The statement `2+10=10+2` demonstrates the Commutative Property for Addition. When we add `2` and `10` together, the order does not matter. This simply states that when we do addition or multiplication, the order of the numbers does not matter. The statement `5*6=30` is real demonstrates the Closure Property for Multiplication.Ĭommutative Property for Addition: If `a` and `b` are real numbers, then `a+b=b+a`Ĭommutative Property for Multiplication: If `a` and `b` are real numbers, then `a*b=b*a` When we multiply them together, we get `30`, which is another real number, and `30` is the only answer we can get by multiplying `5*6`. The statement `5+6=11` is real demonstrates the Closure Property for Addition.īoth `5` and `6` are real numbers. When we add them together, we get `11`, which is another real number, and `11` is the only answer we can get by adding `5+6`. The following examples will show that this is simply a basic (but important) concept.īoth `5` and `6` are real numbers. This looks more complicated than it really is. This simply means that if we add or multiply any two real numbers together, we will get an answer that is also a real number, and there can be only one answer (it is unique).Textbooks sometimes state this using even more mathematical symbols (such as If `a`, `b` `in RR`, and so on). Imaginary numbers have an `i` in them, so they look something like `5i` or `43i`, for example.Ĭlosure Property for Addition: If `a` and `b` are real numbers, then `a+b` is unique and real.Ĭlosure Property for Multiplication: If `a` and `b` are real numbers, then `a*b` is unique and real. Imaginary numbers are very useful, and we will learn about them much later in this course. Simply stated, real numbers are the set of any number you can think of except for imaginary numbers.ĭon't worry if you don't know what an imaginary number is right now. Real numbers include all positive and negative integers, fractions, and decimals. These include all of the positive numbers, all of the negative numbers, and zero. Real Number: Any number on the number line. We need to start by defining what a Real Number is. This understanding will also help us to do things like rearrange problems to make them easier to work with or find steps in our work where we made an error that needs to be fixed. While these theories are not usually used directly to solve problems, it is important to understand them in order to know what is going on when we work problems. We are going to explore a little bit of the theoretical side of Algebra here, and this will help to make sense of some of the definitions we are likely to see in our textbooks. In this lesson, we will look at the Closure Property and the Commutative Property. While these number properties will start to become relevant in matrix algebra and calculus - and become amazingly important in advanced math, a couple years after calculus - they may seem fairly useless to you right now.Algebra 1 Textbook - Chapter 1 - Lesson 21 - Closure Property and Commutative Property Released - May 23, 2017 (My impression is that covering these properties at this stage in your studies is a holdover from the "New Math" fad of the mid-1900s. the Distributive Property (of multiplication over addition). the Commutative Property (of Addition or Multiplication, depending on the context).the Associate Property (of Addition or Multiplication, depending on the context).The basic number properties are as follows: What are the three basic number properties? All physical objects fill a certain volume with a certain amount of stuff, so the property of density is just a description of one thing that all matter does. Dividing the mass by the volume tells you how dense the object is. For instance, matter (any physical object) has the property of density, because an object has a certain amount of material (mass) that occupies a certain amount of volume. Number properties are descriptions of things that numbers do they are names for how numbers behave. Basic Number Properties What are properties of numbers?
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