To determine the sum of [tex]\(\frac{1}{9}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], and [tex]\(\frac{5}{18}\)[/tex], we need to add these fractions together step-by-step. Here's a detailed explanation of the process:
1. Find a common denominator:
- The denominators of the fractions are 9, 3, and 18. The least common multiple (LCM) of these numbers is 18.
2. Convert each fraction to an equivalent fraction with the common denominator of 18:
- [tex]\(\frac{1}{9}\)[/tex] can be converted to [tex]\(\frac{2}{18}\)[/tex] because [tex]\(\frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18}\)[/tex].
- [tex]\(\frac{2}{3}\)[/tex] can be converted to [tex]\(\frac{12}{18}\)[/tex] because [tex]\(\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}\)[/tex].
- [tex]\(\frac{5}{18}\)[/tex] is already with the denominator 18.
3. Add the fractions:
- Now, sum the numerators while keeping the common denominator:
[tex]\[
\frac{2}{18} + \frac{12}{18} + \frac{5}{18} = \frac{2 + 12 + 5}{18} = \frac{19}{18}
\][/tex]
4. Simplify the fraction if possible:
- Since [tex]\(\frac{19}{18}\)[/tex] is already in simplest form, there is no need for further simplification.
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].
The correct answer is:
B. [tex]\(\frac{19}{18}\)[/tex]
