Final answer:
The exact quotient for 1/4 divided by 3/8 is 2/3 because dividing by a fraction is the same as multiplying by its reciprocal. This multiplication results in 8/12, which simplifies to 2/3.
Step-by-step explanation:
The best reason why 2/3 is the exact quotient for 1/4 divided by 3/8 is that when you divide fractions, you multiply by the reciprocal of the divisor. In this case, dividing 1/4 by 3/8 is the same as multiplying 1/4 by the reciprocal of 3/8, which is 8/3. Here's the step-by-step explanation:
Write down the problem: (1/4) ÷ (3/8).
Convert the division of fractions into multiplication by the reciprocal: (1/4) × (8/3).
Multiply the numerators together: 1 × 8 = 8.
Multiply the denominators together: 4 × 3 = 12.
Combine the results: 8/12.
Simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 4: (8 ÷ 4) / (12 ÷ 4) = 2/3.
Therefore, the exact quotient for 1/4 divided by 3/8 is 2/3.