Problem 23 - Fundamentals of Mathematics

Question

For problems \(17-46\), find the value of each expression. $$ m-4, \text { if } m=4 $$

Step-by-Step Solution

Answer

The value of the expression is 0.

Step 1: Substitute the given value of m

The problem asks us to find the value of the expression \(m - 4\) when \(m = 4\). Begin by substituting \(4\) for \(m\) in the expression.

Step 2: Compute the expression

Now, compute the expression by performing the subtraction: \(4 - 4\).

Step 3: Simplify the result

The result of the subtraction \(4 - 4\) is \(0\). Thus, the expression simplifies to \(0\).

Key Concepts

Subtraction

Subtraction is one of the four basic arithmetic operations. It is used to determine the difference between numbers. Imagine you have 4 apples, and you give away all 4. How many are left? Zero apples! This is subtraction in action.
The subtraction of two numbers can be represented as:

• Minuend: the number from which you subtract (here, 4)
• Subtrahend: the number you subtract (also 4)
• Difference: the result after subtraction (0 in this example)

When we write this operation as a math expression, we show it as: \[4 - 4 = 0\].
The order of numbers is very important in subtraction, as changing the order can give you different results. Always remember: minuend first, then subtrahend! This will ensure you subtract correctly.

Substitution

Substitution is a simple yet powerful concept in algebra. It involves replacing a variable in an expression with a given number. In our exercise, the value of the variable \(m\) is given as 4.
Substitution allows us to evaluate expressions easily:

• Identify the variable in the expression - here, it is \(m\).
• Replace \(m\) with 4 in the expression \(m - 4\).

Once you've replaced the variable, the expression becomes \(4 - 4\). By substituting, you essentially convert a general expression into a simpler numeric operation!
It's a crucial step that makes complex expressions manageable and tells you what the expression evaluates to for specific values of the variable.

Variable Evaluation

Variable evaluation is the process of finding the actual numerical result of an expression by performing any operations after substitution has been done. After substituting \(m = 4\), the expression \(m - 4\) becomes \(4 - 4\).
To evaluate:

• Perform the arithmetic operations - first subtraction in this case.
• The expression \(4 - 4\) simplifies to \(0\).
• Thus, the value of the expression when \(m\) is 4 is 0.

Evaluation is about interpreting and simplifying the expression completely. It involves solving any operations and reducing the expression to its simplest form.
Remember, with correct substitution and careful arithmetic, you can evaluate expressions precisely, providing meaningful results in any given context.