Final answer:
To evaluate x/y for x = 2/3 and y = 6/7, multiply x by the reciprocal of y to obtain (2/3) * (7/6), which simplifies to 14/18, and further to 7/9. The given options are incorrect, as the correct answer is 7/9.
Step-by-step explanation:
To evaluate x/y for x = 2/3 and y = 6/7, you will multiply x by the reciprocal of y. Essentially, we turn the division into a multiplication by flipping the second fraction. Therefore, you'll proceed in the following manner:
- First, write down the problem x/y as (2/3) / (6/7).
- Next, flip the second fraction to find its reciprocal, converting our expression to (2/3) * (7/6).
- Then, multiply the numerators together and the denominators together: (2*7) / (3*6).
- You'll get 14/18. However, you're not done yet because 14/18 can be simplified.
- Both numbers divide by 2, which gives us the simplified answer of 7/9.
- Now, you can see none of the given options are correct. The correct evaluation of x/y for the provided values is 7/9, not any of the options (a), (b), (c), or (d).