Final answer:
The difference when the quotient of 3/8 and 1/4 is subtracted from the sum of 2 1/4 and 1 1/7 is 2 3/28. This result is obtained by initially dividing 3/8 by 1/4, then adding 2 1/4 and 1 1/7, and finally subtracting the quotient from this sum.
Step-by-step explanation:
To solve the problem, we need to perform several arithmetic operations with fractions and mixed numbers. The question asks what the difference is when the quotient of 3/8 and 1/4 is subtracted from the sum of 2 1/4 and 1 1/7.
First, calculate the quotient of 3/8 and 1/4 by dividing: 3/8 ÷ 1/4 = 3/8 × 4/1 = 3/2 or 1 1/2.
Next, convert the mixed numbers into improper fractions: 2 1/4 = 9/4 and 1 1/7 = 8/7.
Now, add the two improper fractions: 9/4 + 8/7. To do this, find a common denominator, which is 28. So we have:
63/28 + 32/28 = 95/28. This is equivalent to 3 11/28.
Finally, subtract the quotient (1 1/2) from this sum: 3 11/28 - 1 1/2. First, convert 1 1/2 to 3/2, and find a common denominator (28), yielding 3 11/28 - 42/28 = 3 11/28 - 1 14/28 = 2 3/28, which cannot be further simplified.
Therefore, the correct answer is 2 3/28, which does not match any of the provided options (A, B, C, D), indicating a possible typo in the original question or answer choices.