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1. 2.5 Multiplication of Real Numbers MULTIPLYING REAL NUMBERS 1 GOAL EXAMPLE 1 • Rules for multiplying two real numbers: • If the signs are the same, the product is _______. • If the signs are different, the product is ________. positive negative

2. EXAMPLE 2 Extra Example 1 Find the product. a. (9)(–3) b. c. (–3)3 d. -27 (–4)(–6) 24 (–3)(–3)(–3) 1(–3)(–5) (9)(–3) (–3)(–5) –27 15

3. Extra Example 2 Find the product. a. (–n)(–n) b. (–4)(–x)(–x)(x) c. –(b)3 d. (–y)4 Two negative signs: n2 Three negative signs: –4x3 –(b)(b)(b) = –b3 One negative sign: 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.

4. EXAMPLE 3 PROPERTIES OF MULTIPLICATION • COMMUTATIVE PROPERTY • ASSOCIATIVE PROPERTY • IDENTITY PROPERTY • PROPERTY OF ZERO • PROPERTY OF OPPOSITES Order doesn’t matter. Grouping doesn’t matter. a times 1 equals a. a times 0 equals 0. a times –1 equals –a.

5. Extra Example 3 Evaluate the expression when x = –7. a. 2(–x)(–x) 2(–x)(–x) 2x2 OR simplify first: 2(-7)2 2(49) 98

6. Extra Example 3 (cont.) Evaluate the expression when x = –7. b. OR use the associative property:

7. Checkpoint Find the product. 1. (–2)(4.5)(–10) 2. (–4)(–x)2 3. Evaluate the expression when x = –3: (–1• x)(x) 90 –4x2 –9

8. 2.5 Multiplication of Real Numbers 2 USING MULTIPLICATION IN REAL LIFE GOAL EXAMPLE 4 • VOCABULARY • displacement— The change in the position of an object. May be negative, positive, or zero, while distance may only be positive or zero.

9. VERBAL MODEL Vertical displacement = Velocity • Time LABELS ALGEBRAIC MODEL SOLVE EXAMPLE 5 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. d –12 cm/sec 4.2 sec d = –50.4 cm The leaf has a vertical displacement of –50.4 cm, or 50.4 cm downward.

10. VERBAL MODEL Number of bags Loss per bag Loss = • LABELS ALGEBRAIC MODEL SOLVE 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? a 798 \$1.69 a = \$1348.62 The store loses \$1348.62.

11. Checkpoint 1. A paper airplane descends at a velocity of –14 in./sec. Find the vertical distance traveled in 7.5 sec. 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? –105 in. \$35.28

12. QUESTIONS?