Problem 71 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. $$ -8.3(-1.2)(p) \text { when } p=3 $$

Step-by-Step Solution

Answer

The evaluated expression when \( p=3 \) is 29.88.

Step 1: Understand the Exercise

The exercise is asking to evaluate the given expression, \( -8.3(-1.2)(p) \), by substituting the given value of the variable \( p=3 \).

Step 2: Substitute the Value

Substitute the given value of the variable \( p \) into the expression. So the equation becomes \( -8.3(-1.2)(3) \) .

Step 3: Performing Multiplication Operations

Perform the multiplication operations: First multiply -8.3 by -1.2 to get 9.96, then multiply 9.96 by 3 to get 29.88.

Key Concepts

Variable Substitution

Variable substitution in algebra means replacing a variable with a given value. In our exercise, we have the expression \(-8.3(-1.2)(p)\), and we are told that \(p = 3\).
To substitute, we simply replace every instance of the variable \(p\) with 3 in the expression.

• Original expression: \(-8.3(-1.2)(p)\)
• Substitute \(p = 3\): \(-8.3(-1.2)(3)\)

This step prepares the expression for further operations. Without substitution, we cannot evaluate the expression properly. It is important to double-check that the substitution is done correctly to avoid errors in later calculations.

Expression Evaluation

Expression evaluation involves simplifying the expression step by step until you find its value. After substituting the variable, the expression \(-8.3(-1.2)(3)\) is ready for evaluation.
At this stage, the expression is transformed into a sequence of multiplication operations. Consider each pair of numbers one at a time and simplify as follows:

• Multiply \(-8.3\) by \(-1.2\)
• Next, use the result from the first multiplication to multiply with 3

Following these steps ensures accurate and logical progression through the problem. Keeping track of each result is crucial, as skipping steps or rushing can lead to mistakes. Practice will make you more comfortable with evaluating increasingly complex expressions.

Multiplication Operations

Multiplication operations require you to multiply two numbers to find their product. In the expression \(-8.3(-1.2)(3)\), the task is to multiply three numbers together.
Proceed by handling the operations in pairs:

• First, multiply \(-8.3\) and \(-1.2\). Negative multiplied by negative gives a positive. \((-8.3) \times (-1.2) = 9.96\).
• Then, take the result \(9.96\) and multiply by 3.
• Thus, \(9.96 \times 3 = 29.88\).

Multiplication is often straightforward, but remember the rule for sign changes. Multiplying two negatives results in a positive product. Keeping these foundational rules in mind will help ensure accuracy in your results.