Problem 30 - Beginning and Intermediate Algebra

Question

In each term, give the numerical coefficient. \(\frac{8 x}{9}\)

Step-by-Step Solution

Answer

The numerical coefficient is \(\frac{8}{9}\).

Step 1: Identify the term

Given the term \(\frac{8 x}{9}\), the goal is to find the numerical coefficient, which is the constant factor multiplying the variable.

Step 2: Separate the variable and the numerical part

In \(\frac{8 x}{9}\), identify the variable (\(x\)) and the constant or numerical factor. The fraction \(\frac{8}{9}\) is the numerical part.

Step 3: Determine the numerical coefficient

The coefficient is simply the numerical part of the term, which in this case is \(\frac{8}{9}\).

Key Concepts

Algebra

Algebra is a branch of mathematics that uses symbols, usually letters, to represent numbers and express mathematical relationships. These symbols are known as variables.
Equations in algebra often include both constants (fixed numbers) and variables (symbols representing numbers whose values can change).
For example, in the expression \(\frac{8x}{9}\), \(x\) is the variable.
Algebraic expressions can be simplified or solved to find the value of the unknown variable. By understanding how to manipulate these variables and constants, we can solve various real-world problems.

Terms and Coefficients

In algebra, an expression is made up of terms. Each term is a combination of constants and variables.
For example, in the term \(\frac{8x}{9}\), it's important to identify the parts:

• Numerical part: this is the constant or coefficient, which in this case is \(\frac{8}{9}\)
• Variable part: this is the symbol representing a number, which in this case is \(x\)

The numerical coefficient is the constant that multiplies the variable. It gives the term its weight in equations.
In our example \(\frac{8x}{9}\), the coefficient is \(\frac{8}{9}\). Identifying the numerical coefficient helps understand how much the variable is being scaled in any given term.

Fraction

A fraction represents a part of a whole and is expressed in the form of \(\frac{a}{b}\), where \(a\) is the numerator and \(b\) is the denominator.
In the term \(\frac{8x}{9}\), the fraction \(\frac{8}{9}\) is the numerical coefficient.
Both the numerator and denominator of a fraction play a role in determining this coefficient. The numerator indicates how many parts are taken, while the denominator indicates the total number of equal parts.
Understanding how fractions work helps in dealing with algebraic expressions that include them, simplifying terms, and solving equations effectively.