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

Options

A. `1 1/2`
B. `1 1/4`
C. `1/4`
D. none of these

Answer

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

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

For \(3 \frac{3}{4}\):
- Multiply the whole number (3) by the denominator (4): \(3 \times 4 = 12\)
- Add the numerator (3): \(12 + 3 = 15\)
- So, \(3 \frac{3}{4} = \frac{15}{4}\)

For \(2 \frac{1}{4}\):
- Multiply the whole number (2) by the denominator (4): \(2 \times 4 = 8\)
- Add the numerator (1): \(8 + 1 = 9\)
- So, \(2 \frac{1}{4} = \frac{9}{4}\)

### Step 2: Subtract the Improper Fractions
Now we can subtract the two improper fractions:
\[ \frac{15}{4} - \frac{9}{4} \]

Since the denominators are the same, we can subtract the numerators:
\[ \frac{15 - 9}{4} = \frac{6}{4} \]

### Step 3: Simplify the Resulting Fraction
Now we need to simplify \(\frac{6}{4}\):
- Divide both the numerator and the denominator by their greatest common divisor (2):
\[ \frac{6 \div 2}{4 \div 2} = \frac{3}{2} \]

### Step 4: Convert Back to a Mixed Number (if necessary)
To convert \(\frac{3}{2}\) back to a mixed number:
- Divide 3 by 2, which gives 1 with a remainder of 1.
- So, \(\frac{3}{2} = 1 \frac{1}{2}\)

### Final Answer
Thus, the answer to \(3 \frac{3}{4} - 2 \frac{1}{4}\) is:
\[ 1 \frac{1}{2} \text{ or } 1.5 \]

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