The elevator below the lobby
A parking garage elevator has floors below ground labelled −1, −2, −3. Going up 2 floors from −3 lands you on −1, and going down from floor 2 by 5 puts you at −3. Adding and subtracting integers is just riding that elevator up and down past the lobby.
Numbers below zero
Integers include positive whole numbers, zero, and their negatives (…, −2, −1, 0, 1, 2, …). On a number line, moving left makes a number smaller; moving right makes it larger.
Adding a negative
Adding a negative is the same as subtracting: 5 + (−3) = 5 − 3 = 2.
Order of operations (PEMDAS) tells us to do parentheses and exponents before multiplication/division, then addition/subtraction.