To determine the sum of the fractions [tex]\( \frac{1}{9} \)[/tex], [tex]\( \frac{2}{3} \)[/tex], and [tex]\( \frac{5}{18} \)[/tex], follow these steps:
1. Identify a common denominator for the fractions. The denominators we have are 9, 3, and 18. The least common multiple (LCM) of these denominators is 18.
2. Convert each fraction to an equivalent fraction with a denominator of 18:
- For [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[
\frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18}
\][/tex]
- For [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[
\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}
\][/tex]
- [tex]\( \frac{5}{18} \)[/tex] already has the denominator of 18.
So, we have:
[tex]\[
\frac{2}{18}, \frac{12}{18}, \text{ and } \frac{5}{18}
\][/tex]
3. Add these fractions together, now that they have the same denominator:
[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].
The best answer is:
B. [tex]\( \frac{19}{18} \)[/tex]
