5 Questions
Which property of arithmetic operations states that the order of numbers being added or multiplied does not change the result?
Commutative Property
What is the expression for the commutative property of addition?
a + b = b + a
Which property of arithmetic operations allows us to rewrite 2 × (3 + 4) as 2 × 3 + 2 × 4?
Distributive Property
What is the expression for the associative property of multiplication?
(a × b) × c = a × (b × c)
Which of the following properties does not apply to subtraction?
Commutative Property
Study Notes
Commutative Property
- Applies to addition and multiplication
- States that the order of numbers being added or multiplied does not change the result
- Examples:
- 2 + 3 = 3 + 2
- 2 × 3 = 3 × 2
- Can be expressed as:
- a + b = b + a
- a × b = b × a
Associative Property
- Applies to addition and multiplication
- States that when three or more numbers are added or multiplied, the order in which the operations are performed does not change the result
- Examples:
- (2 + 3) + 4 = 2 + (3 + 4)
- (2 × 3) × 4 = 2 × (3 × 4)
- Can be expressed as:
- (a + b) + c = a + (b + c)
- (a × b) × c = a × (b × c)
Distributive Property
- Applies to multiplication over addition
- States that multiplication distributes over addition
- Examples:
- 2 × (3 + 4) = 2 × 3 + 2 × 4
- 5 × (2 - 3) = 5 × 2 - 5 × 3
- Can be expressed as:
- a × (b + c) = a × b + a × c
- a × (b - c) = a × b - a × c
Commutative Property
- The commutative property applies to both addition and multiplication operations
- Changing the order of numbers being added or multiplied does not affect the result
- Examples of the commutative property in action:
- 2 + 3 = 3 + 2
- 2 × 3 = 3 × 2
- The commutative property can be expressed mathematically as:
- a + b = b + a
- a × b = b × a
Associative Property
- The associative property also applies to both addition and multiplication operations
- The order in which three or more numbers are added or multiplied does not change the result
- Examples of the associative property in action:
- (2 + 3) + 4 = 2 + (3 + 4)
- (2 × 3) × 4 = 2 × (3 × 4)
- The associative property can be expressed mathematically as:
- (a + b) + c = a + (b + c)
- (a × b) × c = a × (b × c)
Distributive Property
- The distributive property applies to multiplication over addition
- Multiplication distributes over addition, meaning that the operation can be applied to each addend separately
- Examples of the distributive property in action:
- 2 × (3 + 4) = 2 × 3 + 2 × 4
- 5 × (2 - 3) = 5 × 2 - 5 × 3
- The distributive property can be expressed mathematically as:
- a × (b + c) = a × b + a × c
- a × (b - c) = a × b - a × c
Learn about the commutative and associative properties in algebra, including their definitions, examples, and expressions. Understand how these properties apply to addition and multiplication.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
