Chapter 2 – Properties of Real Numbers 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? 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?

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

2.5 – Multiplication of Real Numbers Complete the lists Complete the lists The product of a positive number and a negative number is: The product of a positive number and a negative number is: Factor of -3 Factor of -2 Factor of -1 3(-3) = -9 3(-2) = -6 3(-1) = -3 2(-3) = -6 2(-2) = -4 2(-1) = -2 1(-3) = -3 1(-2) = -2 1(-1) = -1 0(-3) = 0 0(-2) = 0 0(-1) = 0 -1(-3) = _____ -1(-2) = _____ -1(-1) = _____ -2(-3) = _____ -2(-2) = _____ -2(-1) = _____

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

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

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

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

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

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

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

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

2.5 – Multiplication of Real Numbers Example 3 Example 3 Evaluate the expression when x = -7 2(-x)(-x) 2(-x)(-x) (-5 · x)(-2/7) (-5 · x)(-2/7)

2.5 – Multiplication of Real Numbers Displacement – is the change in the position of an object and can be positive, negative, or zero. Displacement – is the change in the position of an object and can be positive, negative, or zero. VERTICAL DISPLACEMENT = VERTICAL DISPLACEMENT = VELOCITY · TIME

2.5 – Multiplication of Real Numbers Example 4 Example 4 A leaf floats down from a tree at a velocity of -12 cm/sec. Find the vertical displacement in 4.2 sec.

2.5 – Multiplication of Real Numbers Example 5 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?

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