Questions and Answers
What property is illustrated by the equation $1 + (7 + 9) = (1 + 7) + 9$?
What property is represented by the equation $3(x+2) = 3x + 6$?
Distributive Property
What property is showcased in the equation $3(2+8) = 32 + 38$?
Distributive Property
What property is shown in the equation $2(3) = 3(2)$?
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What property is illustrated by the equation $3+4 = 4+3$?
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What property is shown in the equation $(3*x)(-2) = 3(-2)*x$?
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What property does the equation $3(x+9) = (x+9)*3$ represent?
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Study Notes
Algebraic Properties
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Associative Property:
- Example: 1 + (7 + 9) = (1 + 7) + 9
- This property shows that how numbers are grouped does not change their sum.
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Distributive Property:
- Example: 3(x + 2) = 3x + 6
- This allows for the multiplication of a number by a sum, distributing the multiplier to each addend.
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Distributive Property (alternative example):
- Example: 3(2 + 8) = 32 + 38
- Reinforces that a single factor can be distributed across a sum inside parentheses.
Commutative Properties
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Commutative Property of Multiplication:
- Example: 2(3) = 3(2)
- Indicates that the order of multiplication does not affect the product.
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Commutative Property of Addition:
- Example: 3 + 4 = 4 + 3
- States that the order of addition does not affect the sum.
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Commutative Property (alternative example):
- Example: 3(x + 9) = (x + 9)*3
- Demonstrates that the order in which you multiply does not matter.
Associative Property of Multiplication
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Associative Property of Multiplication:
- Example: (3*x)(-2) = 3(-2)*x
- This property illustrates that when multiplying, how the numbers are grouped does not change the product.
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Prepare for the Algebra 1 Unit 1 test with our comprehensive review flashcards. Each card highlights key properties such as the associative, distributive, and commutative properties, helping solidify your understanding of fundamental algebraic concepts.
