# Why the properties of real numbers are important to know when working with algebra

We will apply most of the following properties to solve various Algebraic problems. This looks like a lot of mindless parenthesis juggling, but the point is that the distributive property applies to arbitrarily long sums and products. Understanding these will help you to manipulate and solve equations, and to understand algebraic relationships.

Properties of Equality Add c to each side Multiply both sides by c Subtract c from both sides Divide both sides by c Properties of Zero 0 added or subtracted to anything equals itself 0 multiplied by anything equals 0 0 divided by anything equals 0 We cannot divide by 0 Zero Product Property If the product of two or more things equals 0, at least one of the values must be 0 Properties and Operations of Fractions Let a, b, c and d be real numbers, variables, or algebraic expressions such that b and d do not equal 0.

Additive Inverse Property If we adda number by the opposite of itself, we will end up with 0. Distributive Property When we are adding and multiplying with a parenthesis, we can distribute the multiplication through the addition.

You will get the same answer regardless of order. Similarly, divison can be thought of as inverse multiplication, but with a restriction that the denominator cannot be equal to 0. Associative Property of Addition We can group numbers in a sum any way we want and get the same answer.

Commutative Property of Addition We can add numbers in any order. There may be 4, 12, or several thousand. Finally we can substitute this expression for the second term back into the equation to get: This is one of the reasons it is so important.

The commutative property is that you can exchange two numbers and still get the same answer. We will use this fact without justification that is, without proof. We are free to change the order to anything that we find easier. You can switch things around and still get the same answer. This book is not going to prove many things, but it would be useful for us to take a look at how this works.

Algebraic Properties Let a, b, and c be real numbers, variables, or algebraic expressions. Multiplicative Identity Property If we multiply 1 to any number, we will end up with the same number.

The associative property is that you can change the grouping i. Commutative Law[ edit ] In general, the order of the items can be changed without affecting the results.

The distributive property means that you can distribute the operation. Well, that is where commutativity comes in. The rule holds even if there are more than three terms: What happens if we use the distributive property on the first term in this expression?

Properties of Negation We must be careful not to make arithmetic mistakes when dealing with negative signs and subtraction.

When working with variables in algebrathese properties still apply.Real numbers are, most likely, all the numbers you can think of!

They consist of zero (0), the positive and negative integers (-3, -1, 2, 4), and all the fractional and decimal values in between (,1/2).

The properties of real numbers are very important in our study of Algebra. These properties can be applied in Algebra because a variable is simply a letter that represents a real number.

The distributive property is one that we apply often when simplifying algebraic expressions. In beginning Algebra, we let the variables stand for some real number. Thus the properties of real numbers can be used when dealing with the variables.

identity: 3+0=0+3=3 x+0=0+x=x This idea is.

Basic Rules of Algebra. There are basic properties in math that apply to all real numbers. When working with variables in algebra, these properties still mi-centre.com will apply most of the following properties to solve various Algebraic problems. o Explain why the properties of real numbers are important to know when working with algebra.

In what ways are they useful for simplifying algebraic expressions? o Incorporate the following five math vocabulary words into the text of your paper.

Aug 20,  · Explain why the properties of real numbers are important to know when working with algebra. In what ways are t?

Why the properties of real numbers are important to know when working with algebra
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