To solve the problem of finding \(1 \frac{2}{5}\) of \(4 \frac{2}{7} \text{ km}\), we can follow these steps:
1. Convert Mixed Numbers to Improper Fractions:
- For \(1 \frac{2}{5}\):
- The whole number part is \(1\).
- The fractional part is \(\frac{2}{5}\).
- To convert \(1 \frac{2}{5}\) to an improper fraction, we multiply the whole number by the denominator and add the numerator:
[tex]\[
1 \cdot 5 + 2 = 5 + 2 = 7
\][/tex]
Thus, \(1 \frac{2}{5} = \frac{7}{5}\).
- For \(4 \frac{2}{7}\):
- The whole number part is \(4\).
- The fractional part is \(\frac{2}{7}\).
- To convert \(4 \frac{2}{7}\) to an improper fraction, we multiply the whole number by the denominator and add the numerator:
[tex]\[
4 \cdot 7 + 2 = 28 + 2 = 30
\][/tex]
Thus, \(4 \frac{2}{7} = \frac{30}{7}\).
2. Multiply the Improper Fractions:
- Now multiply the two improper fractions \(\frac{7}{5}\) (for \(1 \frac{2}{5}\)) and \(\frac{30}{7}\) (for \(4 \frac{2}{7}\)):
[tex]\[
\frac{7}{5} \times \frac{30}{7}
\][/tex]
- To multiply these fractions, multiply the numerators and then the denominators:
[tex]\[
\frac{7 \times 30}{5 \times 7} = \frac{210}{35}
\][/tex]
3. Result:
- The product of \(1 \frac{2}{5}\) and \(4 \frac{2}{7}\) is \(\frac{210}{35}\).
Given the calculation, the improper fractions are \(\frac{7}{5}\) and \(\frac{30}{7}\), and their product is \(\frac{210}{35}\).
Thus, \(1 \frac{2}{5}\) of \(4 \frac{2}{7} \text{ km}\) is \(\frac{210}{35} \text{ km}\).
This should conclude the detailed, step-by-step solution to finding [tex]\(1 \frac{2}{5}\)[/tex] of [tex]\(4 \frac{2}{7} \text{ km}\)[/tex].
