Even vs. Odd: Mastering Multiplication & Division with Negatives

Algebra 1 Grades High School 7:05 Video
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Lesson Description

Explore how the number of negative values affects the outcome of multiplication and division problems. Learn the 'even/odd' rule and apply it to complex expressions.

Video Resource

Multiplying and dividing even and odd numbers of negatives | 7th grade | Khan Academy

Khan Academy

Duration: 7:05
Watch on YouTube

Key Concepts

  • The sign of a product or quotient depends on the number of negative factors.
  • An even number of negative factors results in a positive product or quotient.
  • An odd number of negative factors results in a negative product or quotient.

Learning Objectives

  • Students will be able to determine whether a multiplication or division problem with multiple negative numbers will result in a positive or negative answer.
  • Students will be able to apply the 'even/odd' rule to simplify expressions involving multiplication, division, and exponents with negative bases.

Educator Instructions

  • Introduction (5 mins)
    Briefly review multiplication and division rules with positive and negative numbers when dealing with two numbers. Ask students to recall what they know about multiplying two negatives, a positive and a negative, etc. Preview the video and state that it introduces a shortcut to determine the sign when multiplying many numbers
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Multiplying and dividing even and odd numbers of negatives' for the class. Encourage students to take notes on the key rules and examples provided.
  • Guided Practice (15 mins)
    Work through several example problems with the class. Start with simple multiplication/division of three numbers, then progress to more complex expressions with exponents. Have students come to the board to solve problems and explain their reasoning.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing a variety of problems. Circulate to answer questions and provide assistance as needed.

Interactive Exercises

  • Sign Detective
    Present students with a series of expressions (e.g., -2 * 3 * -1 * -4). Have them determine the sign of the answer without actually calculating the product/quotient. This reinforces the 'even/odd' rule.
  • Exponent Challenge
    Give students expressions with negative bases and exponents (e.g., (-3)^5, (-2)^4). They must determine if the result is positive or negative.

Discussion Questions

  • How does the number of negative signs in a multiplication/division problem affect the final answer?
  • Can you explain in your own words why an even number of negatives results in a positive answer?
  • How can this 'even/odd' rule be helpful when working with exponents and negative bases?

Skills Developed

  • Applying the even/odd rule
  • Simplifying expressions with multiple negative numbers
  • Using the even/odd rule with exponents

Multiple Choice Questions

Question 1:

What is the sign of the result when multiplying 5 negative numbers?

Correct Answer: Negative

Question 2:

Which of the following expressions will result in a positive number?

Correct Answer: -1 * 4 * -2 * -1

Question 3:

What happens when an even number of negative numbers are multiplied together?

Correct Answer: The product is positive

Question 4:

If 'a' is a negative number, what is the sign of a^3?

Correct Answer: Negative

Question 5:

If 'b' is a negative number, what is the sign of b^4?

Correct Answer: Positive

Question 6:

Which expression will result in a negative number?

Correct Answer: (-1)^5

Question 7:

Which expression represents multiplying four negative numbers?

Correct Answer: (-2) * (-2) * (-2) * (-2)

Question 8:

What is the sign of (-1) * (-1) * (-1) / (-1)?

Correct Answer: Positive

Question 9:

If a < 0 and b < 0, what is the sign of (a * a * a) / b?

Correct Answer: Positive

Question 10:

How many negative numbers must be multiplied to get a negative product?

Correct Answer: An odd number

Fill in the Blank Questions

Question 1:

Multiplying an odd number of negative numbers results in a ________ number.

Correct Answer: negative

Question 2:

Multiplying an even number of negative numbers results in a ________ number.

Correct Answer: positive

Question 3:

(-2)^3 equals ________.

Correct Answer: -8

Question 4:

If a is negative, then a^2 is ________.

Correct Answer: positive

Question 5:

If a is positive, then -a is ________.

Correct Answer: negative

Question 6:

A negative divided by a negative is a ________.

Correct Answer: positive

Question 7:

If you multiply 7 negative numbers, the sign of the answer will be ________.

Correct Answer: negative

Question 8:

The expression (-1)^10 evaluates to ________.

Correct Answer: 1

Question 9:

A quotient of 3 negative numbers will result in a ________ number.

Correct Answer: negative

Question 10:

If x < 0, then x * x * x * x will be a ________ number.

Correct Answer: positive

Educational Standards

A1.A.3.2:Simplify polynomial expressions by adding, subtracting, or multiplying. A1.A.3.4:Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x ⨀ y=2x+y.

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