Problem 9 - Elementary Algebra

Question

\(\frac{1}{8} m-\frac{5}{8} m+\frac{3}{8}\)

Step-by-Step Solution

Answer

-\frac{1}{2}m + \frac{3}{8}

Step 1: Combine Like Terms

Identify and combine the like terms involving the variable m. Here we have \(\frac{1}{8}m - \frac{5}{8}m\).

Step 2: Perform Subtraction

Subtract the coefficients of m: \(\frac{1}{8} - \frac{5}{8} = -\frac{4}{8} = -\frac{1}{2} \). Thus, combining the terms gives \(-\frac{1}{2}m\).

Step 3: Add the Constant Term

Combine the result with the constant term: \(-\frac{1}{2}m + \frac{3}{8} \).

Key Concepts

coefficients

In algebra, a **coefficient** is a number that is multiplied by a variable in an algebraic expression. For example, in the term \(\frac{1}{8}m\), \(\frac{1}{8}\) is the coefficient and \m\ is the variable. Coefficients tell us how much of the variable we have. If there is no numerical number next to the variable, the coefficient is understood to be 1. Understanding coefficients is crucial because they help us simplify expressions and solve equations. In the provided exercise, the coefficients are \(\frac{1}{8}\) and \(\frac{5}{8}\) for the variable \m\. By combining these coefficients, we can simplify the expression.

variable subtraction

Variable subtraction involves taking terms with variables and subtracting them by manipulating their coefficients. When subtracting variables, you only subtract the coefficients while the variable remains unchanged. Let's break down the process:

• Identify the like terms. Like terms are terms that have the same variable raised to the same power. In this case, \(\frac{1}{8}m\) and \(\frac{5}{8}m\) are like terms.
• Subtract the coefficients: \(\frac{1}{8} - \frac{5}{8}\)
• Perform the subtraction to get the new coefficient: \(\frac{1}{8} - \frac{5}{8} = -\frac{4}{8} = -\frac{1}{2}\)

After subtracting the coefficients, we get the result \(-\frac{1}{2}m\). This process helps us simplify complex expressions and makes solving equations more manageable.

constants in algebra

A **constant** in algebra is a fixed value that does not change. Unlike variables that can represent different numbers, constants have a single, definite value. For example, in the term \(\frac{3}{8}\), \(\frac{3}{8}\) is a constant. Constants play an essential role in algebraic expressions and equations because they add fixed values to the variable terms. In the given exercise, after combining the like terms and subtracting the coefficients, we still have the constant term \(\frac{3}{8}\). Thus, the final expression becomes:

• Combine the simplified like terms with the constant: \(-\frac{1}{2}m + \frac{3}{8}\)

Accounting for constants ensures the algebraic expression is complete and accurately represents the intended values.