Final answer:
To find the quotient of 2/3 divided by 4/5, multiply 2/3 by the reciprocal of 4/5, which is 5/4. After simplifying, the result is 5/6, which is not among the provided answers, indicating a possible error in the question or options.
Step-by-step explanation:
The question is asking for the quotient when dividing the fraction 2/3 by 4/5. To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 4/5 is 5/4. So, you need to multiply 2/3 by 5/4:
(2/3) × (5/4) = (2 × 5) / (3 × 4) = 10/12
Now, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:
10/12 = (10÷2) / (12÷2) = 5/6
However, this is not one of the provided options. Check the operation again, the simplified form of 10/12 is indeed 5/6 and not an option among A. 8/15, B. 10/12, C. 2/3, or D. 1 and 2/10. None of these answers match 5/6. It seems there might have been a mistake in either the provided answer choices or in the simplification process.