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How can I visualize dividing by a fraction as partial and full groups?

I can't visualize all these "full groups" and "partial groups." Can someone please picture them? Please see my questions red in-line. Please don't use the identity that $\dfrac{a}{b} \div \dfrac{c}{d} \equiv \dfrac{a}{b} \times \dfrac{d}{c} $.

Because $10 ÷ 4/3$ isn't an integer, [I changed the numerator from 10 to 6](https://old.reddit.com/r/learnmath/comments/ckv75r/why_multiplying_by_the_reciprocal_works_while/).

> Let's take a step back and consider what does dividing mean in general. There are a lot of ways of interpreting division, but one way is to say that (for example) 6 ÷ 4 means "if we have 6 items, and we split them into 4 equal groups, how many items will we have in each group?"
> 
> Let's see what happens if we try to apply this to fractions. 6 ÷ 4/3 means we divide 6 into 4/3 equal groups, and we ask how many items is in each (full) group. But what does it mean to have 4/3 of a group? 4/3 is 1 ⅓, so it'd make sense that 4/3 means you have one full group, and then a second "partial" group that's 1/3 the size of the full group.
> 
>Think about how you would physically take items to do this. You could say that "oh, I need a total of four 'partial' groups, since three of the partial groups make a full group. At the end, I'll put three partial groups together to make a full group, and **then count how many are in that final full group."**

If each partial group is $1/3$, then "three of the partial groups make a full group" because $3 \times \dfrac{1}{3} = 3$. And you need 4 partial groups because $4 \times \dfrac{1}{3} = \dfrac{4}{3}$. $\color{red}{\text{1. Then what?  What does "count how many are in that final full group" mean? }}$


> In turn, what does multiplication mean? Again, multiple interpretations, but one of them is that 5 × 3 means "there are 5 items in a group, and there are 3 groups; how many items do you have total?" Again, let's apply this to fractions. 6 × 3/4 means that you have 6 items in a group, but you only have 3/4 of a group. How many do you have total?
> 
> In this case, how would you physically act out this multiplication? You might say, "oh, there should be 6 to a full group, but I have only 3/4 of one. I guess I could make that by making a full group, splitting it into four parts, and throwing away one of the parts."
> 
> But now notice the actions you're taking for both division by one fraction and multiplication by its reciprocal. In both cases, you're breaking the 6 up into 4 parts, and then counting only three of the four parts. The reasoning is a bit different (**in division, you were thinking about the number of "partial groups" and how many partial groups are in a full group**, while in multiplication, you're thinking about how to break down a number into a part of a group which involves first breaking it down into a lot of equal small parts and then putting them back together into a bigger part-of-a-group) but the same 3 and 4 numbers are there in both cases.

$\color{red}{\text{2. I'm nonplussed. In division, how was I counting "how many partial groups are in a full group"?}}$

3. Isn't u/Viola_Buddy wrong to use "group" here? What's a more correct term? "Group" is for Group Theory, but undoubtedly I'm not doing any Group Theory here, when I'm having difficulty with division!