To add the fractions [tex]\(\frac{2}{11}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex], follow these steps:
1. Find a common denominator: The denominators are 11 and 10. The least common multiple (LCM) of these two numbers is 110.
2. Convert fractions to the common denominator:
- For [tex]\(\frac{2}{11}\)[/tex]:
[tex]\[
\frac{2}{11} = \frac{2 \times 10}{11 \times 10} = \frac{20}{110}
\][/tex]
- For [tex]\(\frac{1}{10}\)[/tex]:
[tex]\[
\frac{1}{10} = \frac{1 \times 11}{10 \times 11} = \frac{11}{110}
\][/tex]
3. Add the fractions:
- With the common denominator of 110:
[tex]\[
\frac{20}{110} + \frac{11}{110} = \frac{20 + 11}{110} = \frac{31}{110}
\][/tex]
4. Simplify the fraction:
- The numerator is 31, and the denominator is 110. The greatest common divisor (GCD) of these two numbers is 1, so the fraction is already in its simplest form.
Therefore, the sum of [tex]\(\frac{2}{11}\)[/tex] and [tex]\(\frac{1}{10}\)[/tex] is:
[tex]\[
\boxed{\frac{31}{110}}
\][/tex]
