To find the sum of the fractions [tex]\(\frac{1}{6}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], and [tex]\(\frac{1}{4}\)[/tex], let's go through the process step by step:
1. Identify a common denominator: The common denominator for the fractions [tex]\(\frac{1}{6}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], and [tex]\(\frac{1}{4}\)[/tex] is the least common multiple (LCM) of the denominators 6, 3, and 4. The LCM of 6, 3, and 4 is 12.
2. Convert each fraction to have the common denominator:
- [tex]\(\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}\)[/tex]
- [tex]\(\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}\)[/tex]
- [tex]\(\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}\)[/tex]
3. Add the fractions:
[tex]\[
\frac{2}{12} + \frac{8}{12} + \frac{3}{12} = \frac{2 + 8 + 3}{12} = \frac{13}{12}
\][/tex]
4. Express the sum as a mixed number:
[tex]\[
\frac{13}{12} = 1 \frac{1}{12}
\][/tex]
Hence, the best answer is:
[tex]\[
\boxed{\text{D. } \frac{13}{12}, \text{ or } 1 \frac{1}{12}}
\][/tex]
