How do you do 1 and 1 4ths divided by 2 and 3 4ths?

Answer 1

The big trick here is that nobody actually uses "proper" fractions in math. It's a dry, boring process they teach in grade school that never gets used anywhere except in cookbooks and ratchet sizes. If you're doing pure math, then piss on "proper" fractions. This makes it a ~lot~ easier, and it makes a lot more sense. Nobody will take points off your college paper for it unless you're studying cookbook authorship.

With that in mind, convert those numbers! We're given:

11/4 ÷ 23/4

Which, in actually useful notation, is:

5/4 ÷ 11/4

Now you're at a point where you can do the actual division. With fractions, that's actually surprisingly easy. All you have to do is "cross multiply". That can be done by flipping the fraction that you're dividing by, and then multiplying instead:

5/4 ÷ 11/4

= 5/4 × 4/11

Now all you have to do is multiply the tops and bottoms of the fractions together:

= (5 × 4)/(4 × 11)

(* If you're really on the ball, you'll notice that we could actually eliminate those fours at this point, but let's go ahead with them in)

= 20/44

Now we can factor a four out of both the numerator and denominator:

= 5/11