Proof of Theorems Using Number Properties

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question 1 of 3

Suppose you're trying to show that the product of two odd numbers is odd. You decide to let a and b represent arbitrary odd numbers. Which is a proper way to rewrite a and b to show that they are two odd numbers?

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1. Suppose you're trying to show that the product of two odd numbers is odd. At the end of your proof, you produce 2(2kl + k + l) + 1, where k and l are integers. How do we know that the integer given by 2(2kl + k + l) + 1 is odd?

2. Suppose you're trying to prove that the product of a negative number and a positive number is negative. You let a be an arbitrary negative number, and b an arbitrary positive number. Which of the following way is a proper way to rewrite a as part of your proof?

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About This Quiz & Worksheet

Review in what ways number properties are used when discussing the multiplication of odd and even numbers with this quiz/worksheet combo. Test your knowledge before viewing the lesson and again after watching it to see what you knew and what you might have learned from this lesson.

Quiz & Worksheet Goals

To successfully complete this quiz, you should be able to:

  • Rewrite equations to show the product of two odd numbers is odd
  • Describe how you know whether an integer is odd in a produced equation
  • Explain how to rewrite 'a' in an equation if you wish to show the product of a positive and negative number is negative
  • Understand how a particular expression in an equation represents a specific type of number
  • Identify a statement that demonstrates the distributive property

Skills Practiced

  • Reading comprehension - ensure that you draw the most important information from the lesson, such as how to rewrite equations to reflect specific information
  • Information recall - access the knowledge you've gained regarding the distributive property
  • Knowledge application - use your knowledge to answer questions about integers and expressions in given examples

Additional Learning

If you need to further clarify this information, you can refer to the lesson titled Proof of Theorems Using Number Properties. Details found in this lesson include:

  • Definitions of even, odd and negative numbers
  • What is addressed in the closure property
  • When a variable is arbitrary
  • How to show that the product of two negative numbers is positive
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