Let's solve the given fraction addition problem:

$\frac{2}{21} + \frac{3}{14}$

Step 1: Find the least common denominator (LCD)

The denominators are 21 and 14. The least common denominator of 21 and 14 is their least common multiple (LCM).

• Prime factorization of 21: $21 = 3 \times 7$
• Prime factorization of 14: $14 = 2 \times 7$

The LCM is $42$.

Step 2: Convert each fraction to have the LCD

Now, we will express both fractions with a denominator of 42.

$\frac{2}{21} = \frac{2 \times 2}{21 \times 2} = \frac{4}{42}$ $\frac{3}{14} = \frac{3 \times 3}{14 \times 3} = \frac{9}{42}$

Step 3: Add the fractions

Now that the fractions have the same denominator, we can add them:

$\frac{4}{42} + \frac{9}{42} = \frac{4 + 9}{42} = \frac{13}{42}$

Step 4: Simplify the result

Since 13 is a prime number and does not divide 42, the fraction is already in its simplest form.

Thus, the answer is:

$\frac{13}{42}$

Would you like more details or have any questions? Here are five related problems for practice:

1. Add $\frac{5}{6} + \frac{3}{4}$ and simplify.
2. Subtract $\frac{7}{15} - \frac{2}{5}$ and simplify.
3. Add $\frac{1}{9} + \frac{2}{3}$ and simplify.
4. Subtract $\frac{4}{7} - \frac{1}{14}$ and simplify.
5. Add $\frac{5}{12} + \frac{7}{18}$ and simplify.

Tip: When adding fractions, always find the least common denominator (LCD) before performing the addition!