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 $

Never thought about this. My work with quadratic forms gives many expressions in one line, with a selection of plus and minus signs. It never bothered me, if there is a plus sign it gets added, and all those with minus signs get subtracted. I think most people do that. So,
$$ s + t - u - v + w - x - y + z = (s + t + w + z) - (u + v + x + y)  $$
The analogous usage with multiplication and division signs would be
 $$ s \cdot t \div u  \div  v  \cdot  w  \div  x  \div  y  \cdot  z = \frac{s  t  w  z}{ u  v  x  y}  $$
but I can hardly imagine anyone writing the thing on the left hand side and expecting to be understood. In a single line, we could write $s  t  w  z/( u  v  x  y)$ instead.
Go Figure.
