Problem 2 - Prealgebra

Question

Evaluate each expression if \(a=5, b=12,\) and \(c=4\) $$a-3$$

Step-by-Step Solution

Answer

The value of the expression is 2.

Step 1: Identify the Expression

The given expression to evaluate is \(a - 3\).

Step 2: Substitute the Value

Replace \(a\) in the expression with its given value, which is 5. This gives us \(5 - 3\).

Step 3: Perform the Subtraction

Subtract 3 from 5 to get the result: \(5 - 3 = 2\).

Key Concepts

Understanding the Substitution Method

The substitution method is a key concept in algebra and problem-solving. It's a process used to replace variables with specific values, allowing for the evaluation and simplification of expressions. When you encounter an expression like \(a - 3\), and you're given that \(a = 5\), you will use the substitution method to replace \(a\) with 5. This transforms the expression into numerical form, making it possible to solve it using basic arithmetic operations.Using substitution:- Identify the variables in the expression.- Replace these variables with their given values.- This simplifies the expression so that you can perform arithmetic calculations easily.By mastering the substitution method, you lay a solid foundation for handling more complex algebraic problems. It helps in making abstract expressions tangible by using numbers you can work with.

Mastering Arithmetic Subtraction

Arithmetic subtraction is a fundamental operation in mathematics. It involves finding the difference between two numbers. In simpler terms, it means taking away one number from another.In the expression \(5 - 3\), you perform subtraction as follows:- Start with the larger number at the front, which is 5.- Identify the number you need to subtract, which is 3.- Count backwards from 5 to 3 to find the difference.The result of \(5 - 3\) is 2. Subtraction can often appear in various math problems, and becoming comfortable with it ensures that you can tackle different problems with ease.

Efficient Problem-Solving Steps

Solving math problems can seem challenging at first, but following a structured approach can simplify them. Here are the key problem-solving steps to follow: - **Step 1: Identify the Expression**: Understand what the problem is asking. Look at the variables present and the arithmetic operations required. - **Step 2: Substitute Values**: As soon as you identify the values given for the variables, substitute these numbers in place of the variables in the expression. - **Step 3: Calculate**: Perform the necessary arithmetic operations, such as addition, subtraction, or multiplication, to simplify the expression and find the solution. By following these steps, you can break down complex problems into manageable tasks. This approach not only helps in solving the particular exercise but also improves your overall problem-solving skills by reinforcing a methodical process.