Final answer:
To divide 8 by 1 4/5, convert the mixed number to the improper fraction 9/5, find its reciprocal (5/9), and multiply 8 by 5/9. The result is the quotient 40/9, which is in lowest terms.
Step-by-step explanation:
To divide the number 8 by the fraction 1 4/5, you first need to convert the mixed number into an improper fraction. The fraction 1 4/5 can be rewritten as 9/5 (since 1 4/5 is the same as 5/5 + 4/5 = 9/5). Then, to perform the division, we convert the division process into multiplication by the reciprocal of the divisor. Multiplying by the reciprocal is the same as dividing by the original number, so we multiply 8 by the reciprocal of 9/5, which is 5/9.
The calculation steps are:
1. Convert 1 4/5 to an improper fraction: 5/5 + 4/5 = 9/5.
2. Identify the reciprocal of 9/5, which is 5/9.
3. Multiply 8 by 5/9 to find the quotient.
4. Perform the multiplication: 8 × 5/9 = 40/9.
5. Simplify if necessary. However, 40/9 is already in its lowest terms.
Thus, the quotient, when 8 is divided by 1 4/5, is 40/9 in lowest terms.