What is the value of `5 (1)/(2) + 7 (1)/(2) + 11 (1)/(2)` ?

Options

A. `(49)/(2)`
B. `(25)/(2)`
C. `(29)/(2)`
D. `(27)/(2)`

Answer

To solve the expression \( 5 \frac{1}{2} + 7 \frac{1}{2} + 11 \frac{1}{2} \), we can follow these steps:

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

- For \( 5 \frac{1}{2} \):
\[ 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \]

- For \( 7 \frac{1}{2} \):
\[ 7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2} \]

- For \( 11 \frac{1}{2} \):
\[ 11 \frac{1}{2} = 11 + \frac{1}{2} = \frac{11 \times 2 + 1}{2} = \frac{22 + 1}{2} = \frac{23}{2} \]

### Step 2: Add the Improper Fractions
Now, we add the three improper fractions together:
\[ \frac{11}{2} + \frac{15}{2} + \frac{23}{2} \]

Since they all have the same denominator, we can add the numerators:
\[ = \frac{11 + 15 + 23}{2} = \frac{49}{2} \]

### Step 3: Convert Back to Mixed Number (if needed)
To convert \( \frac{49}{2} \) back to a mixed number:
- Divide 49 by 2:
\[ 49 \div 2 = 24 \quad \text{(whole number)} \]
- The remainder is:
\[ 49 - (24 \times 2) = 49 - 48 = 1 \]
So, \( \frac{49}{2} = 24 \frac{1}{2} \).

### Final Answer
Thus, the value of \( 5 \frac{1}{2} + 7 \frac{1}{2} + 11 \frac{1}{2} \) is:
\[ \frac{49}{2} \quad \text{or} \quad 24 \frac{1}{2} \]

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