Final answer:
To estimate 1/6 of the length of a tabletop by finding half-measurements, divide the table into quarters and eighths, then combine these parts to create sections that are 3/8 of the whole, resulting in six equal sections.
Step-by-step explanation:
To divide a rectangular table top into six equal sections using only the ability to find the halfway point, you would use a process of iterative halving. First, you would find the halfway mark of the table. This would give you two sections, each being half of the table. Next, you would find the halfway mark of one of these halves, dividing that half into two quarters of the original table size. Now you have divided the table into three sections, but they are not equal - two quarters and one half.
To find 1/6th, take one of the quarters and again divide it in half by finding its midpoint. This gives you two sections, each being 1/8 of the original table. By taking one of these eighths and adding it to one of the adjacent quarters, you now have three sections that equal 1/8 + 1/4, or 3/8 of the original table. Finally, you would need to repeat this process on the other half of the table to create three more equivalent sections, each also being 3/8 of the original table, thus ensuring that all six sections are of equal size.