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:
1. Convert each fraction to have a common denominator:
First, identify a common denominator. The denominators here are 9, 3, and 18. The least common multiple (LCM) of these numbers is 18.
2. Convert each fraction to the common 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]
- For [tex]\(\frac{5}{18}\)[/tex]:
[tex]\[
\frac{5}{18} \text{ (already in terms of 18, so it stays the same)}
\][/tex]
3. Add the fractions together:
Now that all fractions have the same denominator, you can add the numerators together:
[tex]\[
\frac{2}{18} + \frac{12}{18} + \frac{5}{18} = \frac{2 + 12 + 5}{18} = \frac{19}{18}
\][/tex]
4. Simplify the fraction:
The fraction [tex]\(\frac{19}{18}\)[/tex] is already in its simplest form as 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 correct choice is:
A. [tex]\(\frac{19}{18}\)[/tex]
