Compare and fill the box with >, < or =
`(3.45 - 6.75 + 2.05)/(0.29 + 0.426 + 0.6) ? (0.175 + 0.7 - 0.45)/(5.95 - 8.25 + 2.40)`

Options

A. `lt`
B. =
C. `gt`
D. Can't be determined

Answer

To solve the given comparison problem step by step, we will evaluate both sides of the inequality separately and then compare the results.

### Step 1: Evaluate the Left-Hand Side (LHS)
The LHS is given as:
\[ \frac{(3.45 - 6.75 + 2.05)}{(0.29 + 0.426 + 0.6)} \]

**Calculating the numerator:**
1. First, calculate \(3.45 - 6.75\):
\[ 3.45 - 6.75 = -3.30 \]
2. Next, add \(2.05\):
\[ -3.30 + 2.05 = -1.25 \]

So, the numerator is \(-1.25\).

**Calculating the denominator:**
1. First, add \(0.29 + 0.426\):
\[ 0.29 + 0.426 = 0.716 \]
2. Next, add \(0.716 + 0.6\):
\[ 0.716 + 0.6 = 1.316 \]

So, the denominator is \(1.316\).

**Final calculation for LHS:**
\[ \text{LHS} = \frac{-1.25}{1.316} \approx -0.950 \]

### Step 2: Evaluate the Right-Hand Side (RHS)
The RHS is given as:
\[ \frac{(0.175 + 0.7 - 0.45)}{(5.95 - 8.25 + 2.40)} \]

**Calculating the numerator:**
1. First, add \(0.175 + 0.7\):
\[ 0.175 + 0.7 = 0.875 \]
2. Next, subtract \(0.45\):
\[ 0.875 - 0.45 = 0.425 \]

So, the numerator is \(0.425\).

**Calculating the denominator:**
1. First, calculate \(5.95 - 8.25\):
\[ 5.95 - 8.25 = -2.30 \]
2. Next, add \(2.40\):
\[ -2.30 + 2.40 = 0.10 \]

So, the denominator is \(0.10\).

**Final calculation for RHS:**
\[ \text{RHS} = \frac{0.425}{0.10} = 4.25 \]

### Step 3: Compare LHS and RHS
Now we compare the two results:
- LHS \(\approx -0.950\)
- RHS \(= 4.25\)

Since \(-0.950 < 4.25\), we can conclude that:
\[ \text{LHS} < \text{RHS} \]

### Final Answer
The comparison can be filled as:
\[ (3.45 - 6.75 + 2.05)/(0.29 + 0.426 + 0.6) < (0.175 + 0.7 - 0.45)/(5.95 - 8.25 + 2.40) \]