Final answer:
To make an entire sock, it will take 18 yards of thread.
Step-by-step explanation:
To find out how many yards of thread it will take to make an entire sock, we need to find the equivalent of 1 sock.
Since 4/6 of a sock requires 2 1/2 yards of thread, we can find the equivalent of 1 sock by multiplying both the numerator and denominator of 4/6 by 2 to make it 8/12.
So, 8/12 of a sock requires 2 1/2 yards of thread. To find out how many yards are needed for a whole sock, we can set up a proportion: 8/12 is to 2 1/2 as 1 is to x, where x represents the number of yards for a whole sock.
Cross-multiplying, we get: 8 * x = 12 * 2 1/2. Solving this equation, we find that x = 18.
Therefore, it will take 18 yards of thread to make an entire sock.