Fill in the boxes by the symbol `lt or gt` to make the given statements true :
`8/15 square 3/5`

Answer

To solve the problem of comparing the fractions \( \frac{8}{15} \) and \( \frac{3}{5} \), we can use two methods: converting them to like fractions or using cross multiplication. Let's go through both methods step by step.

### Method 1: Converting to Like Fractions

1. **Identify the fractions**: We have \( \frac{8}{15} \) and \( \frac{3}{5} \).

2. **Make the denominators the same**: The denominator of the second fraction \( \frac{3}{5} \) can be converted to 15 by multiplying both the numerator and denominator by 3:
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]

3. **Compare the numerators**: Now we have two fractions with the same denominator:
\[ \frac{8}{15} \quad \text{and} \quad \frac{9}{15} \]
Since \( 9 > 8 \), we can conclude:
\[ \frac{3}{5} > \frac{8}{15} \]

### Method 2: Cross Multiplication

1. **Set up the cross multiplication**: We will multiply the numerator of the first fraction by the denominator of the second fraction and vice versa:
\[ 8 \times 5 \quad \text{and} \quad 3 \times 15 \]

2. **Calculate the products**:
- For \( 8 \times 5 \):
\[ 8 \times 5 = 40 \]
- For \( 3 \times 15 \):
\[ 3 \times 15 = 45 \]

3. **Compare the results**: Now we compare the two products:
\[ 40 < 45 \]
This means:
\[ \frac{8}{15} < \frac{3}{5} \]

### Conclusion
From both methods, we find that:
\[ \frac{8}{15} < \frac{3}{5} \]
Thus, we fill in the box with the symbol `lt` (less than).

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