Problem 29 - Beginning and Intermediate Algebra

Question

In each term, give the numerical coefficient. \(\frac{2 x}{5}\)

Step-by-Step Solution

Answer

The numerical coefficient is \( \frac{2}{5} \).

Step 1: Identify the Term

The term given is \(\frac{2x}{5}\).

Step 2: Separate the Coefficients

In the term \(\frac{2x}{5}\), identify the numerical part that is multiplied by the variable \(x\).

Step 3: Simplify the Coefficient

The numerical coefficient can be separated by first understanding that \(\frac{2x}{5}\) is equivalent to \(\frac{2}{5}x\). The numerical coefficient does not change when you take the term apart in this way.

Key Concepts

Understanding Algebraic Terms

An algebraic term is a combination of numbers, variables, and sometimes exponentiation, joined together by multiplication or division. For instance, in the term \(\frac{2x}{5}\), we have a numerical part and a variable. Here, \(\frac{2}{5}\) is a number that multiplies the variable \(\text{x}\). Algebraic terms can be simple like \(3y\), or more complex like \(7a^2b\). Understanding algebraic terms fully is important when manipulating and simplifying expressions or equations.

Simplification

Simplification in algebra involves reducing expressions to their simplest form. This can mean combining like terms or reducing fractions. Taking the term \(\frac{2x}{5}\), the simplification helps in finding its numerical coefficient. By recognizing that dividing by 5 is the same for both numbers and variables, the term simplifies to \( \frac{2}{5}x \). This simplification makes it easy to see that \(\frac{2}{5}\) is the numerical coefficient. Simplifying algebraic expressions helps in solving equations more efficiently and understanding the role of each component within terms.

Variables in Algebra

Variables represent unknown numbers and are typically denoted by letters such as x, y, or z. In the term \(\frac{2x}{5}\), the variable is \( x \). Variables can stand alone or be multiplied by constants or other variables. In an algebraic equation or expression, the variable's value can change depending on the equation's constraints and components. Working with variables is fundamental to solving algebraic expressions, where terms like \( \frac{2}{5} x \) are simplified to understand the relationship between numerical coefficients and variables.