Insert `ltorgt` in the box.
`3(41)/(45)square3(10)/(45)`

Answer

To solve the problem of comparing the two mixed numbers \(3 \frac{41}{45}\) and \(3 \frac{10}{45}\), we will follow these steps:

### Step 1: Convert the mixed numbers to improper fractions.
To convert a mixed number to an improper fraction, we use the formula:
\[ \text{Improper Fraction} = ( \text{Whole Number} \times \text{Denominator} + \text{Numerator} ) / \text{Denominator} \]

For \(3 \frac{41}{45}\):
\[ = \frac{3 \times 45 + 41}{45} = \frac{135 + 41}{45} = \frac{176}{45} \]

For \(3 \frac{10}{45}\):
\[ = \frac{3 \times 45 + 10}{45} = \frac{135 + 10}{45} = \frac{145}{45} \]

### Step 2: Compare the improper fractions.
Now we have:
- \(3 \frac{41}{45} = \frac{176}{45}\)
- \(3 \frac{10}{45} = \frac{145}{45}\)

Since both fractions have the same denominator (45), we can compare the numerators directly:
- \(176\) (from \(3 \frac{41}{45}\))
- \(145\) (from \(3 \frac{10}{45}\))

### Step 3: Determine which is greater.
Since \(176 > 145\), we can conclude that:
\[ \frac{176}{45} > \frac{145}{45} \]

### Step 4: Write the final comparison.
Thus, we can insert the appropriate symbol in the box:
\[ 3 \frac{41}{45} > 3 \frac{10}{45} \]

### Final Answer:
The answer is:
\[ 3 \frac{41}{45} > 3 \frac{10}{45} \]

---