To add the fractions [tex]\(\frac{1}{6}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex], follow these steps:
1. Find a common denominator:
The denominators of the fractions are 6 and 3. The least common denominator (LCD) of 6 and 3 is 6.
2. Convert each fraction to an equivalent fraction with the common denominator:
- The fraction [tex]\(\frac{1}{6}\)[/tex] already has the denominator 6, so it remains [tex]\(\frac{1}{6}\)[/tex].
- The fraction [tex]\(\frac{1}{3}\)[/tex] needs to be converted to have a denominator of 6. Multiply both the numerator and the denominator of [tex]\(\frac{1}{3}\)[/tex] by 2 to get:
[tex]\[
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
\][/tex]
3. Add the fractions:
Now that both fractions have the same denominator, add the numerators and keep the common denominator:
[tex]\[
\frac{1}{6} + \frac{2}{6} = \frac{1 + 2}{6} = \frac{3}{6}
\][/tex]
4. Simplify the fraction:
The fraction [tex]\(\frac{3}{6}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
[tex]\[
\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}
\][/tex]
Therefore, the simplified answer is:
[tex]\[
\frac{1}{6} + \frac{1}{3} = \frac{1}{2}
\][/tex]
The correct answer among the given choices is:
[tex]\(\frac{1}{2}\)[/tex]
