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The question asks you to add and simplify the following two fractions:

\[
\frac{2}{66} + \frac{2}{55}
\]

### Step 1: Find the Least Common Denominator (LCD)
The denominators are 66 and 55. To add these fractions, we first need to find the least common denominator (LCD). To do this, we find the least common multiple (LCM) of 66 and 55.

- The prime factors of 66 are \(2 \times 3 \times 11\).
- The prime factors of 55 are \(5 \times 11\).

The LCM is found by taking the highest powers of all the prime factors involved:

\[
LCM(66, 55) = 2 \times 3 \times 5 \times 11 = 330
\]

So, the least common denominator is 330.

### Step 2: Convert Both Fractions to Have the Same Denominator
Now, we convert both fractions to have the denominator of 330:

\[
\frac{2}{66} = \frac{2 \times 5}{66 \times 5} = \frac{10}{330}
\]
\[
\frac{2}{55} = \frac{2 \times 6}{55 \times 6} = \frac{12}{330}
\]

### Step 3: Add the Fractions
Now that both fractions have the same denominator, we can add them:

\[
\frac{10}{330} + \frac{12}{330} = \frac{10 + 12}{330} = \frac{22}{330}
\]

### Step 4: Simplify the Fraction
Finally, we simplify the fraction \(\frac{22}{330}\). The greatest common divisor (GCD) of 22 and 330 is 22, so we divide both the numerator and denominator by 22:

\[
\frac{22 \div 22}{330 \div 22} = \frac{1}{15}
\]

### Final Answer:
\[
\frac{2}{66} + \frac{2}{55} = \frac{1}{15}
\]

Would you like a further explanation of any step, or do you have any other questions?

Here are 5 related questions:
1. How do you find the least common denominator of more complex fractions?
2. What are some methods to simplify fractions quickly?
3. Can you explain how prime factorization helps in finding the LCM?
4. How would the solution change if the fractions had variables?
5. How do you subtract fractions with different denominators?

**Tip:** Always simplify fractions as the last step after adding or subtracting them.

Learn how to add and simplify fractions using the problem 2/66 + 2/55. This step-by-step solution demonstrates finding the least common denominator (LCD), adding fractions, and simplifying the result. Suitable for students in Grades 5-7.

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