[`3 1/4`-`2 1/3`]

Options

A. `1 1/12`
B. `1/12`
C. `1 1/11`
D. `11/12`

Answer

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

### Step 1: Convert the mixed numbers to improper fractions
First, we need to convert both mixed numbers into improper fractions.

For \(3 \frac{1}{4}\):
- Multiply the whole number (3) by the denominator (4): \(3 \times 4 = 12\)
- Add the numerator (1): \(12 + 1 = 13\)
- So, \(3 \frac{1}{4} = \frac{13}{4}\)

For \(2 \frac{1}{3}\):
- Multiply the whole number (2) by the denominator (3): \(2 \times 3 = 6\)
- Add the numerator (1): \(6 + 1 = 7\)
- So, \(2 \frac{1}{3} = \frac{7}{3}\)

### Step 2: Find the least common multiple (LCM) of the denominators
The denominators are 4 and 3. The LCM of 4 and 3 is 12.

### Step 3: Convert the fractions to have a common denominator
Now we need to convert both fractions to have the common denominator of 12.

For \(\frac{13}{4}\):
- Multiply both the numerator and denominator by 3:
\[ \frac{13 \times 3}{4 \times 3} = \frac{39}{12} \]

For \(\frac{7}{3}\):
- Multiply both the numerator and denominator by 4:
\[ \frac{7 \times 4}{3 \times 4} = \frac{28}{12} \]

### Step 4: Subtract the fractions
Now we can subtract the two fractions:
\[ \frac{39}{12} - \frac{28}{12} = \frac{39 - 28}{12} = \frac{11}{12} \]

### Final Answer
Thus, the answer to \(3 \frac{1}{4} - 2 \frac{1}{3}\) is \(\frac{11}{12}\).

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