Fill in the boxes the correct symbol out of `gt,lt and =.`
`(1)/(-3) square (-1)/(4)`

Answer

To solve the inequality \( \frac{1}{-3} \) and \( \frac{-1}{4} \), we will follow these steps:

### Step 1: Rewrite the fractions
First, we rewrite \( \frac{1}{-3} \) as \( -\frac{1}{3} \) to make it easier to compare.

**Hint:** Remember that a negative sign in the denominator can be moved to the numerator.

### Step 2: Find a common denominator
Next, we need to find a common denominator for the two fractions. The denominators are 3 and 4. The least common multiple (LCM) of 3 and 4 is 12.

**Hint:** To find the LCM of two numbers, list their multiples and find the smallest common one.

### Step 3: Convert both fractions
Now, we convert both fractions to have a denominator of 12:
- For \( -\frac{1}{3} \):
\[ -\frac{1}{3} = -\frac{1 \times 4}{3 \times 4} = -\frac{4}{12} \]
- For \( -\frac{1}{4} \):
\[ -\frac{1}{4} = -\frac{1 \times 3}{4 \times 3} = -\frac{3}{12} \]

**Hint:** When converting fractions to a common denominator, multiply both the numerator and denominator by the same number.

### Step 4: Compare the numerators
Now that both fractions have the same denominator, we can compare the numerators:
- We have \( -4 \) (from \( -\frac{4}{12} \)) and \( -3 \) (from \( -\frac{3}{12} \)).
- Since \( -4 < -3 \), we conclude that \( -\frac{4}{12} < -\frac{3}{12} \).

**Hint:** When comparing negative numbers, the number that is less negative is greater.

### Step 5: Write the final inequality
Thus, we can write:
\[ -\frac{1}{3} < -\frac{1}{4} \]
or in terms of the original fractions:
\[ \frac{1}{-3} < \frac{-1}{4} \]

### Conclusion
The correct symbol to fill in the box is \( < \).

**Final Answer:** \( \frac{1}{-3} < \frac{-1}{4} \)