Is there a name for the rule ?
Edit, because I should have looked it up before I posted the question:
Is there a name for the rule ? 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, . Now, using these, we can rewrite the equation this way:
(This is the step my question is about.)
(and I'd like an explicit explanation of this step, too.)