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Mastering Multiplication and Division of Real Numbers: Core Concepts and Examples

This chapter focuses on the essential rules for multiplying and dividing real numbers, specifically integers. It covers the effects of multiplying and dividing numbers based on their signs, highlighting that the product of like signs is positive while the product of unlike signs is negative. Additionally, it introduces key properties, including the property of zero and the identity property. Examples and exercises guide students through finding products and quotients, reinforcing their understanding of these fundamental mathematical operations.

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Mastering Multiplication and Division of Real Numbers: Core Concepts and Examples

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  1. Chapter 2.4/2.6 Notes: Multiplying and Dividing Real Numbers Goal: You will multiply and divide real numbers.

  2. Rules for Multiplying Integers: • Multiplying two numbers with the same sign will ALWAYS equal a positive number. i.e. 4(8) = ___ i.e. -9(-5) = ____ • Multiplying two numbers with different signs will ALWAYS equal a negative number. i.e. 4(-9) = ____ i.e. -10(50) = ____

  3. Find the product. Ex.1: 2(-5)(-4) Ex.2: Ex.3: -14(2)(-4) • Properties of Multiplication: • Property of Zero: The product of a number and 0 is 0. i.e. -3 • 0 = ___ i.e. 5(0) = ____

  4. The identity property states that the product of a number a and 1 is a. The number 1 is called the multiplicative identity. • The reciprocal of a nonzero number a, written as , is called the multiplicative inverse of a. i.e. ____ i.e. ___ i.e. The multiplicative inverse of is _____.

  5. Rules for Dividing Integers: • Dividing two numbers with the same sign will ALWAYS equal a positive number. i.e. 28 ÷ 7 = ___ i.e. -15 ÷ -3 = ___ • Dividing two numbers with different signs will ALWAYS equal a negative number. i.e. -16 ÷ 4 = ___ i.e. 99 ÷ -11 = ___

  6. Find the quotient. Ex.4: 68 ÷ -4 Ex.5: -45 ÷ -15 Ex.6: Ex.7:

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