Find the rational number halfway between 1/5 and 1/6

What properties allow transformation to be used as a problem solving tool

Given the points a(-2, 1) and b(8, 6), find the coordinates of the point c on directed line segment ab, that partitions ab in the ration 2: 3.

Agarden consists of an apple tree, a pear tree, cauliflowers, and heads of cabbage. there are 40 vegetables in the garden. 24 of them are cauliflowers. what is the ratio of the number of cauliflowers to the number of heads of cabbage?