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# 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:

## 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?

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Answer

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

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Question

State whether the following statement is true or false:

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

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Answer

True

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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

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