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Questions and Answers
Which of the following is a property of adding integers?
Which of the following is a property of adding integers?
What is the result of multiplying any integer by -1?
What is the result of multiplying any integer by -1?
Which of the following is an example of a prime integer?
Which of the following is an example of a prime integer?
What is the result of dividing 12 by 3?
What is the result of dividing 12 by 3?
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What is the term for integers that are divisible by 2?
What is the term for integers that are divisible by 2?
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A temperature of -5°C can be represented by which type of integer?
A temperature of -5°C can be represented by which type of integer?
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Study Notes
Integers
Definition
- A set of whole numbers, including:
- Positive integers (1, 2, 3, ...)
- Negative integers (-1, -2, -3, ...)
- Zero (0)
Properties
- Closure: The result of adding, subtracting, multiplying, or dividing integers is always an integer.
- Commutative Property: The order of integers does not change the result of addition or multiplication.
- Associative Property: The order in which integers are added or multiplied does not change the result.
- Distributive Property: Multiplication distributes over addition.
Types of Integers
- Even integers: Divisible by 2 (..., -4, -2, 0, 2, 4, ...)
- Odd integers: Not divisible by 2 (..., -3, -1, 1, 3, ...)
- Prime integers: Only divisible by 1 and themselves (2, 3, 5, 7, 11, ...)
Operations on Integers
- Addition: Combine two or more integers to get a sum.
- Subtraction: Find the difference between two integers.
- Multiplication: Combine two or more integers to get a product.
- Division: Divide one integer by another, resulting in a quotient and possibly a remainder.
Real-World Applications
- Counting and measuring quantities
- Representing temperatures (e.g., -5°C, 0°C, 5°C)
- Financial transactions (e.g., +$10, -$5, $0)
Integers
Definition
- Integers are a set of whole numbers including positive integers, negative integers, and zero.
Properties
- Integers are closed under addition, subtraction, multiplication, and division.
- The commutative property applies to integers in addition and multiplication.
- The associative property applies to integers in addition and multiplication.
- The distributive property applies to integers, where multiplication distributes over addition.
Types of Integers
Even Integers
- Even integers are divisible by 2, such as ..., -4, -2, 0, 2, 4, ...
Odd Integers
- Odd integers are not divisible by 2, such as ..., -3, -1, 1, 3, ...
Prime Integers
- Prime integers are only divisible by 1 and themselves, such as 2, 3, 5, 7, 11, ...
Operations on Integers
Addition
- Addition combines two or more integers to get a sum.
Subtraction
- Subtraction finds the difference between two integers.
Multiplication
- Multiplication combines two or more integers to get a product.
Division
- Division divides one integer by another, resulting in a quotient and possibly a remainder.
Real-World Applications
- Integers are used for counting and measuring quantities.
- Integers represent temperatures, such as -5°C, 0°C, and 5°C.
- Integers are used in financial transactions, such as +$10, -$5, and $0.
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Description
Learn about integers, including their definition, properties, and rules. Discover the closure, commutative, and associative properties of integers.
