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Chapter 2 – Properties of Real Numbers

Chapter 2 – Properties of Real Numbers. 2.5 – Multiplication of Real Numbers. 2.5 – Multiplication of Real Numbers. Today we will be learning how to: Multiply real numbers using properties of multiplication Multiply real numbers to solve real- life problems.

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Chapter 2 – Properties of Real Numbers

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  1. Chapter 2 – Properties of Real Numbers 2.5 – Multiplication of Real Numbers

  2. 2.5 – Multiplication of Real Numbers • Today we will be learning how to: • Multiply real numbers using properties of multiplication • Multiply real numbers to solve real-life problems

  3. 2.5 – Multiplication of Real Numbers • Suppose you download songs from iTunes. The songs are automatically charged to your parents credit card. At the end of each month, you must pay your parents back. Suppose each song costs $2.00 and you download 8 songs. How can you use integers to model the debt you owe your parents?

  4. 2.5 – Multiplication of Real Numbers • Remember: Multiplication can be modeled as repeated addition. • Example: 4(-2) = • (-2) + (-2) + (-2) + (-2) = • -8

  5. 2.5 – Multiplication of Real Numbers • Complete the lists • The product of a positive number and a negative number is:

  6. 2.5 – Multiplication of Real Numbers • Example 1 Find the product • (9)(-3) • 8(- ½ )(-6) • (-3)3 • (-2)(- ½ )(-3)(-5)

  7. 2.5 – Multiplication of Real Numbers • Multiplying Real Numbers • The product of two real numbers with the same sign is the product of their absolute values. • The product is positive • The product of two real numbers with different signs is the OPPOSITE of the product of their absolute values. • The product is negative

  8. 2.5 – Multiplication of Real Numbers • Example 2 Find the product. • (-n)(-n) • (-4)(-x)(-x)(x) • -(b)3 • (-y)4

  9. 2.5 – Multiplication of Real Numbers • Properties of Multiplication • Commutative Property • The order in which two numbers are multiplied does not change the product • a · b = b · a • 3(-2) = (-2)3

  10. 2.5 – Multiplication of Real Numbers • Properties of Multiplication • Associative Property • The way you group three numbers when multiplying does not change the product • (a · b) · c = a · (b · c) • (-6 · 2) · 3 = -6 · (2 · 3)

  11. 2.5 – Multiplication of Real Numbers • Properties of Multiplication • Identity Property • The product of a number and 1 is the number • 1 · a = a • (-4) · 1 = -4

  12. 2.5 – Multiplication of Real Numbers • Properties of Multiplication • Property of Zero • The product of a number and 0 is 0 • a · 0 = 0 • (-2) · 0 = 0

  13. 2.5 – Multiplication of Real Numbers • Properties of Multiplication • Property of Opposites • The product of a number and -1 is the opposite of the number • (-1) · a = -a • (-1)(-3) = 3

  14. 2.5 – Multiplication of Real Numbers • Example 5 A grocery store runs a sale where customers can get two bags of spinach for the price of one. The store normally charges $1.69 per bag. How much will they be losing in sales if they give away 798 free bags?

  15. 2.5 – Multiplication of Real Numbers HOMEWORK Page 96 #16 – 56 even

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