To find the area of Nina's garden, we multiply the length by the width.
First, we start with the given dimensions:
- Length = \(4 \frac{1}{5}\) meters
- Width = \(\frac{3}{10}\) meter
Step 1: Convert the mixed number to an improper fraction
The length \(4 \frac{1}{5}\) can be converted to an improper fraction: \[ 4 \frac{1}{5} = \frac{(4 \times 5) + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5} \]
Step 2: Multiply the fractions
Now we can calculate the area by multiplying the length by the width: \[ \text{Area} = \text{Length} \times \text{Width} = \frac{21}{5} \times \frac{3}{10} \]
Step 3: Multiply the fractions
To multiply the fractions, we multiply the numerators and the denominators: \[ \text{Area} = \frac{21 \times 3}{5 \times 10} = \frac{63}{50} \]
Step 4: Convert to a mixed number (if necessary)
Now, we convert \(\frac{63}{50}\) to a mixed number: \[ 63 \div 50 = 1 \quad \text{with a remainder of } 13 \] So, \(\frac{63}{50} = 1 \frac{13}{50}\).
Final Answer
The area of Nina’s garden is \( \frac{63}{50} \) square meters or \( 1 \frac{13}{50} \) square meters.