Solve the Fraction Addition: 1/7 + 1/8 Step-by-Step

To solve this problem, we'll follow these steps:

• Step 1: Identify the common denominator.
• Step 2: Convert each fraction to have this common denominator.
• Step 3: Add the converted fractions.
• Step 4: Simplify the result.

Now, let's work through each step:
Step 1: The denominators are 7 and 8. Their product is $7 \times 8 = 56$. So, the common denominator is 56.
Step 2: Convert $\frac{1}{7}$ to have a denominator of 56 by multiplying numerator and denominator by 8: $\frac{1 \times 8}{7 \times 8} = \frac{8}{56}$.
Convert $\frac{1}{8}$ to have a denominator of 56 by multiplying numerator and denominator by 7: $\frac{1 \times 7}{8 \times 7} = \frac{7}{56}$.
Step 3: Add these equivalent fractions: $\frac{8}{56} + \frac{7}{56} = \frac{8 + 7}{56} = \frac{15}{56}$.
Step 4: The fraction $\frac{15}{56}$ is already in its simplest form.
Therefore, the solution to the problem is $\frac{15}{56}$.