To solve the expression [tex]\(\frac{\frac{5}{11}}{4}\)[/tex], we should follow these steps:
1. Rewrite the division of fractions as a single fraction. The given expression is a compound fraction, and the general rule for dividing by a fraction is to multiply by its reciprocal. Therefore, we have:
[tex]\[
\frac{\frac{5}{11}}{4} = \frac{5}{11} \div 4
\][/tex]
2. Convert the integer 4 into a fraction, which would be [tex]\(\frac{4}{1}\)[/tex]. So, the expression becomes:
[tex]\[
\frac{5}{11} \div \frac{4}{1}
\][/tex]
3. To divide by a fraction, multiply by its reciprocal. The reciprocal of [tex]\(\frac{4}{1}\)[/tex] is [tex]\(\frac{1}{4}\)[/tex]. Thus, the expression becomes:
[tex]\[
\frac{5}{11} \times \frac{1}{4}
\][/tex]
4. Multiply the numerators together and the denominators together:
[tex]\[
\frac{5 \times 1}{11 \times 4} = \frac{5}{44}
\][/tex]
The simplified fraction is [tex]\(\frac{5}{44}\)[/tex]. When converted to a decimal, this fraction equals approximately:
[tex]\[
0.11363636363636363
\][/tex]
Therefore, the result of the expression [tex]\(\frac{\frac{5}{11}}{4}\)[/tex] is approximately [tex]\(0.11363636363636363\)[/tex].
