To determine the total distance the postman will cover, we can follow these steps.
1. Convert the Mixed Numbers to Improper Fractions:
- For the distance walked per day, [tex]\(5 \frac{3}{5}\)[/tex]:
- First, multiply the whole number (5) by the denominator of the fraction (5): [tex]\(5 \times 5 = 25\)[/tex].
- Then add the numerator of the fraction (3): [tex]\(25 + 3 = 28\)[/tex].
- So, [tex]\(5 \frac{3}{5}\)[/tex] can be written as the improper fraction [tex]\(\frac{28}{5}\)[/tex].
- For the number of days, [tex]\(5 \frac{1}{2}\)[/tex]:
- First, multiply the whole number (5) by the denominator of the fraction (2): [tex]\(5 \times 2 = 10\)[/tex].
- Then add the numerator of the fraction (1): [tex]\(10 + 1 = 11\)[/tex].
- So, [tex]\(5 \frac{1}{2}\)[/tex] can be written as the improper fraction [tex]\(\frac{11}{2}\)[/tex].
2. Multiply the Fractions to Find the Total Distance:
- Multiply the improper fractions:
[tex]\[
\frac{28}{5} \times \frac{11}{2}
\][/tex]
- First, multiply the numerators: [tex]\(28 \times 11 = 308\)[/tex].
- Then, multiply the denominators: [tex]\(5 \times 2 = 10\)[/tex].
- So, the product of the fractions is:
[tex]\[
\frac{308}{10}
\][/tex]
3. Simplify the Fraction:
- Divide the numerator by the denominator: [tex]\(308 \div 10 = 30.8\)[/tex].
- Therefore, the total distance the postman will cover in [tex]\(5 \frac{1}{2}\)[/tex] days is [tex]\(30.8\)[/tex] km.
4. Summary:
- The postman walks 5.6 km per day (since [tex]\(\frac{28}{5} = 5.6\)[/tex]).
- In [tex]\(5 \frac{1}{2}\)[/tex] days, he will cover a total distance of [tex]\(30.8\)[/tex] km.
So, the postman will cover a distance of [tex]\(30.8\)[/tex] km in [tex]\(5 \frac{1}{2}\)[/tex] days.
