To find the sum of [tex]\( \frac{1}{6}, \frac{2}{3} \)[/tex], and [tex]\( \frac{1}{4} \)[/tex], we need to add these fractions together.
First, we convert all the fractions to have a common denominator:
1. The denominators are 6, 3, and 4. The least common multiple (LCM) of these numbers is 12.
2. Convert each fraction to have the denominator of 12:
- For [tex]\( \frac{1}{6} \)[/tex]:
[tex]\[
\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
\][/tex]
- For [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\][/tex]
- For [tex]\( \frac{1}{4} \)[/tex]:
[tex]\[
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
\][/tex]
3. Now, add the converted fractions:
[tex]\[
\frac{2}{12} + \frac{8}{12} + \frac{3}{12} = \frac{2 + 8 + 3}{12} = \frac{13}{12}
\][/tex]
Thus, the sum of [tex]\( \frac{1}{6} + \frac{2}{3} + \frac{1}{4} \)[/tex] is [tex]\( \frac{13}{12} \)[/tex].
The best answer among the given choices is:
C. [tex]\( \frac{13}{12} \)[/tex], or [tex]\(1 \frac{1}{12} \)[/tex].
