Problem 60 - Algebra 1

Question

Evaluate the expression for the given value of the variable. $$ 5 y^{5} \text { when } y=2 $$

Step-by-Step Solution

Answer

The result is 27.5.

Step 1: Identify and Substitute

In the expression 'c + 15', 'c' is a variable and the exercise tells us to substitute 'c = 12.5', so replace 'c' with '12.5'.

Step 2: Evaluate the Expression

After substituting, we have the expression '12.5 + 15'. Add 12.5 and 15 to simplify the expression.

Key Concepts

Variable Substitution

Variables are symbols used to represent numbers in mathematical expressions, enabling flexibility and generalization in calculations. In our exercise, the variable is \(c\), which has the given value. To substitute means to replace the variable with a specified value. This action allows us to transform a general expression into a specific numeric expression.
For example:

• Given the expression \(c + 15\) and instructed that \(c = 12.5\), we substitute \(c\) with \(12.5\).
• This substitution changes the expression to \(12.5 + 15\).

Variable substitution is a foundational concept in algebra that simplifies problem-solving by allowing the manipulation of expressions with specific numeric values. This transformation is often the first critical step before further evaluation or simplification.

Evaluating Expressions

Once the variables in an expression are replaced with their specific values, the next step is to evaluate the expression. Evaluating means performing the calculations required to simplify the expression to a single number.
In our example:

• After substituting, the expression becomes \(12.5 + 15\).
• The task now is to calculate the sum to find the value of the expression.

The process of evaluating includes following the mathematical operations as they appear, which in our case is addition.
Always remember to perform calculations accurately, observing proper arithmetic procedures, to ensure you arrive at the correct answer.

Basic Arithmetic Operations

Basic arithmetic operations form the backbone of evaluating algebraic expressions. For this problem, we focus on addition, which is a straightforward operation of combining numbers.
When performing addition:

• Align the numbers correctly if working on paper.
• Add each digit starting from the rightmost part (for whole numbers), applying any carry-over as needed.

For our expression \(12.5 + 15\):- Calculate precisely: First, add the fractions (if any) then proceed to whole numbers. The correct evaluation gives the result of \(27.5\).
Operations like addition are fundamental and frequently occur in algebra, serving as building blocks for more complex computations.
Understanding and mastering basic arithmetic helps in efficiently tackling more challenging problems.