To solve the problem of finding the sum of [tex]\(\frac{1}{9}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], and [tex]\(\frac{5}{18}\)[/tex], we need to follow these steps:
Step 1: Express all fractions with a common denominator.
- The denominators we have are 9, 3, and 18. The least common denominator (LCD) for these numbers is 18.
Step 2: Convert each fraction to have the LCD as the new denominator.
- Convert [tex]\(\frac{1}{9}\)[/tex] to a fraction with a denominator of 18:
[tex]\[
\frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18}
\][/tex]
- Convert [tex]\(\frac{2}{3}\)[/tex] to a 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 remains the same:
[tex]\[
\frac{5}{18} = \frac{5}{18}
\][/tex]
Step 3: Add the fractions together.
- Now add the fractions with the common denominator:
[tex]\[
\frac{2}{18} + \frac{12}{18} + \frac{5}{18} = \frac{2 + 12 + 5}{18} = \frac{19}{18}
\][/tex]
Step 4: Check if the fraction can be simplified.
- [tex]\(\frac{19}{18}\)[/tex] is already in its simplest form because 19 and 18 have no common factors 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]\(\frac{19}{18}\)[/tex].
The best answer is:
A. [tex]\(\frac{19}{18}\)[/tex]
