9. $$ 3 \frac{1}{2}+2 \frac{3}{4}+1 \frac{5}{8} $$

Question

UpStudy AI · Accepted Answer

To solve the expression $$ 3 \frac{1}{2} + 2 \frac{3}{4} + 1 \frac{5}{8} $$, follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, convert each mixed number to an improper fraction.

1. **$$ 3 \frac{1}{2} $$:**
   $$
   3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}
   $$

2. **$$ 2 \frac{3}{4} $$:**
   $$
   2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}
   $$

3. **$$ 1 \frac{5}{8} $$:**
   $$
   1 \frac{5}{8} = \frac{1 \times 8 + 5}{8} = \frac{13}{8}
   $$

### Step 2: Find a Common Denominator
The denominators are 2, 4, and 8. The least common denominator (LCD) is **8**.

Convert each fraction to have the denominator of 8:

1. **$$ \frac{7}{2} $$:**
   $$
   \frac{7}{2} = \frac{7 \times 4}{2 \times 4} = \frac{28}{8}
   $$

2. **$$ \frac{11}{4} $$:**
   $$
   \frac{11}{4} = \frac{11 \times 2}{4 \times 2} = \frac{22}{8}
   $$

3. **$$ \frac{13}{8} $$:**
   $$
   \frac{13}{8} \text{ remains the same.}
   $$

### Step 3: Add the Fractions
Now, add all the fractions together:

$$
\frac{28}{8} + \frac{22}{8} + \frac{13}{8} = \frac{28 + 22 + 13}{8} = \frac{63}{8}
$$

### Step 4: Convert Back to a Mixed Number
Finally, convert the improper fraction back to a mixed number:

$$
\frac{63}{8} = 7 \frac{7}{8}
$$

### **Answer:**
$$
3 \frac{1}{2} + 2 \frac{3}{4} + 1 \frac{5}{8} = 7 \frac{7}{8}
$$
$$ 7 \frac{7}{8} $$

9. \( 3 \frac{1}{2}+2 \frac{3}{4}+1 \frac{5}{8} \)