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2.5 Multiplication of Real Numbers GOAL 1 MULTIPLYING REAL NUMBERS Rules for multiplying two real numbers: positive •If the signs are the same, the product is _______. negative •If the signs are different, the product is ________. EXAMPLE 1 Extra Example 1 Find the product. a. (9)(–3) -27 1 b. (8) ( 6) 2 (–4)(–6) 24 c. (–3)3 (–3)(–3)(–3) (9)(–3) –27 1 d. ( 2) ( 3)( 5) 2 1(–3)(–5) (–3)(–5) 15 EXAMPLE 2 Extra Example 2 Find the product. a. (–n)(–n) Two negative signs: n2 b. (–4)(–x)(–x)(x) Three negative signs: –4x3 c. –(b)3 One negative sign: –(b)(b)(b) = –b3 d. (–y)4 Four negative signs: (–y)(–y)(–y)(–y) = y4 SUMMARY: An even number of negative signs results in a positive product, and an odd number of negative signs results in a negative product. PROPERTIES OF MULTIPLICATION •COMMUTATIVE PROPERTY Order doesn’t matter. •ASSOCIATIVE PROPERTY Grouping doesn’t matter. •IDENTITY PROPERTY a times 1 equals a. •PROPERTY OF ZERO a times 0 equals 0. •PROPERTY OF OPPOSITES a times –1 equals –a. EXAMPLE 3 Extra Example 3 Evaluate the expression when x = –7. a. 2(–x)(–x) 2 ( 7) ( 7) OR simplify first: 2 7 7 14 7 98 2(–x)(–x) 2x2 2(-7)2 2(49) 98 Extra Example 3 (cont.) Evaluate the expression when x = –7. b. 2 5 x 7 2 5( 7) 7 2 35 7 10 OR use the associative property: 2 5 x 7 2 5( 7) 7 2 5 7 7 5(2) 10 Checkpoint Find the product. 1. (–2)(4.5)(–10) 90 2. (–4)(–x)2 –4x2 3. Evaluate the expression when x = –3: (–1• x)(x) –9 2.5 Multiplication of Real Numbers GOAL 2 USING MULTIPLICATION IN REAL LIFE VOCABULARY •displacement— The change in the position of an object. May be negative, positive, or zero, while distance may only be positive or zero. EXAMPLE 4 Extra Example 4 A leaf floats down from a tree at a velocity of –12 cm/sec. Find the vertical distance traveled in 4.2 sec. VERBAL MODEL Vertical = Velocity • Time displacement LABELS d ALGEBRAIC MODEL SOLVE –12 cm/sec 4.2 sec cm d 12 (4.2 sec) sec d = –50.4 cm The leaf has a vertical displacement of –50.4 cm, or 50.4 cm downward. EXAMPLE 5 Extra 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? VERBAL MODEL LABELS ALGEBRAIC MODEL SOLVE Loss = Number of bags a 798 • Loss per bag $1.69 $1.69 a 798 bags bag a = $1348.62 The store loses $1348.62. Checkpoint 1. A paper airplane descends at a velocity of –14 in./sec. Find the vertical distance traveled in 7.5 sec. –105 in. 2. After a recent flood, a store owner sells 294 cans of green beans at a reduced price because their labels were ruined. Because the price the store originally paid for the beans is more than the reduced price, the store loses $0.12 on each can of beans sold. How much will the store lose if it sells all 294 cans of beans? $35.28 QUESTIONS?