To solve the problem [tex]\(1 \frac{1}{5} \times 2 \frac{1}{5}\)[/tex], follow these steps:
1. Convert the mixed numbers to improper fractions:
- For [tex]\(1 \frac{1}{5}\)[/tex]:
[tex]\[
1 \frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{6}{5}
\][/tex]
- For [tex]\(2 \frac{1}{5}\)[/tex]:
[tex]\[
2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}
\][/tex]
2. Multiply these improper fractions:
[tex]\[
\frac{6}{5} \times \frac{11}{5} = \frac{6 \times 11}{5 \times 5} = \frac{66}{25}
\][/tex]
3. Convert the improper fraction back to a mixed number:
- Divide the numerator by the denominator to find the quotient and the remainder:
[tex]\[
66 \div 25 = 2 \, \text{with a remainder of} \, 16
\][/tex]
- So, the mixed number is:
[tex]\[
2 \frac{16}{25}
\][/tex]
Therefore, the result of [tex]\(1 \frac{1}{5} \times 2 \frac{1}{5}\)[/tex] is [tex]\(2 \frac{16}{25}\)[/tex].
