To find the sum of the fractions [tex]\(\frac{1}{9}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], and [tex]\(\frac{5}{18}\)[/tex], follow these steps:
### Step 1: Find a common denominator
The denominators of the given fractions are 9, 3, and 18. To add the fractions easily, we need a common denominator that all the original denominators can divide into.
The least common multiple (LCM) of 9, 3, and 18 is 18.
### Step 2: Convert each fraction to have the common denominator
Convert each fraction so that they all have a denominator of 18:
- [tex]\(\frac{1}{9}\)[/tex] converts to [tex]\(\frac{1 \times 2}{9 \times 2} = \frac{2}{18}\)[/tex]
- [tex]\(\frac{2}{3}\)[/tex] converts to [tex]\(\frac{2 \times 6}{3 \times 6} = \frac{12}{18}\)[/tex]
- [tex]\(\frac{5}{18}\)[/tex] is already in terms of 18, so it remains [tex]\(\frac{5}{18}\)[/tex]
### Step 3: Add the numerators
Now that the fractions all have the same denominator, add their numerators:
[tex]\[
\frac{2}{18} + \frac{12}{18} + \frac{5}{18} = \frac{2 + 12 + 5}{18} = \frac{19}{18}
\][/tex]
### Step 4: Simplify the result (if necessary)
The fraction [tex]\(\frac{19}{18}\)[/tex] is already in its simplest form because 19 and 18 have no common divisors other than 1.
Therefore, the sum of [tex]\(\frac{1}{9}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], and [tex]\(\frac{5}{18}\)[/tex] is:
[tex]\[
\boxed{\frac{19}{18}}
\][/tex]
Thus, the best answer is:
B. [tex]\(\frac{19}{18}\)[/tex]
