Final answer:
To solve (3/8) ÷ 2(2/5), first find the reciprocal of 2(2/5) to convert the division into multiplication. Multiply (3/8) by the reciprocal (5/12) to get 15/96, which simplifies to 5/32. The correct answer is option b, 5/32.
Step-by-step explanation:
To solve the division problem (3/8) ÷ 2(2/5), we first need to address the operation and then simplify the resulting fraction.
Dividing by a number is the same as multiplying by its reciprocal. Therefore, to divide by 2(2/5), we multiply by the reciprocal of this number. First, we convert 2(2/5) to an improper fraction. Since 2 = 10/5, 2(2/5) becomes 10/5 + 2/5, which is 12/5. Now, the reciprocal of 12/5 is 5/12. Our division problem becomes (3/8) × (5/12).
Next, we multiply the numerators together and the denominators together. So, we get (3 × 5) in the numerator and (8 × 12) in the denominator.
(3 × 5) / (8 × 12) = 15 / 96. This can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3. After simplification, we get 5/32. Therefore, the correct answer to (3/8) ÷ 2(2/5) is 5/32, which corresponds to option b in the question.