`3 (3)/(4)-1(1)/(2)=?`

Options

A. `2(1)/(2)`
B. `2(1)/(4)`
C. `1(1)/(2)`
D. `1(1)/(4)`

Answer

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

### Step 1: Convert the mixed numbers to improper fractions
- For \( 3 \frac{3}{4} \):
\[ 3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \]

- 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 with improper fractions
Now we can rewrite the original expression:
\[ 3 \frac{3}{4} - 1 \frac{1}{2} = \frac{15}{4} - \frac{3}{2} \]

### Step 3: Find a common denominator
The denominators are 4 and 2. The least common denominator (LCD) is 4. We need to convert \( \frac{3}{2} \) to have a denominator of 4:
\[ \frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4} \]

### Step 4: Subtract the fractions
Now we can subtract the two fractions:
\[ \frac{15}{4} - \frac{6}{4} = \frac{15 - 6}{4} = \frac{9}{4} \]

### Step 5: Convert the improper fraction back to a mixed number
To convert \( \frac{9}{4} \) back to a mixed number:
- Divide 9 by 4, which gives 2 with a remainder of 1.
- Thus, \( \frac{9}{4} = 2 \frac{1}{4} \).

### Final Answer
The final answer is:
\[ 2 \frac{1}{4} \]

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