Evaluate each expression. See Example 5. -8 + (-4) (-6) ÷ 12 4 - (-3)

Verified step by step guidance

1. First, rewrite the expression clearly to understand the order of operations: \(-8 + (-4) \times (-6) \div 12 \times 4 - (-3)\).
2. Apply the order of operations (PEMDAS/BODMAS): start with multiplication and division from left to right before addition and subtraction.
3. Calculate the product \((-4) \times (-6)\), remembering that multiplying two negative numbers results in a positive number.
4. Next, divide the result of the multiplication by 12, then multiply that quotient by 4, following the left-to-right rule for multiplication and division.
5. Finally, perform the addition and subtraction operations in order: add \(-8\) to the result from the previous step, then subtract \(-3\) (which is equivalent to adding 3).

Key Concepts

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses first, then multiplication and division from left to right, followed by addition and subtraction from left to right. This ensures consistent and correct evaluation of expressions.

Multiplication and Division of Negative Numbers

Multiplying or dividing negative numbers follows specific rules: the product or quotient of two negatives is positive, while that of a positive and a negative is negative. Understanding these rules is essential for correctly simplifying expressions involving negative values.

Simplifying Algebraic Expressions

Simplifying expressions involves combining like terms and performing arithmetic operations step-by-step to reduce the expression to its simplest form. This process requires careful attention to signs and operation order to avoid errors.