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Algebra 1 Section 1.5
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Multiplication 3 • 5 = 5 + 5 + 5 3x means 3 • x
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Properties of Multiplication
Commutative Property: If you multiply two numbers together in different orders, the product is the same. ab = ba
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Properties of Multiplication
Associative Property: If you group numbers differently when multiplying, the product is the same. a(bc) = (ab)c
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Properties of Multiplication
Multiplicative Identity Property: The product of any number and one is that number. a • 1 = 1 • a = a
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Properties of Multiplication
Distributive Property: The product of a number and a sum is equal to the sum of the products of the number and each addend. a(b + c) = ab + ac
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Properties of Multiplication
Zero Property of Multiplication: The product of any number and zero is zero. a • 0 = 0
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Multiplication A product is the answer to a multiplication problem
A factor is any number that is being multiplied in the problem
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Multiplication Notice the pattern: 3(-5) = -15 2(-5) = -10 1(-5) = -5
0(-5) = 0 -1(-5) = 5 -2(-5) = 10 -3(-5) = 15
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Multiplication If the factors are both positive or both negative, the product is positive. If one factor is positive and the other is negative, the product is negative.
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Example 1 a. -2(9) = ____ b. -4(-6) = ____ -18 24
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Multiplication If there is an even number of negative factors, the product is positive. If there is an odd number of negative factors, the product is negative.
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Example 2 a. -2(-3)(-5) = ____ b. 4(-3)(-1) = ____ -30 12
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Multiplication With Fractions
It is not necessary to have a common denominator. Canceling first is usually easier. Mixed numbers must be converted to improper fractions before multiplying.
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Definition A unit multiplier is a fraction with two different expressions for the same quantity in the numerator and the denominator. Used to change the units of a number
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Using Unit Multipliers
1 ft. 12 in. 60 in. = 5 ft. 12 in. 1 ft. 5 ft. = 60 in.
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Example 6 2.54 cm a. 53.25 in. 1 in. = 135.255 cm 1 ft. b. 51 in.
17 1 ft. 12 in. = ft. 17 4 b. 51 in. 4 = 4¼ ft.
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Example 6 5280 ft. 1 mi. 12 in. 1 ft. c. 2 mi. = 126,720 in.
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Homework: pp
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