Sure, let's go through the steps to add and simplify the fractions [tex]\(\frac{1}{7}\)[/tex] and [tex]\(\frac{1}{35}\)[/tex].
1. Find a common denominator:
- The denominators are 7 and 35.
- The least common multiple (LCM) of 7 and 35 is 35.
2. Rewrite each fraction with the common denominator:
- For [tex]\(\frac{1}{7}\)[/tex], we need to multiply both the numerator and the denominator by 5 to get the common denominator of 35:
[tex]\[
\frac{1}{7} = \frac{1 \times 5}{7 \times 5} = \frac{5}{35}
\][/tex]
3. Add the fractions:
- Now we have [tex]\(\frac{5}{35}\)[/tex] and [tex]\(\frac{1}{35}\)[/tex].
- Add these fractions by simply adding their numerators, keeping the common denominator:
[tex]\[
\frac{5}{35} + \frac{1}{35} = \frac{5 + 1}{35} = \frac{6}{35}
\][/tex]
4. Simplify the result:
- The fraction [tex]\(\frac{6}{35}\)[/tex] is already in its simplest form since the greatest common divisor (GCD) of 6 and 35 is 1.
So, [tex]\(\frac{1}{7} + \frac{1}{35} = \frac{6}{35}\)[/tex], and it is already in its simplest form. The final result is [tex]\(\frac{6}{35}\)[/tex].
