Renaming fractions is also called "borrowing" - it's because you borrow fraction parts from the wholes of a mixed number.
this is necessary when, if you subtract, the subtracted fraction part is bigger than the fraction part of the number from which you subtract: so here 3/4 is bigger than 1/4 and we need to borrow
if we wanted to subtract 3/4 from 4 1/4 then you're stuck: how do you subtract 3/4 from 1/4? you can't, but you can change 4 1/4 into 3 5/4 !!!! it's the same number, you just borrowed from the whole unmbers and put into the fraction!
now we can subtract: 3 5/4-3/4 is 3 2/4
this is necessary when, if you subtract, the subtracted fraction part is bigger than the fraction part of the number from which you subtract: so here 3/4 is bigger than 1/4 and we need to borrow
if we wanted to subtract 3/4 from 4 1/4 then you're stuck: how do you subtract 3/4 from 1/4? you can't, but you can change 4 1/4 into 3 5/4 !!!! it's the same number, you just borrowed from the whole unmbers and put into the fraction!
now we can subtract: 3 5/4-3/4 is 3 2/4