Certainly! Let's solve the problem step-by-step.
We need to find the sum of [tex]\(\frac{1}{6}\)[/tex] and [tex]\(\frac{1}{7}\)[/tex].
### Step 1: Find a common denominator
To add fractions, we need to find a common denominator. The denominators are 6 and 7. The least common multiple (LCM) of 6 and 7 is 42.
### Step 2: Convert each fraction to have the common denominator
Next, we convert each fraction so they both have the denominator of 42.
- For [tex]\(\frac{1}{6}\)[/tex]:
[tex]\(\frac{1}{6} = \frac{1 \times 7}{6 \times 7} = \frac{7}{42}\)[/tex]
- For [tex]\(\frac{1}{7}\)[/tex]:
[tex]\(\frac{1}{7} = \frac{1 \times 6}{7 \times 6} = \frac{6}{42}\)[/tex]
### Step 3: Add the fractions
Now, we add the fractions with the common denominator:
[tex]\[
\frac{7}{42} + \frac{6}{42} = \frac{7 + 6}{42} = \frac{13}{42}
\][/tex]
### Step 4: Simplify if possible
The fraction [tex]\(\frac{13}{42}\)[/tex] is already in its simplest form, as 13 is a prime number and does not divide evenly into 42.
### Step 5: Identify the correct answer
Among the given choices:
A. [tex]\(\frac{15}{42}\)[/tex]
B. [tex]\(\frac{13}{42}\)[/tex]
C. [tex]\(\frac{2}{13}\)[/tex]
D. [tex]\(\frac{1}{42}\)[/tex]
The correct answer is:
[tex]\[
\boxed{2: \frac{13}{42}}
\][/tex]
