Certainly! Let's work through the problem of multiplying [tex]\(5\)[/tex] by [tex]\(\frac{5}{7}\)[/tex] and simplifying the answer step-by-step.
1. Multiply the given numbers:
[tex]\[
5 \cdot \frac{5}{7}
\][/tex]
2. Multiply the whole number by the numerator:
[tex]\[
5 \cdot 5 = 25
\][/tex]
3. Keep the denominator the same:
[tex]\[
\frac{25}{7}
\][/tex]
4. Simplify the improper fraction [tex]\(\frac{25}{7}\)[/tex] to a mixed number:
- Determine how many times the denominator 7 can go into the numerator 25:
[tex]\[
25 \div 7 = 3 \text{ (whole number part)}
\][/tex]
- Find the remainder of the division:
[tex]\[
25 - (7 \cdot 3) = 25 - 21 = 4
\][/tex]
Thus, the fraction part of the mixed number is [tex]\(\frac{4}{7}\)[/tex].
5. Combine the whole number and the fraction:
[tex]\[
3 \frac{4}{7}
\][/tex]
Therefore, the simplified answer expressed as a mixed number is:
[tex]\[
3 \frac{4}{7}
\][/tex]
The improper fraction [tex]\(\frac{25}{7}\)[/tex] simplifies to the mixed number [tex]\(3 \frac{4}{7}\)[/tex].
