Recipe is based on e.g. 5 eggs, but I want a smaller output so I want to use only 3 eggs[1]. I set the slide rule so that 3 is lined up under 5.

Then for any other ingredient in the recipe, say 7 tablespoons of milk, I look up 7 on the upper scale and read off 4.2 on the lower scale.

It doesn't matter which scale is upper or lower, and you don't have to keep track of whether you're multiplying or dividing, you just pick one to mean "recipe amount" and one to mean "actual amount". You anchor them against each other based on the critical ingredient, and then read off all other amounts. That's part of what makes it so easy to use even for children.

[1]: Or maybe I'm cooking to use up an ingredient about to expire, so I want to use all of my seven eggs, and so on.