What's the ratio of one-third to one-half?

What's the ratio of one-third to one-half?

1 / 3:1 / 2 = 2:3, so the ratio of 1 / 3 to 1 / 2 is 2:3
Learning from the sea

Half to one-third and 16 to 8

No

7 / 8 minus 1 / 2 minus 1 / 3 = 7 / 8 minus (1 / 2 minus 1 / 3) = 7 / 8 minus 1 / 6 = 17 / 24 right and wrong

Wrong

Observe the following formulas: half = one by half; one sixth = two by one-third = half minus one-third
Observe the following numbers and find out the rule. Half = one minus half, one sixth = one half minus one third. Write out the conjecture process of one in 240. Use a to express the rule

1/2＝1/﹙1×2﹚＝1－1/2
1/6＝1/﹙2×3﹚＝1/2－1/3
1/12＝1/﹙3×4﹚＝1/3－1/4
………………………………
1/A﹙A＋1﹚＝1/A－1/﹙A＋1﹚
1/240＝1/﹙15×16﹚＝1/15－1/16.