> Why is (1/2) / (1/4) = 2? It's because there are 2 quarters in every half That sounds like looking for a "trick" to me, rather than the much simpler generic

> Why is (1/2) / (1/4) = 2? It's because there are 2 quarters in every half That sounds like looking for a "trick" to me, rather than the much simpler generic rearrangement. Trying to cram that phrase into more complex ones I'd start thinking "Wait, how many five eighths are there in seventy sixteenths?" If the question is "what is (1/2) / (1/4)" and you can't see it, then the idea of rearranging the equation and why rearranging it is OK is pretty important and general. (5/8) / (70/16) = x 5/8 = 70x / 16 5 . 16/8 = 70x 5 . 2 = 70x 10 = 70x 1/7 = x That seems simpler to me than "There is one seventh of seventy sixteenths in five eighths" and it requires knowing how basic multiplication and division works, and that the equals sign means that the things on both sides are equal, so if we multiply both sides by the same number or divide by the same number then that's OK. That can then lead into why you need to be careful about values being 0 or why sometimes you have to add ± to an answer. You can also just generally explore rearrangements, try out different modifications and see if it makes things simpler, go back and try others.