Select your language

Suggested languages for you:
Log In Start studying!
StudySmarter - The all-in-one study app.
4.8 • +11k Ratings
More than 3 Million Downloads
Free
|
|

All-in-one learning app

  • Flashcards
  • NotesNotes
  • ExplanationsExplanations
  • Study Planner
  • Textbook solutions
Start studying

Mixed Expressions

Mixed Expressions

Different types of expressions exist to communicate various algebraic functions. The type of expression explored in this article is the mixed expression. First, recall that a rational expression is an algebraic fraction whose numerator and denominator are both polynomials. For example, is a rational expression. Now, remember that mixed fractions are a combination of a whole number and a proper fraction, for example, . Similarly, a mixed expression is a combination of monomials and rational expressions. Therefore, is an example of a mixed expression.

Mixed expressions: Meaning and examples

Consider the expression: . Here, 3 is a monomial and is a rational expression. Such an expression is called a mixed expression.

A mixed expression is a combination of monomials and rational expressions.

The following are more examples of mixed expressions:

From the second example, you can see that a variable acting as the monomial in the mixed expression is possible.

Converting mixed expressions to rational expressions

Mixed expressions are commonly converted to rational expressions. The process of converting mixed expressions to rational expressions is also similar to the method of converting mixed fractions to improper fractions. To convert a mixed expression involving a monomial and a rational expression to a rational expression, use the following steps:

  1. Write down the denominator of the rational expression of the mixed expression as the denominator of the converted mixed expression.
  2. In the numerator, add the numerator of the rational expression of the original mixed expression with the monomial multiplied by the denominator of the rational expression.
  3. Once the addition is performed, the result is the required rational expression.

Simplifying mixed expressions: Solved examples

Let's take a closer look at how to simplify mixed expressions with the following two solved examples.

Express the following mixed expression as a rational expression:

Solution

Express the following mixed expression as a rational expression:

Solution

Mixed expressions - Key takeaways

  • A mixed expression is a combination of monomials and rational expressions.
  • An example of a mixed expression is:
  • Mixed expressions are commonly converted into rational expressions using the following steps:
    1. Write down the denominator of the rational expression of the mixed expression as the denominator of the converted mixed expression.
    2. In the numerator, add the numerator of the rational expression of the original mixed expression with the monomial multiplied by the denominator of the rational expression.
    3. Once the addition is performed, the result is the required rational expression.

Frequently Asked Questions about Mixed Expressions

A mixed expression is a combination of monomials and rational expressions.

To convert a mixed expression involving a monomial and a rational expression to a rational expression, follow the following steps:

1) Write down the denominator of the rational expression of the mixed expression as the denominator of the converted mixed expression.

2) In the numerator, add the numerator of the rational expression of the original mixed expression with the monomial multiplied by the denominator of the rational expression.

3) Once the addition is performed, the result is the required rational expression.

To convert a mixed expression involving a monomial and a rational expression to a rational expression, follow the following steps:

1) Write down the denominator of the rational expression of the mixed expression as the denominator of the converted mixed expression.

2) In the numerator, add the numerator of the rational expression of the original mixed expression with the monomial multiplied by the denominator of the rational expression.

3) Once the addition is performed, the result is the required rational expression.

To convert a mixed expression involving a monomial and a rational expression to a rational expression, follow the following steps:

1) Write down the denominator of the rational expression of the mixed expression as the denominator of the converted mixed expression.

2) In the numerator, add the numerator of the rational expression of the original mixed expression with the monomial multiplied by the denominator of the rational expression.

3) Once the addition is performed, the result is the required rational expression.

Final Mixed Expressions Quiz

Question

What is a rational expression?

Show answer

Answer

A rational expression is an algebraic fraction whose numerator and denominator are both polynomials.

Show question

Question

State whether the following statement is true or false:

A mixed expression is a combination of monomials and rational expressions.

Show answer

Answer

True

Show question

Question

State whether the following statement is true or false:

A mixed expression must contain exactly 1 monomials.

Show answer

Answer

False

Show question

Question

State whether the following statement is true or false:

A mixed expression must contain exactly 1 polynomial.

Show answer

Answer

False

Show question

More about Mixed Expressions
60%

of the users don't pass the Mixed Expressions quiz! Will you pass the quiz?

Start Quiz

Discover the right content for your subjects

No need to cheat if you have everything you need to succeed! Packed into one app!

Study Plan

Be perfectly prepared on time with an individual plan.

Quizzes

Test your knowledge with gamified quizzes.

Flashcards

Create and find flashcards in record time.

Notes

Create beautiful notes faster than ever before.

Study Sets

Have all your study materials in one place.

Documents

Upload unlimited documents and save them online.

Study Analytics

Identify your study strength and weaknesses.

Weekly Goals

Set individual study goals and earn points reaching them.

Smart Reminders

Stop procrastinating with our study reminders.

Rewards

Earn points, unlock badges and level up while studying.

Magic Marker

Create flashcards in notes completely automatically.

Smart Formatting

Create the most beautiful study materials using our templates.

Sign up to highlight and take notes. It’s 100% free.