Problem 100 - Algebra 1

Question

Evaluate the expression. $$-16+(-6) \cdot(-8)$$

Step-by-Step Solution

Answer

32

Step 1: Solve the Multiplication

Begin by solving the multiplication within the expression. That is \(-6 \cdot -8\), which equals 48. Rule in mathematics: the product of two negative numbers is a positive number.

Step 2: Perform the Addition

Now, replace in the original equation the multiplication expression with the result obtained at step 1. The expression is now \(-16 + 48\). This equals 32.

Step 3: Solution

The result of the expression \(-16+(-6) \cdot(-8)\) after following the order of operations is 32. Always remember to follow the order of operations and that the product of two negative numbers is a positive number.

Key Concepts

Expression Evaluation

When faced with an algebraic expression like \(-16 + (-6) \cdot (-8)\), the task is to evaluate or simplify it down to a single number.The goal is to follow a given set of mathematical rules known as the Order of Operations.This order dictates which mathematical operations should be performed first to ensure accurate and consistent results.

This can be remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).This expression contains multiplication and addition, so according to the order:

• The multiplication \((-6) \cdot (-8)\) must be completed first.
• Once the first operation is resolved, move to the addition by plugging the result into the expression.

Always tackle operations one step at a time to avoid mistakes.

Multiplication of Integers

Multiplying integers, especially when dealing with negative numbers, is made simple by understanding the basic rules.These apply regardless of whether you're multiplying just two numbers or more.

For \((-6) \cdot (-8)\), both numbers are negative. The rule to remember is:

• When multiplying two integers with the same sign, the result is positive.
• Negative \(\times\) Negative = Positive
• So, \((-6) \cdot (-8) = 48\)

By mastering these rules, you can tackle more complex expressions effortlessly.

Addition with Integers

After resolving the multiplication, you're left with a new expression: \(-16 + 48\). Now, focus on adding integers. This involves a few intuitive steps:

• If both numbers were positive or negative, you'd simply add their absolute values and keep the original sign.
• In this case, \(-16\) is negative and 48 is positive.

The approach here is to subtract the smaller absolute value from the larger one:

• Subtract 16 (absolute value of \(-16\)) from 48.
• This gives 32, and since 48 is positive, the result remains positive.

This intuitive balance helps manage expressions with mixed signs effectively.