Evaluate each expression. [-8+(-4)(-6)/12] / [4-(-3)]

Verified step by step guidance

1. Start by evaluating the expression inside the first set of brackets: \(-8 + \frac{(-4)(-6)}{12}\).
2. Calculate the product \((-4)(-6)\), which is \(24\).
3. Substitute \(24\) back into the expression: \(-8 + \frac{24}{12}\).
4. Divide \(24\) by \(12\) to simplify the expression: \(-8 + 2\).
5. Now, evaluate the expression inside the second set of brackets: \(4 - (-3)\), which simplifies to \(4 + 3\).

Key Concepts

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating expressions, operations within parentheses are performed first, followed by exponents, then multiplication and division from left to right, and finally addition and subtraction.

Negative Numbers and Multiplication

Understanding how to work with negative numbers is crucial in algebra. When multiplying two negative numbers, the result is positive, while multiplying a negative number by a positive number yields a negative result. This concept is essential for correctly evaluating expressions that involve negative values, as seen in the given expression where (-4) and (-6) are multiplied.

Fraction Simplification

Fraction simplification involves reducing fractions to their simplest form, which can make calculations easier. This process includes dividing the numerator and denominator by their greatest common divisor (GCD). In the context of the given expression, simplifying the result of the numerator before dividing by the denominator can lead to a clearer and more manageable solution.