To find the sum of the fractions [tex]\( \frac{1}{6} \)[/tex], [tex]\( \frac{2}{3} \)[/tex], and [tex]\( \frac{1}{4} \)[/tex] and determine which option is correct, we proceed step-by-step as follows:
1. Identify the fractions:
[tex]\[
\frac{1}{6}, \quad \frac{2}{3}, \quad \frac{1}{4}
\][/tex]
2. Convert the fractions to decimals for initial sum calculation:
[tex]\[
\frac{1}{6} \approx 0.16666666666666666
\][/tex]
[tex]\[
\frac{2}{3} \approx 0.6666666666666666
\][/tex]
[tex]\[
\frac{1}{4} = 0.25
\][/tex]
3. Add the decimal equivalents:
[tex]\[
0.16666666666666666 + 0.6666666666666666 + 0.25 = 1.0833333333333333
\][/tex]
4. Convert the sum back to a fraction and simplify:
[tex]\[
1.0833333333333333 = \frac{13}{12}
\][/tex]
Thus, the simplified fraction sum is:
[tex]\[
\frac{13}{12}
\][/tex]
5. Compare the result with the given options:
A. [tex]\(\frac{2}{72} = \frac{1}{36}\)[/tex]
B. [tex]\(\frac{11}{12}\)[/tex]
C. [tex]\(\frac{13}{12}\)[/tex], or [tex]\(1 \frac{1}{12}\)[/tex]
D. [tex]\(\frac{4}{12} = \frac{1}{3}\)[/tex]
The correct option that matches our result of [tex]\( \frac{13}{12} \)[/tex] is:
[tex]\[
\boxed{\text{C}}
\][/tex]
