To simplify [tex]\( 8 \div \frac{3}{5} \)[/tex], follow these steps:
1. Understand the Division of Fractions:
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of [tex]\(\frac{3}{5}\)[/tex] is [tex]\(\frac{5}{3}\)[/tex].
2. Rewrite the Division as Multiplication:
[tex]\[
8 \div \frac{3}{5} = 8 \times \frac{5}{3}
\][/tex]
3. Perform the Multiplication:
Multiply the whole number 8 by the reciprocal [tex]\(\frac{5}{3}\)[/tex]:
[tex]\[
8 \times \frac{5}{3} = \frac{8 \times 5}{3} = \frac{40}{3}
\][/tex]
4. Convert the Fraction to a Mixed Number:
To convert [tex]\(\frac{40}{3}\)[/tex] into a mixed number, divide 40 by 3:
- 40 divided by 3 is 13 with a remainder of 1.
- This means [tex]\(\frac{40}{3}\)[/tex] can be written as [tex]\(13 \frac{1}{3}\)[/tex].
So, [tex]\( 8 \div \frac{3}{5} = 13 \frac{1}{3} \)[/tex].
The correct answer is [tex]\( \boxed{13 \frac{1}{3}} \)[/tex].
