Compare the fractions given below and put appropriate symbol `(lt, gt or =)` in the box.
`1/(3)square1/(5)`

Answer

To compare the fractions \( \frac{1}{3} \) and \( \frac{1}{5} \), we can follow these steps:

### Step 1: Identify the fractions
We have two fractions to compare:
- \( \frac{1}{3} \)
- \( \frac{1}{5} \)

### Step 2: Find a common denominator
To compare the fractions, we need to have the same denominator. The denominators here are 3 and 5. The least common multiple (LCM) of 3 and 5 is 15.

### Step 3: Convert the fractions
Now, we will convert both fractions to have the common denominator of 15.

- For \( \frac{1}{3} \):
\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \]

- For \( \frac{1}{5} \):
\[ \frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15} \]

### Step 4: Compare the numerators
Now that both fractions have the same denominator, we can compare their numerators:
- \( 5 \) (from \( \frac{5}{15} \))
- \( 3 \) (from \( \frac{3}{15} \))

Since \( 5 > 3 \), we can conclude that:
\[ \frac{1}{3} > \frac{1}{5} \]

### Step 5: Write the comparison symbol
We can now write the appropriate symbol in the box:
\[ \frac{1}{3} \, \text{(gt)} \, \frac{1}{5} \]

### Final Answer:
\[ \frac{1}{3} > \frac{1}{5} \]

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