Chapter 2 – Properties of Chapter 2 – Properties of Real NumbersReal Numbers

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

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

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Remember: Multiplication can be modeled as Remember: Multiplication can be modeled as repeated addition.repeated addition. Example: 4(-2) = Example: 4(-2) = (-2) + (-2) + (-2) + (-2) = (-2) + (-2) + (-2) + (-2) = -8-8

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Complete the listsComplete 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 -3Factor of -3 Factor of -2Factor of -2 Factor of -1Factor of -1

3(-3) = -93(-3) = -9 3(-2) = -63(-2) = -6 3(-1) = -33(-1) = -3

2(-3) = -62(-3) = -6 2(-2) = -42(-2) = -4 2(-1) = -22(-1) = -2

1(-3) = -31(-3) = -3 1(-2) = -21(-2) = -2 1(-1) = -11(-1) = -1

0(-3) = 00(-3) = 0 0(-2) = 00(-2) = 0 0(-1) = 00(-1) = 0

-1(-3) = _____-1(-3) = _____ -1(-2) = _____-1(-2) = _____ -1(-1) = _____-1(-1) = _____

-2(-3) = _____-2(-3) = _____ -2(-2) = _____-2(-2) = _____ -2(-1) = _____-2(-1) = _____

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Example 1Example 1Find the productFind the product (9)(-3)(9)(-3) 8(- ½ )(-6)8(- ½ )(-6) (-3)(-3)33

(-2)(- ½ )(-3)(-5)(-2)(- ½ )(-3)(-5)

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Multiplying Real NumbersMultiplying Real Numbers The product of two real numbers with the same The product of two real numbers with the same

sign is the product of their absolute values.sign is the product of their absolute values. The product is positive The product is positive

The product of two real numbers with different The product of two real numbers with different signs is the OPPOSITE of the product of their signs is the OPPOSITE of the product of their absolute values.absolute values.

The product is negativeThe product is negative

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Example 2Example 2Find the product.Find the product. (-n)(-n)(-n)(-n) (-4)(-x)(-x)(x)(-4)(-x)(-x)(x) -(b)-(b)33

(-y)(-y)44

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Properties of MultiplicationProperties of Multiplication Commutative PropertyCommutative Property

The order in which two numbers are multiplied does not The order in which two numbers are multiplied does not change the productchange the product

a a · b = b · a· b = b · a 3(-2) = (-2)33(-2) = (-2)3

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Properties of MultiplicationProperties of Multiplication Associative PropertyAssociative Property

The way you group three numbers when multiplying The way you group three numbers when multiplying does not change the productdoes not change the product

(a (a · b) · c = a · (b · c)· b) · c = a · (b · c) (-6 · 2) · 3 = -6 · (2 · 3)(-6 · 2) · 3 = -6 · (2 · 3)

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Properties of MultiplicationProperties of Multiplication Identity PropertyIdentity Property The product of a number and 1 is the numberThe product of a number and 1 is the number 1 1 · a = a· a = a (-4) · 1 = -4(-4) · 1 = -4

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Properties of MultiplicationProperties of Multiplication Property of ZeroProperty of Zero The product of a number and 0 is 0The product of a number and 0 is 0 a a · 0 = 0· 0 = 0 (-2) · 0 = 0(-2) · 0 = 0

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Properties of MultiplicationProperties of Multiplication Property of OppositesProperty of Opposites The product of a number and -1 is the opposite of The product of a number and -1 is the opposite of

the numberthe number (-1) (-1) · a = -a· a = -a (-1)(-3) = 3(-1)(-3) = 3

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Example 3Example 3Evaluate the expression when x = -7Evaluate the expression when x = -7 2(-x)(-x)2(-x)(-x)

(-5 (-5 · x)(-2/7)· x)(-2/7)

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

DisplacementDisplacement – is the change in the position – is the change in the position of an object and can be positive, negative, or of an object and can be positive, negative, or zero.zero.

VERTICAL DISPLACEMENT = VERTICAL DISPLACEMENT = VELOCITY VELOCITY · ·

TIMETIME

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Example 4Example 4A leaf floats down from a tree at a velocity of -12 A leaf floats down from a tree at a velocity of -12

cm/sec. Find the vertical displacement in 4.2 sec.cm/sec. Find the vertical displacement in 4.2 sec.

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

Example 5Example 5A grocery store runs a sale where customers can get A grocery store runs a sale where customers can get

two bags of spinach for the price of one. The two bags of spinach for the price of one. The store normally charges $1.69 per bag. How much store normally charges $1.69 per bag. How much will they be losing in sales if they give away 798 will they be losing in sales if they give away 798 free bags?free bags?

2.5 – Multiplication of Real Numbers2.5 – Multiplication of Real Numbers

HOMEWORKHOMEWORK

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