Problem 93 - Elementary Algebra Within Reach

Question

In Exercises 89-96, evaluate the expression. $$ (-6)(-4) $$

Step-by-Step Solution

Answer

The result of (-6)(-4) is 24.

Step 1: Understand the problem

The problem requires evaluating the multiplication of two negative numbers: -6 and -4.

Step 2: Using the rules of multiplication

Multiplication of two negative numbers yields a positive result. Hence, multipling -6 and -4 is similar to multiplying 6 and 4, without their negative signs. Thus, (-6)(-4) = 6 * 4.

Step 3: Solve the multiplication

Multiply 6 by 4, which equals to 24.

Key Concepts

Rules of Multiplication

Multiplying numbers can be straightforward, but adding negative signs into the mix might seem a bit tricky at first. However, the rules of multiplication for negative numbers are uncomplicated and consistent. The basic rule is as follows: when you multiply two negative numbers, the result is positive. Conversely, multiplying a negative number by a positive number results in a negative outcome. It's essential to memorize these rules:

• Negative times negative equals positive: \((-6) \times (-4) = 24\)
• Negative times positive yields negative: \((-6) \times 4 = -24\)
• Positive times positive remains positive: \((6) \times 4 = 24\)

Understanding these rules helps simplify the process of solving mathematical problems that involve both positives and negatives.

Evaluating Expressions

Evaluating expressions involving multiplication isn't just about applying rules but also about understanding the components involved. In the expression \((-6) \times (-4)\), first identify each term and their operations. Here we encounter two crucial tasks:

• Determine the operation: This is multiplication in our exercise.
• Identify the nature of numbers: Both numbers, \(-6\) and \(-4\), are negative.

Once these are recognized, apply the multiplication rules, specifically for negative numbers. Finally, you perform the arithmetic operation (if necessary, simplified to multiplying their absolute values, \(6 \times 4\)), resulting in 24. This approach not only provides the answer but also builds confidence in performing similar tasks.

Algebraic Problem Solving

Algebraic problem solving often involves manipulating expressions to find solutions. In our exercise, we're dealing with simple algebraic operations, but understanding these builds a foundation for more complex problems. The expression \((-6) \times (-4)\) is solved by following systematic algebraic steps:

• Identify the operation and the numbers involved.
• Apply arithmetic or algebraic rules, such as multiplication rules for negative numbers.
• Perform the mathematical operation to find the solution.

Viewing each problem as a set of steps makes it manageable. This systematic approach is vital across algebra, making even challenging problems easier to tackle when broken down into smaller, actionable parts.