`4(1)/(2)-(5)/(8)+12(1)/(4)-3(1)/(8)=?`

Options

A. `12 (1)/(4)`
B. 13
C. `12 (3)/(4)`
D. 12

Answer

To solve the expression \( 4\frac{1}{2} - \frac{5}{8} + 12\frac{1}{4} - 3\frac{1}{8} \), we will follow these steps:

### Step 1: Convert mixed numbers to improper fractions
1. Convert \( 4\frac{1}{2} \) to an improper fraction:
\[ 4\frac{1}{2} = 4 \times 2 + 1 = 8 + 1 = \frac{9}{2} \]
2. Convert \( 12\frac{1}{4} \) to an improper fraction:
\[ 12\frac{1}{4} = 12 \times 4 + 1 = 48 + 1 = \frac{49}{4} \]

### Step 2: Rewrite the expression
Now, we can rewrite the expression using the improper fractions:
\[ \frac{9}{2} - \frac{5}{8} + \frac{49}{4} - \frac{3}{8} \]

### Step 3: Find a common denominator
The denominators are 2, 8, and 4. The least common multiple (LCM) of these denominators is 8. We will convert each fraction to have a denominator of 8:
1. Convert \( \frac{9}{2} \):
\[ \frac{9}{2} = \frac{9 \times 4}{2 \times 4} = \frac{36}{8} \]
2. \( \frac{5}{8} \) remains \( \frac{5}{8} \).
3. Convert \( \frac{49}{4} \):
\[ \frac{49}{4} = \frac{49 \times 2}{4 \times 2} = \frac{98}{8} \]
4. \( \frac{3}{8} \) remains \( \frac{3}{8} \).

### Step 4: Rewrite the expression with a common denominator
Now the expression becomes:
\[ \frac{36}{8} - \frac{5}{8} + \frac{98}{8} - \frac{3}{8} \]

### Step 5: Combine the fractions
Combine all the fractions:
\[ \frac{36 - 5 + 98 - 3}{8} = \frac{36 + 98 - 5 - 3}{8} = \frac{126}{8} \]

### Step 6: Simplify the fraction
Now simplify \( \frac{126}{8} \):
\[ \frac{126 \div 2}{8 \div 2} = \frac{63}{4} \]

### Step 7: Convert to mixed number (if necessary)
To convert \( \frac{63}{4} \) to a mixed number:
\[ 63 \div 4 = 15 \quad \text{(remainder 3)} \]
Thus, \( \frac{63}{4} = 15\frac{3}{4} \).

### Final Answer
The final answer is:
\[ 15\frac{3}{4} \]