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Chapter 1: Problem 65

List the terms in each expression. $$ 2 a+\frac{a}{b}+5 b $$

Short Answer

Expert verified
The terms are \(2a\), \(\frac{a}{b}\), and \(5b\).

Step by step solution

01

Identify the terms in the expression

The expression given is \(2a + \frac{a}{b} + 5b\). Terms in an expression are separated by addition or subtraction operators. Look for these operators to isolate each term.
02

List the individual terms from the expression

In the given expression, \(2a + \frac{a}{b} + 5b\), the terms are separated by the plus signs (+). Thus, the terms are: 1. \(2a\) 2. \(\frac{a}{b}\) 3. \(5b\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Terms in Algebra
In algebra, an expression is a combination of numbers, variables, and operations.
The simplest components of an expression are known as 'terms'.
Terms are the separate parts of an algebraic expression that are added or subtracted.
For instance, in the expression \(2a + \frac{a}{b} + 5b \), each part between the plus signs is a term.
In this example:
  • \(2a\)
  • \(\frac{a}{b}\)
  • \(5b\)
are the terms.
Terms can consist of variables, coefficients (numbers in front of the variables), and constants (standalone numbers).
Understanding what constitutes a term is the first step in working with algebraic expressions.
Addition and Subtraction in Expressions
When working with algebraic expressions, it's crucial to recognize the role of addition and subtraction.
These operations separate the expression into terms.
For example, in the expression \(2a + \frac{a}{b} + 5b \), the plus signs separate the expression into three distinct terms.
Each term can then be manipulated individually where needed.
Here are some key points to remember:
  • Add like terms (terms with the same variables and exponents) to simplify an expression.
  • Subtract like terms in the same way.
  • Unlike terms (terms with different variables or exponents) cannot be combined by addition or subtraction.
By understanding how addition and subtraction work in expressions, you can simplify complex algebraic problems.
Isolating Terms
Isolating terms in an algebraic expression is a fundamental skill required to solve equations.
To isolate a term means to get it by itself on one side of the equation.
Here's how to do it:
  • Identify the terms you need to isolate.
  • Use addition or subtraction to move other terms to the opposite side of the equation.
  • For example, in the expression \(2a + \frac{a}{b} = 5b \), you might want to isolate \(2a\).
  • This involves moving \(\frac{a}{b} \) to the other side: \(2a = 5b - \frac{a}{b} \).
By following these steps, you can isolate and solve for specific variables, making complex equations simpler to handle.
Practice isolating terms to strengthen your algebra skills!

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