denominator: [tex]\(5 \times 5 = 25\)[/tex]
5. Form the new fraction:
- The product of the numerators is the new numerator, and the product of the denominators is the new denominator. Therefore, we get [tex]\(\frac{33}{25}\)[/tex].
Hence, the quotient of [tex]\(\frac{3}{5} \div \frac{5}{11}\)[/tex] is [tex]\(\frac{33}{25}\)[/tex].
Thus, the correct answer is:
A. [tex]\(\frac{33}{25}\)[/tex]
