To add the fractions $\frac{5}{6} + \frac{3}{4}$, we need a common denominator.

Step 1: Find the least common denominator (LCD)

The denominators are 6 and 4. The least common denominator of 6 and 4 is 12.

Step 2: Convert each fraction to have the denominator of 12

• $\frac{5}{6}$ becomes $\frac{10}{12}$ (multiply both numerator and denominator by 2).
• $\frac{3}{4}$ becomes $\frac{9}{12}$ (multiply both numerator and denominator by 3).

Step 3: Add the fractions

Now that both fractions have the same denominator, add the numerators: $\frac{10}{12} + \frac{9}{12} = \frac{19}{12}$

Final Answer:

$\frac{19}{12}$ This is an improper fraction, and it can also be written as a mixed number: $1 \frac{7}{12}$

Would you like further clarification or details? Here are some related questions:

1. How do you simplify fractions like $\frac{19}{12}$?
2. What is the process for finding the least common denominator for fractions with different denominators?
3. How do you convert improper fractions to mixed numbers?
4. What happens if the fractions have the same denominator already?
5. How would you subtract fractions with different denominators?

Tip: When adding or subtracting fractions, always make sure to find the least common denominator to simplify the process!