## Multiplying Rational Numbers

### Johnny WolfeSanta Rosa District Schools

#### Description

To multiply rational expressions, you multiply the numerators and multiply the denominators.

#### 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 "Multiplying Rational Numbers" (see attached file).

- "Multiplying Rational Numbers" Examples (see attached file).

- "Multiplying Rational Numbers" Worksheet (see attached file).

- "Multiplying Rational Numbers" Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for "Multiplying Rational Numbers" Examples (see attached file).

2. Have marking pens (for overhead).

3. Have "Multiplying Rational Numbers" Examples(see attached file) prepared and ready to demonstrate to students.

4. Have enough copies of "Multiplying Rational Numbers" Worksheet (see attached file) for each student.

5. Have enough copies of "Multiplying Rational Numbers" 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 decimals, percents, scientific notation, radicals, abolute value, or logarithms. This lesson does not address square roots or inverse relationships. This lesson does not address square roots.

1. Describe the process for multiplying rational numbers (see # 1 on attached file "Multiplying Rational Numbers" Examples). Answer student questions and comments.

2. Do Example # 2 (see attached file "Multiplying Rational Numbers" Examples). Discuss why denominators cannot equal zero. Answer student questions and comments.

3. Do Example # 3 (see attached file "Multiplying Rational Numbers" Examples). Discuss GCF and reducing fractions to simplest form. Answer student questions and comments.

4. Discuss Thought Provoker (see # 4 on attached file "Multiplying Rational Numbers" Examples). Answer student questions and comments.

5. Discuss Thought Provoker (see # 5 on attached file "Multiplying Rational Numbers" Examples). Answer student questions and comments.

6. Review with students the Cross-Product rule (see # 6 on attached file "Multiplying Rational Numbers" Examples). Answer student questions and comments.

7. Do Example # 7 (on attached file "Multiplying Rational Numbers" Examples). Stress that each polynomial must be written in factored form and then simplified. Answer student questions and comments.

8. Work example # 8 (see attached file "Multiplying Rational Numbers" Examples). Answer student questions and comments.

9. Work example # 9 (see attached file "Multiplying Rational Numbers" Examples). Answer student questions and comments.

10. Distribute the "Multiplying Rational Numbers" Worksheet(see attached file).

11. Distribute the "Multiplying Rational Numbers" Checklist (see attached file). Describe what constitutes an "A," "B," "C," "D," and an "F" in the Checklist.

12. The student will write their response on the worksheet.

13. 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 "Multiplying Rational Numbers" Checklist (see attached file).

#### Extensions

Give the students a rectangle with rational length and width. Have the students determine its area.