For anyone confused about the end.. he's not trying to reduce it further after 28/15. This is simply the answer to 7/3÷5/4. If you use a calculator to solve 7/3÷5/4 the answer is 1.86666666... if you use a calculator to do 28/15 the answer is 1.86666666... there is no reducing further, the answer is 28/15. He's just showing how to work the math using fractions, all his math is correct. I hope this helps clear some confusion in the comments.
Im not understand how the fraction values can be changed in value as done here with the 5/4 which is 1.25, to 1? I get the kcf to make the math easier to work with, but not how we can change values of what would have 1.86 if we were to purely divide (7/3)/(5/4) = 1.86 please explain
I agree that we should not teach people to memorize algorithms at a young age. While I, along with a lot of other people, despise Common Core math, I understand and agree with what the intended purpose is (spend more time on why we do something, for example, why the quotient of two fractions is equal to dividend fraction times the reciprocal of the divisor fraction). I think you explain how the gears turn better than the current Common Core standards.