Problem 54 - Prealgebra

Question

Evaluate each expression. $$4 a, a=-6$$

Step-by-Step Solution

Answer

The value of the expression is -24.

Step 1: Understand the Problem

We need to evaluate the expression given a specific value of the variable. The expression is \(4a\), and we need to substitute \(a = -6\) into this expression.

Step 2: Substitute the Value of the Variable

Replace the variable \(a\) in the expression with the given value \(-6\). So, the expression becomes \(4(-6)\).

Step 3: Perform the Multiplication

Calculate the multiplication of \(4\) and \(-6\). The product is \(4 \times -6 = -24\).

Key Concepts

Evaluation of Expressions

When faced with the task of evaluating an expression, you are essentially finding its value by substituting variables with their given numerical amounts. This process is fundamental in algebra, as it helps to make abstract concepts more concrete. For this particular problem, the expression given is \(4a\), where \(a = -6\). The goal is simply to find the actual number that represents this expression when \(a\) is substituted with \(-6\).

Here’s how you can generally approach evaluation of expressions:

• Identify the variable in the expression.
• Carefully substitute the variable with the given number.
• Simplify the expression by performing basic arithmetic operations.

This substitution process transforms the algebraic expression into a single arithmetic operation that can be easily solved.

Multiplication

Multiplication is an essential arithmetic operation that involves scaling one number by another. In this expression, the term \(4a\) implies that \(4\) is to be multiplied by the value of \(a\), which is given as \(-6\). Multiplication is straightforward when dealing with positive numbers, but when one or both of the numbers are negative, it is important to understand the rules that govern such operations.

When multiplying numbers, whether positive or negative:

• A positive number multiplied by a positive number results in a positive product.
• A positive number multiplied by a negative number results in a negative product.
• Likewise, a negative number multiplied by a positive number results in a negative product.
• Two negative numbers multiplied together yield a positive product.

In our expression, \(4 \times -6\) results in \(-24\), since a positive number multiplied by a negative number gives a negative product.

Negative Numbers

Negative numbers are numbers less than zero, situated on the left side of the zero on the number line. They are used to represent values less than nothing, often necessary for indicating a loss, decrease, or reversal. Understanding how to work with negative numbers is crucial in algebra and arithmetic.

Here are important points to keep in mind when working with negative numbers:

• Adding a negative number is equivalent to subtracting that number from the other number.
• Subtracting a negative number is equivalent to adding that number.
• When multiplying, as mentioned earlier, a positive times a negative yields a negative, whereas two negatives multiplied give a positive.

In the context of our problem, after substituting \(a = -6\) into the expression \(4a\), we perform the multiplication \(4 \times -6\), which results in \(-24\). Understanding these rules helps ensure accurate calculations in more complex algebraic expressions.