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. Identify the Least Common Denominator (LCD):
The denominators we have are [tex]\(6\)[/tex], [tex]\(3\)[/tex], and [tex]\(4\)[/tex]. The LCD of these numbers is [tex]\(12\)[/tex].
2. Convert Each Fraction to an Equivalent Fraction with the LCD:
- 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. Add the Fractions:
Now, add the fractions with the common denominator:
[tex]\[
\frac{2}{12} + \frac{8}{12} + \frac{3}{12} = \frac{2 + 8 + 3}{12} = \frac{13}{12}
\][/tex]
4. Simplify the Fraction (if necessary):
The fraction [tex]\(\frac{13}{12}\)[/tex] is already in its simplest form. You can also express it as a mixed number:
[tex]\[
\frac{13}{12} = 1 \frac{1}{12}
\][/tex]
The best answer is:
A. [tex]\(\frac{13}{12}\)[/tex], or [tex]\(1 \frac{1}{12}\)[/tex].
