To add the fractions $\frac{1}{12} + \frac{2}{7}$, follow these steps:

Step 1: Find the Least Common Denominator (LCD)

The denominators are 12 and 7. Their least common multiple (LCM) is:

$\text{LCM}(12,7) = 12 \times 7 = 84$

Step 2: Convert Each Fraction to Have the LCD

Rewrite each fraction with a denominator of 84:

$\frac{1}{12} = \frac{1 \times 7}{12 \times 7} = \frac{7}{84}$

$\frac{2}{7} = \frac{2 \times 12}{7 \times 12} = \frac{24}{84}$

Step 3: Add the Fractions

Now, add the numerators:

$\frac{7}{84} + \frac{24}{84} = \frac{7 + 24}{84} = \frac{31}{84}$

Final Answer:

$\frac{31}{84}$

This fraction is already in its simplest form.

Would you like further details or explanations?

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Related Questions:

1. How do you find the least common denominator of two fractions?
2. What are some strategies to simplify fractions?
3. How do you convert improper fractions to mixed numbers?
4. How do you subtract fractions with different denominators?
5. Can you explain the difference between proper and improper fractions?

Tip:

When adding fractions, always check if the final answer can be simplified by dividing both numerator and denominator by their greatest common factor (GCF).