## Mixed Expressions and Complex Fractions

### Johnny WolfeSanta Rosa District Schools

#### Description

Algebraic expressions such as (a + b/c), and (5 + (x-y)/(x+3)) are called mixed expressions. Changing mixed expressions to rational expressions is similar to changing mixed numbers to improper fractions.

#### Objectives

Understands that numbers can be represented in a variety of equivalent forms using integers, fractions, decimals, and percents, scientific notation, exponents, radicals, absolute value, or logarithms.

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for "Mixed Expressions and Complex Fractions" (see attached file).
- "Mixed Expressions and Complex Fractions" Examples (see attached file).
- "Mixed Expressions and Complex Fractions" Worksheet (see attached file).
- "Mixed Expressions and Complex Fractions" Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for "Mixed Expressions and Complex Fractions" Examples (see attached file).
2. Have marking pens (for overhead).
3. Have "Mixed Expressions and Complex Fractions" Examples (see attached file) prepared and ready to demonstrate to students.
4. Have enough copies of "Mixed Expressions and Complex Fractions" Worksheet (see attached file) for each student.
5. Have enough copies of "Mixed Expressions and Complex Fractions" Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals, solving quadratic equations, and factoring. NOTE: This lesson does not address percents, scientific notation, radicals, absolute value or logarithms. This lesson does not address square roots. Also this lesson does not address inverse relationships.

1. Give students an example of a mixed expression. Review with students how to change a mixed number to an improper fraction and then show the resemblance for changing a mixed expression to a rational expression (see # 1 on attached file "Mixed Expressions and Complex Fractions" Examples). Answer student questions and comments.

2. Work Example # 2 (see attached file "Mixed Expressions and Complex Fractions" Examples). Work with students on recognizing this type of problem as a mixed expression. Answer student questions and comments.

3. Work Example # 3 (see attached file "Mixed Expressions and Complex Fractions" Examples). Answer student questions and comments.

4. Go over definition of a complex fraction then give some examples (see # 4 on attached file "Mixed Expressions and Complex Fractions" Examples). Answer student questions and comments.

5. Work Example # 5 (see attached file "Mixed Expressions and Complex Fractions" Examples). Answer student questions and comments.

6. Do Example # 6 (see attached file "Mixed Expressions and Complex Fractions" Examples). Go over shortcut. Answer student questions and comments.

7. Help students develop the Simplifying Complex Fraction Rule (see # 7 on attached file "Mixed Expressions and Complex Fractions" Examples).

8. Work Example # 8 (see attached file "Mixed Expressions and Complex Fractions" Examples). Answer student questions and comments.

9. Work example # 9 (see attached file "Mixed Expressions and Complex Fractions" Examples). Answer student questions and comments.

10. Ease student apprehension and nervousness. Discuss how to separate the expressions and then put them back together (see # 10 on attached file "Mixed Expressions and Complex Fractions" Examples). Answer student questions and comments.

11. Work example # 11 (see attached file "Mixed Expressions and Complex Fractions" Examples). Answer student questions and comments.

12. Distribute the "Mixed Expressions and Complex Fractions" Worksheet (see attached file).

13. Distribute the "Mixed Expressions and Complex Fractions" Checklist (see attached file). Describe what is required from the students based on the checklist.
14. The student will write their response on the worksheet.

15. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

The student worksheet will be collected and scored according to the "Mixed Expressions and Complex Fractions" Checklist (see attached file).

#### Extensions

Give students the solution to a complex fraction and have them develop as many expressions as they can that equal the given complex fraction.