What will come in place of question mark (?) .
`1/4 + 3 1/2 + 1 1/4 + 1 1/2 = ?`

Options

A. `2 1/2 `
B. `5//21`
C. 3
D. 4

Answer

To solve the equation \( \frac{1}{4} + 3 \frac{1}{2} + 1 \frac{1}{4} + 1 \frac{1}{2} = ? \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. For \( 3 \frac{1}{2} \):
\[ 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \]

2. For \( 1 \frac{1}{4} \):
\[ 1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4} \]

3. For \( 1 \frac{1}{2} \):
\[ 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \]

### Step 2: Rewrite the Expression
Now we can rewrite the entire expression using improper fractions:
\[ \frac{1}{4} + \frac{7}{2} + \frac{5}{4} + \frac{3}{2} \]

### Step 3: Find a Common Denominator
The denominators are 4 and 2. The least common multiple (LCM) of 4 and 2 is 4. We will convert all fractions to have a denominator of 4.

1. \( \frac{1}{4} \) remains \( \frac{1}{4} \).
2. Convert \( \frac{7}{2} \) to a denominator of 4:
\[ \frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4} \]
3. \( \frac{5}{4} \) remains \( \frac{5}{4} \).
4. Convert \( \frac{3}{2} \) to a denominator of 4:
\[ \frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4} \]

### Step 4: Add the Fractions
Now we can add all the fractions together:
\[ \frac{1}{4} + \frac{14}{4} + \frac{5}{4} + \frac{6}{4} = \frac{1 + 14 + 5 + 6}{4} = \frac{26}{4} \]

### Step 5: Simplify the Fraction
Now we simplify \( \frac{26}{4} \):
\[ \frac{26 \div 2}{4 \div 2} = \frac{13}{2} \]

### Step 6: Convert to Mixed Number
To convert \( \frac{13}{2} \) to a mixed number:
\[ 13 \div 2 = 6 \quad \text{(remainder 1)} \]
So, \( \frac{13}{2} = 6 \frac{1}{2} \).

### Final Answer
Thus, the final answer is:
\[ \boxed{6 \frac{1}{2}} \]