Here’s an argument that I could not settle with my math/algebra teacher many many years ago. I was told that no matter what number you times by “zero”, the answer is “zero”. So I asked the teacher to explain. If I am holding a nickel in my hand and you “times” that nickel by “zero”, how can the answer be “zero” when I still have the nickel in my hand? I flunked a lot of tests, lol.
Teacher - "Now you have zero. Would you like to try addition?"
First, take this alegbraic equality:
a + b = c
Then, subsitute "4a - 3a" for "a", and "4b - 3b" for "b":
4a - 3a + 4b - 3b = 4c - 3c
Then move "-3a" on the left to "+3a" on the right, and
move "4c" on the right to "-4c" on the left:
4a + 4b - 4c = 3a + 3b - 3c
Then use the distributive property to isolate common factors on each side:
4(a + b - c) = 3(a + b - c)
4 = 3