Final answer:
Dividing 4/5 by 8 is the same as multiplying 4/5 by the reciprocal of 8, which is 1/8. When multiplied out, the expression simplifies to 1/10.
Step-by-step explanation:
When asked which expression is equivalent to the division of 4/5 by 8, we need to understand the relationship between division and multiplication by reciprocals. Dividing by a number is the same as multiplying by its reciprocal. Therefore, dividing 4/5 by 8 is equivalent to multiplying 4/5 by the reciprocal of 8, which is 1/8.
To solve this, you write the expression as a multiplication problem: 4/5 × 1/8. Next, multiply the numerators and multiply the denominators: (4 × 1)/(5 × 8) = 4/40. Finally, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which in this case is 4. So, the simplified form of the expression is 1/10.