Insert `ltorgt` in the box.
`1(6)/(10)square1(5)/(10)`

Answer

To solve the problem of comparing the fractions \(1\frac{6}{10}\) and \(1\frac{5}{10}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert both mixed numbers into improper fractions.

For \(1\frac{6}{10}\):
- Multiply the whole number (1) by the denominator (10):
\[ 1 \times 10 = 10 \]
- Add the numerator (6) to this result:
\[ 10 + 6 = 16 \]
- Therefore, \(1\frac{6}{10}\) can be written as:
\[ \frac{16}{10} \]

For \(1\frac{5}{10}\):
- Multiply the whole number (1) by the denominator (10):
\[ 1 \times 10 = 10 \]
- Add the numerator (5) to this result:
\[ 10 + 5 = 15 \]
- Therefore, \(1\frac{5}{10}\) can be written as:
\[ \frac{15}{10} \]

### Step 2: Compare the Improper Fractions
Now we have the two improper fractions:
- \( \frac{16}{10} \)
- \( \frac{15}{10} \)

Since the denominators are the same, we can directly compare the numerators:
- \(16\) (from \( \frac{16}{10} \)) and \(15\) (from \( \frac{15}{10} \)).

### Step 3: Determine the Relationship
Since \(16 > 15\), we can conclude that:
\[ \frac{16}{10} > \frac{15}{10} \]
This means:
\[ 1\frac{6}{10} > 1\frac{5}{10} \]

### Step 4: Insert the Correct Symbol
Thus, we can insert the symbol in the box:
\[ 1\frac{6}{10} \, \text{(greater than)} \, 1\frac{5}{10} \]

### Final Answer
The answer is:
\[ 1\frac{6}{10} > 1\frac{5}{10} \]

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