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Questions and Answers
Which property ensures that when we have three or more rational numbers, the order in which we perform the operation does not change the result?
Which of the following operations is commutative for rational numbers?
What is the correct statement about division of rational numbers?
Which of the following is true about whole numbers?
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What is a result of the commutative property of multiplication of rational numbers?
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Which of the following operations has closure property for rational numbers?
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What can be said about the subtraction of rational numbers?
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Which property is demonstrated by the equation $a(b+c) = ab + ac$?
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What can be said about the multiplication of rational numbers?
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Which property is demonstrated by the equation $(a+b)+c = a+(b+c)$?
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Study Notes
Properties of Operations
- Addition is associative for whole numbers and integers, meaning that the order in which numbers are added does not change the result.
- Subtraction is not associative for whole numbers and integers, meaning that the order in which numbers are subtracted affects the result.
Multiplication
- Multiplication is associative for whole numbers and integers, meaning that the order in which numbers are multiplied does not change the result.
- For any three whole numbers or integers a, b, and c, a × (b × c) = (a × b) × c.
Division
- Division is not associative for whole numbers and integers, meaning that the order in which numbers are divided affects the result.
Properties of Rational Numbers
- Rational numbers are closed under the operations of addition, subtraction, and multiplication.
- Addition and multiplication are commutative for rational numbers, meaning that the order of the numbers does not affect the result.
- Subtraction and division are not commutative for rational numbers, meaning that the order of the numbers affects the result.
Associativity of Operations for Rational Numbers
- The associativity of the four operations for rational numbers can be seen from the table:
- Addition: (a + b) + c = a + (b + c)
- Subtraction: Not associative
- Multiplication: (a × b) × c = a × (b × c)
- Division: Not associative
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Description
Verify the associativity of addition, subtraction, multiplication, and division operations for natural numbers. Check if the order of numbers changes the result.
