Allocation and proportion is a little tricky. Although these expressions aren't quite different from their English equivalents, there are a few differences that you will need to pay extra attention to.
ずつ is a rather straightforward particle that splits things up into groups, creating ratios. Say you have X number of kids and Y number of mothers to watch the kids. Say there are 100 kids, but you want a chaperon every four kids. To tell the mothers this, you could say 子供４人に１人ずつ、お母さんがついてください。You can do the math as to how many mothers there are.
In 1, of all the 100 kids now in groups of 10, two mothers are allotted to each.
May two mothers follow with every ten kids?
Think of it as grouping things from the start of a line/process until the end. It is implied that the allocation is repeated so that the intended ratio is carried out in turn.
Please pass out to each and every person one of these twenty magazines.
In English, it is more common for someone to say “give three pieces of paper to each kid” than “give three pieces of paper to every ten kids”. We want to make things grammatically singular in number and say “to each group of ten kids”. Saying group is not that necessary in Japanese because ずつ does that already.
You can, though, paraphrase ずつ out of the sentence. Compare and contrast the following sets of sentences.
3a. It'll be fifteen cards to each person. We'll put the rest face down here.
3b. So there will be fifteen cards for each person, we'll pass out the cards to everyone.
4a. Bind up textbooks in groups of two, novels in groups of ten, and magazines in groups of twenty with three cords.
4b. To make bundles, bind so that textbooks are in sets of two, novels in ten, and magazines in twenty with three cords.
As you can see, all ずつ does is mark how much the identified recipient(s) are going to get. Some expressions that you will constantly see include 少しずつ (little by little) and わずかずつ (similar to the first but smaller in degree).
To arrange them in twos.
Kids will receive two candies each.
It's best to eat a little bit at a time.
She recovered little by little.
Two sheets each please.
Please enter the bus one by one.
He put aside a few dollars every day.
The river water level rose little by little yesterday.
Please learn these words one word at a time.
I came to understand the bottom of it little by little.
Orthography Note: づつ is also correct but old-fashioned.
～わりで has some interchangeability withずつ. Rather than being involved with the flow of work or time, this pattern just shows a rate/proportion. So, if the numbers of the whole situation are not certainly known, you can’t use ～わりで. In spoken speech, however, ずつ and ～わりで are often omitted out of the sentence.
At ten miles an hour, when will you arrive at your destination?
ずつ still gets used in math texts, but because it needs context to be understood clearly, it is usually limited to the spoken language. ～わりで, on the other hand, clearly states things in more mathematical terms, so it is more indicative of the written language.