To find the sum of the fractions [tex]\( \frac{1}{9} \)[/tex], [tex]\( \frac{2}{3} \)[/tex], and [tex]\( \frac{5}{18} \)[/tex], we can follow these steps:
1. Convert the fractions to a common denominator:
- The common denominator for [tex]\( \frac{1}{9} \)[/tex], [tex]\( \frac{2}{3} \)[/tex], and [tex]\( \frac{5}{18} \)[/tex] can be determined by finding the least common multiple (LCM) of the denominators 9, 3, and 18. The LCM of 9, 3, and 18 is 18.
2. Express each fraction with the common denominator of 18:
- [tex]\( \frac{1}{9} = \frac{2}{18} \)[/tex] (multiplying numerator and denominator by 2)
- [tex]\( \frac{2}{3} = \frac{12}{18} \)[/tex] (multiplying numerator and denominator by 6)
- [tex]\( \frac{5}{18} \)[/tex] already has the denominator of 18.
3. Add the fractions:
[tex]\[
\frac{2}{18} + \frac{12}{18} + \frac{5}{18} = \frac{2 + 12 + 5}{18} = \frac{19}{18}
\][/tex]
4. Simplify the result if necessary:
- In this case, [tex]\( \frac{19}{18} \)[/tex] is already in its simplest form.
Thus, 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].
Therefore, the best answer is:
C. [tex]\( \frac{19}{18} \)[/tex]
