`{:("ColumnA"," ","Column B"),(2//3 - 3//4,,3//4 - 4//5):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To compare the values in Column A and Column B, we will simplify both expressions step by step.

### Step 1: Simplify Column A
Column A is given as \( \frac{2}{3} - \frac{3}{4} \).

To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12.

Convert each fraction to have a denominator of 12:
- For \( \frac{2}{3} \):
\[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]
- For \( \frac{3}{4} \):
\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]

Now, we can subtract:
\[ \frac{2}{3} - \frac{3}{4} = \frac{8}{12} - \frac{9}{12} = \frac{8 - 9}{12} = \frac{-1}{12} \]

### Step 2: Simplify Column B
Column B is given as \( \frac{3}{4} - \frac{4}{5} \).

Again, we need a common denominator. The LCM of 4 and 5 is 20.

Convert each fraction to have a denominator of 20:
- For \( \frac{3}{4} \):
\[ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \]
- For \( \frac{4}{5} \):
\[ \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20} \]

Now, we can subtract:
\[ \frac{3}{4} - \frac{4}{5} = \frac{15}{20} - \frac{16}{20} = \frac{15 - 16}{20} = \frac{-1}{20} \]

### Step 3: Compare Column A and Column B
Now we have:
- Column A: \( \frac{-1}{12} \)
- Column B: \( \frac{-1}{20} \)

Both fractions are negative. To compare them, we look at their denominators. The fraction with the smaller denominator is greater in value when both are negative.

Since:
- The denominator of Column A is 12
- The denominator of Column B is 20

We know that:
\[ \frac{-1}{12} > \frac{-1}{20} \]

Thus, Column A is greater than Column B.

### Conclusion
Column A is greater than Column B.