Explain why it is necessary to rename 4 1/4 if you subtract three fourths from it.

Well when you have to subtract you check your numerator. You would realize you cannot do 1/4 minus 3/4 for your numerator is to small to go into the other. You cannot do 1 minus 3 with a positive answer. That is how you know you have to rename 4 1/4 in order to subtract it to 3/4

It is necessary because 4 and 1/4 minus 3/4 equals 3 and 2/4 so you have to 3 and 2/4 to 3 and 1/2