To find the sum of the fractions [tex]\( \frac{1}{9} \)[/tex], [tex]\( \frac{2}{3} \)[/tex], and [tex]\( \frac{5}{18} \)[/tex], we'll follow a step-by-step process to combine these fractions.
1. Identify a common denominator: The denominators of the given fractions are 9, 3, and 18. The least common multiple (LCM) of these numbers is 18.
2. Convert each fraction to have the common denominator:
- [tex]\( \frac{1}{9} \)[/tex] can be converted to its equivalent fraction with a denominator of 18:
[tex]\[
\frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18}
\][/tex]
- [tex]\( \frac{2}{3} \)[/tex] can be converted to its equivalent fraction with a denominator of 18:
[tex]\[
\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}
\][/tex]
- [tex]\( \frac{5}{18} \)[/tex] already has the common denominator, so it stays the same:
[tex]\[
\frac{5}{18}
\][/tex]
3. Add the fractions:
[tex]\[
\frac{2}{18} + \frac{12}{18} + \frac{5}{18} = \frac{2 + 12 + 5}{18} = \frac{19}{18}
\][/tex]
Therefore, the sum of [tex]\( \frac{1}{9} \)[/tex], [tex]\( \frac{2}{3} \)[/tex], and [tex]\( \frac{5}{18} \)[/tex] is [tex]\( \frac{19}{18} \)[/tex].
So, the correct answer is:
C. [tex]\( \frac{19}{18} \)[/tex]
