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!