In this lesson, we are going to go over the different properties of real numbers (ℜ). Understanding the properties of real numbers will help us simplify numerical and algebraic expressions, solve equations, and more as we progress in studying algebra. Show For clarity, “properties” in this context refer to the characteristics or behaviors of real numbers under the operations of addition and/or multiplication that are accepted even without proof. In fact, the terms axioms and properties can be used interchangeably here because axioms are properties that are self-evidently true. Therefore, the statements or propositions that will be presented here don’t require any proof. In other words, the properties or axioms of real numbers are just one of many basic foundations of mathematics. To keep it organized, I decided to divide the properties of real numbers into three (3) parts. The first one involves the addition operation. The second involves the operation of multiplication. While the third combines the operations of addition and multiplication. Addition Properties of Real NumbersSuppose a, b, and c represent real numbers. 1) Closure Property of Addition
2) Commutative Property of Addition
3) Associative Property of Addition
4) Additive Identity Property of Addition
5) Additive Inverse Property
Multiplication Properties of Real NumbersSuppose a, b, and c represent real numbers. 6) Closure Property of Multiplication
7) Commutative Property of Multiplication
8) Associative Property of Multiplication
9) Multiplicative Identity Property of Multiplication
10) Multiplicative Inverse Property
The Property of Multiplication together with Addition11) Distributive Property of Multiplication over Addition Suppose a, b, and c represent real numbers.
You might also be interested in: Classifying Real Numbers Properties of Equality What are the properties of real numbers?The main properties of Real numbers are: Closure property. Commutative property. Associative property.
What are the 11 properties of real numbers?What Are the Properties of Real Numbers?. Additive identity.. Multiplicative identity.. Commutative property of addition.. Commutative property of multiplication.. Associative property of addition.. Associative property of multiplication.. Distributive property of multiplication.. How many properties are there in real number?The following are the four main properties of real numbers: Commutative property. Associative property. Distributive property.
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