Is there a name for the rule $a \div (b \times c) = a \div b \div c$? Edit, because I should have looked it up before I posted the question:
Is there a name for the rule $a \div (b \div c) = a \div b \times c$  ? I ran across this in Liping Ma's book, Knowing and Teaching Mathematics, and I have searched the internet for a name for this rule to no avail. It is not the distributive law, but it is rather similar. Thank you!
From Ma's book, p. 59 discussing "dividing by a number is equivalent to multiplying by its reciprocal":
"We can use the knowledge that students have learned to prove the rule that dividing by a fraction is equivalent to multiplying by its reciprocal. They have learned the commutative law. They have learned how to take off and add parentheses. They have also learned that a fraction is equivalent to to the result of a division, for example, $ \frac{1}{2} = 1 \div 2 $  . Now, using these, we can rewrite the equation this way:
$ 1\frac{3}{4} \div \frac{1}{2} \to $


$1\frac{3}{4} \div (1 \div 2) \to $


$1\frac{3}{4} \div 1 \times 2 \to  $ (This is the step my question is about.)


$1\frac{3}{4} \times 2 \div 1 \to $ (and I'd like an explicit explanation of this step, too.)


$1\frac{3}{4} \times 2\to$
$1\frac{3}{4} \times (2 \div 1) \to $

I suppose that $a,b,c$ are rational (or real) numbers. In this case your starting expression is equivalent to:
$$
\dfrac{a}{b\times c}=a\times \dfrac{1}{b}\times \dfrac{1}{c}=\left(a \times \dfrac{1}{b} \right)\times \dfrac{1}{c}=\dfrac{a \times \dfrac{1}{b}}{c}=\dfrac{ \dfrac{a}{b}}{c}
$$
so you can see that this property does not need a special name since it is simply the application of the definition of inverse and of associativity for the product.
