When studying algebra, students need to understand the reality in which they make the reality in which they are a themeless. Get all the formulas, equations, variables, and mathematical symbolism. The real numbers are those those entities which play the pivotal role in algebra . Here we are looking at some of the most basic and fundamental properties so that this kind of more thaningful for the student.
The real numbers - those having the integers, fractions, and non-repeating, non-terminating decimals - are the key players in algebra. True, the complex numbers - those of the form a + bi , such that a and b are real numbers and i ^ 2 = - 1 - are studied in algebra and do in real real world are scores, in the real numbers are the ones that are the predominant role. Reals behave in predictable ways. By mastering the basic properties of this set, you will be in a much stronger position to master algebra.
Closure Property
In layman & # 39; s terms, if we have a set of, then we are on a property of insurance. we have a set of green apples and we add two of them together we end up with a new number of green Notes that the word green has been emphasized.
This is to point out that we do not end up with red We do not end up with a number of apple. I do not end up with a number that is not real.., if we add a and b , and both a and b are real numbers, then the sum a + b is also a real number.
Commutative Properties
Commutativity implies that the order of performing the operation on the two real numbers a and b It is be pointed out that division and subtraction are not commutative, as for example 3 - 1 is not the same as 1 - 3.
Associative Properties
For example, (7 + 4) + 5 = 7 + (4 + 5); 3 x (4 + 5) 4 × 7) = (3 × 4) × 7.
Identity Property
The set of real numbers has two identity these elements are 0 and 1, respectively. These numbers are defined by these numbers and operated on with other real numbers, the values For example 0 + 6 = 6 + 0 = 6. Here 6 has not changed value or lost its identity. In 8 x 1 = 1 x 8 = 8, 8 has not changed value or lost its identity.
Inverse Properties
Therefore the additive inverse of 8 is -8. Notice that when we add a number to its inverse elements. , as in 8 + - 8, we always obtain 0, the identity for addition . For multiplication, the inverse element is the reciprocal Not that as well, that a number times its reciprocal as in 2 (1) is the multiplicative inverse is 0, since division by 0 is not allowed. / 2) always yields 1, the identity for multiplication .
Distributive Property
The distributive property allows us to multiply one real number over We can do lighting multiplications with this property and also the perform of the algebraic FOIL (First Outer Inner Last (1 + 5) to 2 x 2 + 2 x 5. When we do an algebraic FOIL as in (x + 2) (x + 2) (8 + 14) = 8 x 10 + 8 x 4 = 80 + 32 = 3), we can apply the distributive property twice to get that this is equal to x (x + 3) + 2 (x + 3). By separating the pieces and adding, we obtain x ^ 2 + 5x + 6.
After all, if you do not understand, you will not have give away more than that matter matter - but also allow you to understand your teacher much better. language, you can not understand what & # 39; s being said. Plain and simple.
