1. The problem is to express the division of 23 by 5 in terms of quotient and remainder. 2. The division algorithm states that for integers $a$ and $b$ (with $b \neq 0$), there exist unique integers $q$ (quotient) and $r$ (remainder) such that: $$a = b \times q + r$$ where $0 \leq r < |b|$. 3. Here, $a = 23$ and $b = 5$. We want to find $q$ and $r$ such that: $$23 = 5 \times q + r$$ with $0 \leq r < 5$. 4. Dividing 23 by 5, we get: $$23 \div 5 = 4 \text{ remainder } 3$$ which means $q = 4$ and $r = 3$. 5. Substitute back to verify: $$5 \times 4 + 3 = 20 + 3 = 23$$ which matches the original number. 6. Therefore, the division expression is: $$23 = 5 \times 4 + 3$$ This confirms the quotient is 4 and the remainder is 3.