1. Problem: Evaluate $8\times 3 - 3\times 5 + \dfrac{45}{15}$. 2. Formula and rules: Use the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division evaluated left to right, then Addition and Subtraction evaluated left to right. 3. Identify operations: The expression contains two multiplications and one division and no parentheses or exponents. 4. Compute multiplications and the division first, evaluating left to right. - Compute $8\times 3 = 24$. - Compute $3\times 5 = 15$. - Compute $\dfrac{45}{15} = 3$. 5. Substitute the computed values into the expression to get $24 - 15 + 3$. 6. Evaluate left to right: $24 - 15 = 9$. 7. Then compute $9 + 3 = 12$. 8. Final answer: The value of the expression is $12$.