To find the product of the fractions [tex]\(\frac{5}{11}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex], we need to multiply the numerators together and the denominators together. Here’s the detailed step-by-step solution:
1. Identify the numerators and denominators of the fractions:
- Numerator of the first fraction: [tex]\(5\)[/tex]
- Denominator of the first fraction: [tex]\(11\)[/tex]
- Numerator of the second fraction: [tex]\(3\)[/tex]
- Denominator of the second fraction: [tex]\(4\)[/tex]
2. Multiply the numerators together:
[tex]\[
5 \times 3 = 15
\][/tex]
3. Multiply the denominators together:
[tex]\[
11 \times 4 = 44
\][/tex]
4. Construct the product fraction:
[tex]\[
\frac{15}{44}
\][/tex]
So, the product of [tex]\(\frac{5}{11}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex] is [tex]\(\frac{15}{44}\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{15}{44}}
\][/tex]
