Multiply and simplify your answer. Write it as a mixed number.

[tex]\[ 5 \cdot \frac{5}{7} \][/tex]

A. [tex]\(\frac{25}{7}\)[/tex]

B. [tex]\(3 \frac{4}{7}\)[/tex]

C. [tex]\(\frac{10}{7}\)[/tex]

D. [tex]\(1 \frac{3}{7}\)[/tex]



Answer :

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].