Basic algebraic properties of real numbers, Mathematics

Assignment Help:

These can be expressed in terms of two fundamental operations of addition and multiplication.

If a, b and c are any three real numbers, then;

    1.          i.  a + b = b + a

This property is called commutative property of addition. According to this property, addition can be carried out in any order and irrespective of this we obtain the same result.

  1. a.b = b.a

This property is called commutative property of multiplication.

    2.          i.   (a + b) + c = a + ( b + c)

This property is referred to as associative property of addition. According to this property, elements can be grouped according to any manner and irrespective of the grouping we obtain the same result.

  1. (a.b).c = a.(b.c)

This property is referred to as the associative property of multiplication.

      3.           a.(b + c) = a.b + a.c or (a + b).c = a.c + b.c

This property is referred to as distributive property. This is generally employed to expand a product into a sum or the other way round. That is, to rewrite a sum as a product.

      4.        i.   a + 0 = 0 + a = a 

This property is referred to as identity property under addition. That is, 0 when added to a real number returns back the number itself which is same or identical to itself. Thus 0 is the identity element under addition.

  1. a.1 = 1.a = a   

This property is referred to as identity property under multiplication. That is, when a real number is multiplied by 1, we get back the same number.

Thus the element 1 is the multiplicative identity.

         5.    i.    a + (-a) = (-a) + a = 0

This property is referred to as inverse property under addition. According to this property, for every element a, there exists another element - a such that the addition of the both gives us zero. The element - a is referred to as the additive inverse of the element a. On a number line, an element and its additive inverse lie at equi-distant from the origin.

  1.  1212_algebraic properties.png

This property is referred to as inverse property under multiplication. According to this property for every element a, a ≠ 0, there exists another element 1/a such that the multiplication of a and 1/a results in 1. The element 1/a is referred to as multiplicative inverse element.

     6.        i.   If a + x = a + y, then x = y.   

This property is referred to as the cancelation property. According to this property a constant quantity when present on both sides of the equation can be canceled without disturbing the balance which exists between the expressions.

  1. If a≠0 and ax = ay, then x = y.

This property is referred to as the cancelation property under multiplication.

     7.          i.   a.0 = 0.a = 0

This property is referred to as the zero factor property. According to this property any real number a, if multiplied by zero would yield a zero. This can be also put as: if one of the factors happens to be zero, irrespective of other factors, the product of all these factors would yield a zero.

  1. If a.b = 0, then a = 0 or b = 0 or both.

According to this property, the product of any two real numbers a and b is zero if one of them happens to be zero, that is either a = 0 or b = 0 or both of them happen to be equal to zero.


Related Discussions:- Basic algebraic properties of real numbers

Constrcut the adjacency matrix, Constrcut the adjacency matrix and the adja...

Constrcut the adjacency matrix and the adjacency lists for the graph G belowr.

Find x if one ball is drawn at random from the box, A box contains 12 balls...

A box contains 12 balls out of which x are black .if one ball is drawn at random from the box  what is the probability that it will be a black ball ? If 6 more black balls are   pu

Estimate the probability, The following (artificial) data record the length...

The following (artificial) data record the length of stay (in days) spent on a psychiatric ward for 28 consecutive patients who have been sectioned under the mental health act, cla

Finding the LCM, what is the LCM of 18, 56 and 104 show working

what is the LCM of 18, 56 and 104 show working

Find sampling interval - horizontal and vertical asymptote, In a digital fi...

In a digital filter, one of the parameters in its difference equation is given by the formula a) Show that the above formula has one horizontal and one vertical asymptote.

Linear programming, #question.As office manager of her firm, Marcellyne has...

#question.As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and hol

Surface area with polar coordinates, Surface Area with Polar Coordinates ...

Surface Area with Polar Coordinates We will be searching for at surface area in polar coordinates in this part.  Note though that all we're going to do is illustrate the formu

Linear programming , Use the simplex method to solve the following LP Probl...

Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0

Derivative for parametric equations, Derivative for Parametric Equations ...

Derivative for Parametric Equations dx/dy = (dx/dt) / (dy/dt) ,         given dy/dt ≠ 0 Why would we wish to do this? Well, remind that in the arc length section of the Appl

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd