Final answer:
To divide 7/8 by 1/2, we multiply 7/8 by the reciprocal of 1/2, which is 2/1. This results in a product of 14/8, which simplifies to 7/4. Thus, the correct answer is 7/4.
Step-by-step explanation:
To perform the division 7/8 ÷ 1/2, we can convert the division into a multiplication by taking the reciprocal of 1/2. The reciprocal of a fraction is simply flipping the numerator and denominator so for 1/2, it becomes 2/1. With this information, we can now rewrite the problem as a multiplication: 7/8 × 2/1.
To multiply fractions, you multiply the numerators together and then multiply the denominators together. So, multiplying the numerators 7 and 2 gives us 14. Multiplying the denominators 8 and 1 gives us 8. Therefore, our multiplication of fractions yields 14/8.
14/8 can be simplified by dividing both the numerator and denominator by their greatest common factor which is 2. This gives us 7/4. Hence, dividing 7/8 by 1/2 is equal to 7/4, which is answer choice (A) 7/4.