Simplify: 2/8 + 5/12 and can you show the work

To simplify \( \frac{2}{8} + \frac{5}{12} \), let's follow these steps:

### Step 1: Simplify each fraction, if possible
- \( \frac{2}{8} \) simplifies to \( \frac{1}{4} \), because both 2 and 8 can be divided by 2.
- \( \frac{5}{12} \) is already in its simplest form.

So now the expression is:
\[
\frac{1}{4} + \frac{5}{12}
\]

### Step 2: Find a common denominator
To add fractions, we need a common denominator. The least common denominator (LCD) of 4 and 12 is 12.

- To convert \( \frac{1}{4} \) to a fraction with denominator 12, multiply both the numerator and denominator by 3:
  \[
  \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
  \]
- \( \frac{5}{12} \) already has denominator 12, so it stays the same.

### Step 3: Add the fractions
Now that both fractions have the same denominator, we can add them:
\[
\frac{3}{12} + \frac{5}{12} = \frac{3 + 5}{12} = \frac{8}{12}
\]

### Step 4: Simplify the result
Finally, simplify \( \frac{8}{12} \) by dividing both the numerator and denominator by 4:
\[
\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}
\]

### Final Answer:
\[
\frac{2}{8} + \frac{5}{12} = \frac{2}{3}
\]

Let me know if you'd like more details or have any questions!

Here are 5 related questions to consider:
1. What is the least common denominator (LCD) of other pairs of fractions, like \( \frac{3}{5} + \frac{2}{7} \)?
2. How do you subtract fractions with different denominators?
3. What are the steps for multiplying two fractions together?
4. How can you simplify a complex fraction like \( \frac{5/6}{2/3} \)?
5. How do you convert improper fractions to mixed numbers?

**Tip**: Always simplify fractions as early as possible—it makes the calculations easier!

Learn how to simplify and add fractions like 2/8 + 5/12 with detailed steps. This problem covers important concepts such as finding the least common denominator and simplifying fractions. Suitable for students in Grades 4-6.

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