Reciprocal numbers and why the shortcut for fraction division works (6th grade math)
First we study reciprocal numbers: if the product of two numbers is 1, they are reciprocal numbers. From this, we can see that the answer to the division 1 ÷ (3/4) will be the reciprocal of 3/4, or 4/3.
DIVISION as a process has to do with "fitting": how many times does (the divisor) FIT into the (dividend). This is the thought that we develop in trying to understand WHY the common shortcut for fraction division works (the shortcut being, instead of dividing, multiply by the reciprocal of the divisor).
Some students may find the explanation a bit confusing, which is alright. You can use the shortcut without understanding all these details, but it is always nice if you CAN grasp how and why things work "behind the scenes". That's what makes math fascinating!
See also
Fraction division: concept and applications
Math Mammoth Grade 6 curriculum