To determine the sum of the fractions [tex]\(\frac{1}{26}\)[/tex] and [tex]\(\frac{1}{13}\)[/tex], we need to follow these steps:
1. Identify the Least Common Denominator (LCD):
The denominators of the fractions are 26 and 13. To find the LCD, we look for the smallest number that both 26 and 13 can divide into without leaving a remainder.
Since 26 is a multiple of 13 (i.e., [tex]\(26 = 13 \times 2\)[/tex]), the LCD of 26 and 13 is 26.
2. Convert the fractions to have the same denominator:
The first fraction is already [tex]\(\frac{1}{26}\)[/tex], so it does not need any modification. Now, we need to convert [tex]\(\frac{1}{13}\)[/tex] to a fraction with a denominator of 26.
To do this, multiply both the numerator and the denominator of [tex]\(\frac{1}{13}\)[/tex] by 2:
[tex]\[
\frac{1}{13} = \frac{1 \times 2}{13 \times 2} = \frac{2}{26}
\][/tex]
3. Add the fractions:
Now that both fractions have the same denominator, we can easily add them by adding their numerators and keeping the denominator the same:
[tex]\[
\frac{1}{26} + \frac{2}{26} = \frac{1 + 2}{26} = \frac{3}{26}
\][/tex]
4. Simplify the fraction:
The fraction [tex]\(\frac{3}{26}\)[/tex] is already in its simplest form since the greatest common divisor (GCD) of 3 and 26 is 1.
Thus, the sum of [tex]\(\frac{1}{26}\)[/tex] and [tex]\(\frac{1}{13}\)[/tex] is:
[tex]\[
\boxed{\frac{3}{26}}
\][/tex]
