Which of the following options is incorrect?

Options

A. `3/4gt2/3`
B. `4/5gt1/3`
C. `9/7gt1`
D. `1/2lt1/4`

Answer

To determine which of the given fractions is incorrect, we will compare each pair of fractions step by step.

### Step 1: Compare 3/4 and 2/3
1. Find a common denominator for 3/4 and 2/3. The least common multiple (LCM) of 4 and 3 is 12.
2. Convert 3/4 to a fraction with a denominator of 12:
\[ 3/4 = (3 \times 3) / (4 \times 3) = 9/12 \]
3. Convert 2/3 to a fraction with a denominator of 12:
\[ 2/3 = (2 \times 4) / (3 \times 4) = 8/12 \]
4. Compare 9/12 and 8/12. Since 9/12 > 8/12, this comparison is correct.

### Step 2: Compare 4/5 and 1/3
1. Find a common denominator for 4/5 and 1/3. The LCM of 5 and 3 is 15.
2. Convert 4/5 to a fraction with a denominator of 15:
\[ 4/5 = (4 \times 3) / (5 \times 3) = 12/15 \]
3. Convert 1/3 to a fraction with a denominator of 15:
\[ 1/3 = (1 \times 5) / (3 \times 5) = 5/15 \]
4. Compare 12/15 and 5/15. Since 12/15 > 5/15, this comparison is correct.

### Step 3: Compare 9/7 and 1
1. Convert 1 to a fraction with a denominator of 7:
\[ 1 = 7/7 \]
2. Compare 9/7 and 7/7. Since 9/7 > 7/7, this comparison is correct.

### Step 4: Compare 1/2 and 1/4
1. Find a common denominator for 1/2 and 1/4. The LCM of 2 and 4 is 4.
2. Convert 1/2 to a fraction with a denominator of 4:
\[ 1/2 = (1 \times 2) / (2 \times 2) = 2/4 \]
3. Compare 2/4 and 1/4. Since 2/4 > 1/4, this comparison is correct.

### Conclusion
After comparing all pairs of fractions, we find that all comparisons are correct. However, the question asks us to identify the incorrect option. Since all comparisons are accurate, we conclude that there is no incorrect option among the provided fractions.