What is the 'physical' explanation of a division by a fraction?

Question

For example, dividing by 2, means we cut something in two.

But dividing by 0.5, can only be explained with multiplying something by 2.

So, is there a "physical" explanation of dividing by 0.5? Is it "I divide by an entity that internally multiplies' or something as so bizarre?

Answer 1

I once heard: "If you feed a kid $Y$ grams of chocolate he would have a density of $X$ $\rm gr/cm^3$ of chocolate in his blood. But if you feed half a boy chocolate he will have $2X$ $\rm gr/cm^3$ of chocolate in his blood".

Answer 2

$$\frac{1}{0.5} = \frac{2(\not{.5})}{\not{.5}} = 2.$$

$$\frac{1}{\frac12} = \frac{2\cdot\not{\frac{1}{2}}}{\not{\frac12}} = 2.$$

---

In words, "how many times does one-half fit into the whole?"

And more generally, "how many times does $\;\dfrac1n\;$ fit into $\;1\;$?"

Answer 3

Along the same lines as Pedro Tamaroff's answer:

If you have ten ounces of vodka and each cocktail requires one ounce, then you can make ten cocktails.

If you have ten ounces of vodka and each cocktail requires only half an ounce, then you can make twenty cocktails. In other words, halving the vodka doubles the number of drinks. (Unfortunately, nobody will be happy with these drinks.)