6 Questions
Which property of real numbers states that the order of the numbers being added or multiplied does not change the result?
Commutative Property
What is the result of adding, subtracting, multiplying, or dividing two real numbers?
Always a real number
Which property of real numbers allows us to rearrange the order in which numbers are added or multiplied?
Associative Property
What is the purpose of the additive identity in real numbers?
To leave the number unchanged when added
Which property of real numbers states that multiplication distributes over addition?
Distributive Property
What is the purpose of the multiplicative identity in real numbers?
To leave the number unchanged when multiplied
Study Notes
Properties of Real Numbers
Closure Property
- The result of adding, subtracting, multiplying, or dividing two real numbers is always a real number.
- Example: 2 + 3 = 5, 5 is a real number.
Commutative Property
- The order of the numbers being added or multiplied does not change the result.
- Example: 2 + 3 = 3 + 2, 2 × 3 = 3 × 2.
Associative Property
- The order in which numbers are added or multiplied does not change the result.
- Example: (2 + 3) + 4 = 2 + (3 + 4), (2 × 3) × 4 = 2 × (3 × 4).
Distributive Property
- Multiplication distributes over addition.
- Example: 2 × (3 + 4) = 2 × 3 + 2 × 4.
Identity Property
- There exists a real number that, when added to or multiplied by a real number, leaves it unchanged.
- Example: 0 is the additive identity (a + 0 = a), 1 is the multiplicative identity (a × 1 = a).
Inverse Property
- For each real number, there exists another real number that, when added or multiplied, results in the identity.
- Example: for each real number a, there exists -a such that a + (-a) = 0, and a^(-1) such that a × a^(-1) = 1.
Properties of Real Numbers
Closure Property
- The result of adding, subtracting, multiplying, or dividing two real numbers is always a real number.
Commutative Property
- The order of the numbers being added or multiplied does not change the result, for example, 2 + 3 = 3 + 2, and 2 × 3 = 3 × 2.
Associative Property
- The order in which numbers are added or multiplied does not change the result, for example, (2 + 3) + 4 = 2 + (3 + 4), and (2 × 3) × 4 = 2 × (3 × 4).
Distributive Property
- Multiplication distributes over addition, for example, 2 × (3 + 4) = 2 × 3 + 2 × 4.
Identity Property
- There exists a real number that, when added to or multiplied by a real number, leaves it unchanged, specifically, 0 is the additive identity (a + 0 = a), and 1 is the multiplicative identity (a × 1 = a).
Inverse Property
- For each real number, there exists another real number that, when added or multiplied, results in the identity, for example, for each real number a, there exists -a such that a + (-a) = 0, and a^(-1) such that a × a^(-1) = 1.
The quiz covers the properties of real numbers, including closure, commutative, and associative properties with examples.
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