To solve the problem of adding the two numbers $\frac{6 \frac{7}{8}} + \frac{3}{2}$, we can follow these steps:

Step 1: Convert the mixed number into an improper fraction.

The first number is $6 \frac{7}{8}$. To convert this to an improper fraction: $6 \frac{7}{8} = \frac{6 \times 8 + 7}{8} = \frac{48 + 7}{8} = \frac{55}{8}.$

Step 2: Add the improper fractions.

Now we need to add $\frac{55}{8}$ and $\frac{3}{2}$.

First, find a common denominator. The least common denominator (LCD) of 8 and 2 is 8. So we convert $\frac{3}{2}$ into a fraction with denominator 8: $\frac{3}{2} = \frac{3 \times 4}{2 \times 4} = \frac{12}{8}.$

Now we can add the two fractions: $\frac{55}{8} + \frac{12}{8} = \frac{55 + 12}{8} = \frac{67}{8}.$

Step 3: Simplify the result.

The result $\frac{67}{8}$ is an improper fraction, which can be converted into a mixed number. Divide 67 by 8: $67 \div 8 = 8 \text{ remainder } 3.$ So, $\frac{67}{8} = 8 \frac{3}{8}.$

Final Answer:

The sum of $6 \frac{7}{8} + \frac{3}{2}$ is $8 \frac{3}{8}$.

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:

1. How do you convert mixed numbers into improper fractions?
2. What is the least common denominator and why is it important?
3. How do you simplify improper fractions to mixed numbers?
4. What steps do you follow when adding two fractions with different denominators?
5. How would this problem change if the numbers were negative?

Tip: When adding mixed numbers, always convert them into improper fractions first for easier calculations!