To find an expression equivalent to [tex]\(\frac{4}{5} \div 8\)[/tex], we need to remember that dividing by a number is the same as multiplying by its reciprocal.
Let's break down the problem step by step:
1. Identify the Reciprocals:
- The original expression is [tex]\(\frac{4}{5} \div 8\)[/tex].
- To divide by 8, we can multiply by the reciprocal of 8. The reciprocal of 8 is [tex]\(\frac{1}{8}\)[/tex].
2. Convert the Division to Multiplication by the Reciprocal:
- Replace the division operation with multiplication by the reciprocal:
[tex]\[
\frac{4}{5} \div 8 = \frac{4}{5} \times \frac{1}{8}
\][/tex]
3. Perform the Multiplication:
- Multiply the numerators together and the denominators together:
[tex]\[
\frac{4}{5} \times \frac{1}{8} = \frac{4 \times 1}{5 \times 8} = \frac{4}{40}
\][/tex]
4. Simplify the Fraction:
- Simplify [tex]\(\frac{4}{40}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[
\frac{4}{40} = \frac{4 \div 4}{40 \div 4} = \frac{1}{10}
\][/tex]
Thus, the expression equivalent to [tex]\(\frac{4}{5} \div 8\)[/tex] is [tex]\(\frac{1}{10}\)[/tex].
Since we need to match this to one of the given choices, the correct choice is [tex]\(\frac{1}{10}\)[/tex]. However, none of the exact answers provided directly match [tex]\(\frac{1}{10}\)[/tex]. Seeing as the mathematical operations provided don't result in simplification towards [tex]\(\frac{1}{10}\)[/tex], it indicates an error in the provided options or misstatement of the original problem context.
Assuming we stick to the intent of understanding equivalent expressions and derivation, the equivalent simplified multiplication expression remains [tex]\(\frac{1}{10}\)[/tex].
