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For operations like adding and multiplying, the key concept is understanding the "identity element." The identity element, when used in the operation, leaves the original number unchanged. For addition, it's 0 (x + 0 = x). For multiplication, it's 1 (x * 1 = x). It's like starting with a fresh batch of cookies in Cookie Clicker – you need that initial 1 to get the whole operation going!