To find the sum of the fractions [tex]\( \frac{1}{6} \)[/tex], [tex]\( \frac{2}{3} \)[/tex], and [tex]\( \frac{1}{4} \)[/tex], follow these steps:
1. Find a common denominator:
- The denominators of the fractions are 6, 3, and 4.
- The least common multiple (LCM) of 6, 3, and 4 is 12.
2. Convert each fraction to have a common denominator of 12:
- [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. Simplify if needed:
[tex]\(\frac{13}{12}\)[/tex] is already in its simplest form.
So, the sum of [tex]\( \frac{1}{6} \)[/tex], [tex]\( \frac{2}{3} \)[/tex], and [tex]\( \frac{1}{4} \)[/tex] is [tex]\( \frac{13}{12} \)[/tex].
Given the multiple-choice options, the best answer is:
A. [tex]\( \frac{13}{12} \)[/tex]
