Consider the ring \((\mathbb{Z}, +, \times)\), where \(\mathbb{Z}\) represents the set of integers, \(+\) denotes the addition operation, and \(\times\) denotes the multiplication operation. In this context, we can express \(9 + 1\) as \((9) * (1) = 10\), where \((9)\) and \((1)\) are the equivalence classes of integers modulo 10 under addition.