To add the mixed number \(1\) and the fractions \(\frac{1}{2}\), \(\frac{1}{2}\), \(\frac{1}{4}\), and \(\frac{5}{8}\), follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \(1\) can be considered as \(\frac{1}{1}\) or just \(1\).

### Step 2: Convert all fractions to have a common denominator
The fractions involved are:
- \( \frac{1}{2} \)
- \( \frac{1}{2} \)
- \( \frac{1}{4} \)
- \( \frac{5}{8} \)

The least common denominator (LCD) for 2, 4, and 8 is 8. Let's convert each fraction:

- \( \frac{1}{2} = \frac{4}{8} \) 
- \( \frac{1}{2} = \frac{4}{8} \) 
- \( \frac{1}{4} = \frac{2}{8} \) 
- \( \frac{5}{8} \) stays the same

### Step 3: Add the fractions together
Now, add the fractions:
\[
1 + \frac{4}{8} + \frac{4}{8} + \frac{2}{8} + \frac{5}{8}
\]

Combine the fractions:
\[
\frac{4 + 4 + 2 + 5}{8} = \frac{15}{8}
\]

### Step 4: Convert the improper fraction to a mixed number
\(\frac{15}{8}\) is equal to \(1 \frac{7}{8}\).

### Step 5: Add the whole numbers together
Now add the whole number \(1\) to the mixed number \(1 \frac{7}{8}\):
\[
1 + 1 \frac{7}{8} = 2 \frac{7}{8}
\]

So, the sum is \(2 \frac{7}{8}\).

Would you like more details or have any questions?

Here are some related questions:
1. How do you simplify fractions after addition?
2. How do you find the least common denominator for multiple fractions?
3. What steps are involved in converting a mixed number to an improper fraction?
4. How do you subtract fractions from a whole number?
5. What is the difference between adding mixed numbers and adding fractions?

**Tip:** Always convert mixed numbers to improper fractions when performing addition or subtraction to make the calculations easier.

Learn how to add mixed numbers and fractions step-by-step with a detailed solution. This problem involves converting mixed numbers to improper fractions, finding a common denominator, adding fractions, and converting the result back to a mixed number. Suitable for students in Grades 4-6.

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