I'm studying analytic geometry in Khan Academy and I'm struggling at dividing segments when given ratios like 1:3, 5:6, 2:1 and finding their fractions. According to what I read and learned from them and other sources, 5:6 would be , but in some problems,khan academy says it's . Another problem I'm struggling with is: "find B between A and C, such as Bc is 6 times what AC is, according to what they do in some of their explanations, AC is , and BC is , so the fraction for the bigger segment should be 6/7. But they say it's just 5/6. This doesn't make sense for me, not only because it contradicts some of the things they say in other problems, but because if you multiply a segment 6 times, it should be 6 times bigger, not five times as the following emojis show.
Sorry if my question and the way I ask it is childish, but english is not my first language, and this is the fisrt time I use it to write anything about math. I'd be so grateful if anyone teaches me the proper way to divide segments or just tells me if I'm not wrong and it's just a mistake from Khan Academy
https://en.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-dividing-segments/e/dividing-line-segments By the way, that's the problem I'm struggling with.