Letter Equation Solver

Introduction for letter equation solver:

In algebra equation solver, the solver solves the equations using the substitution and elimination method. Generally equations are written in the form of x and y variables. Instead of, we can use letters also example a, b and c etc. The equation is like 2a + 3b = c, where c is a constant value. The equation is solved step by step using the substitution and elimination method by the solver. First take two letter equation and solve to get a or b. The solver first find either a or b, and substitute first value of a or b in the next equation to get the solutions.


Letter equation solver's methods and steps:


Steps in letter equation for the solvers:

Substitution method for letter equation solvers:

First express the equation, b in terms of a in any one of the given equations.

Substitute this value of b in another equation.

Then the solvers solve the obtained equation in step 2 and find the value of a.

Solver, substitutes’ the value of a in equation step 1 taken and find the value of b.

Elimination method for letter equation solvers:

If necessary the solver multiply the given equation by suitable constants so as to make the coefficient of one of the variables, numerically equal.

Then the solver do next step numerically equal coefficient are opposite in sign, add the new equations otherwise subtract them.

Solver now solve the linear equation so obtained .this gives the value of first variable.

Then finally the solvers substitute the value of this variable in any of the given equations and find the value of the other variable.


Letter equation examples:


Example 1:

Solve the 4 equations: 3a + 2b = 7 and 2a + 2b = 6, x + y = 5 and 2x + y = 7

Solution:

3a + 2b = 7------------------ (1)

2a + 2b = 6----------------- (2)

Take first two equations

Multiply the equation (2) by -1

3a + 2b = 7 ---------- (1)

-2a – 2b = -6 ---------- (2)

a           = 1

Substitute x = 1 in (2)

2(1) + 2b = 6

2 + 2b = 6

2 + 2b – 2 = 6 -2 (now the solvers subtract 2 on both side)

2b = 4

`(2b)/(2) ` = `4/2` (now the solvers divide 2 on both side)

b = 2

Values are (a,b) is (1,2)

Example 2:

Solve the equation: a + b =5 and 2a + b =5.

Solution:

a + b =5 -------------- (1)

2a + b =5 ----------- (2)

Express in terms of x of first equation

a = b - 5

Here solver substitutes the value of x in (2)

2(b-5) +b =5

2b- 10 + b = 5

3b -10 = 5 (add 10 on both side)

3b + 10 -10 = 5 + 10

3b = 15

`(3b)/(3)` = ` (15)/(3)` (divide by 3 on both sides)

b = 5

Substitute b = 5 in (1)

a + 5 =5 (here the solver subtract 5 on both side)

a - 5 = 5-5

a = 0

Therefore (a,b) is (0,5)

Online Number Pattern Solver

Introduction :

Number pattern: A sequence of numbers that follow a certain pattern. Pattern describes the relationship between the numbers. Pattern is also referred as sequence. In pattern, there can be any number of members.

Example: 1, 5, 9, 13, 17, 21, 25, __?

Explanation: Starts at 1 and jumps 4 every time, therefore next number is 25 + 4 = 29.

1, 5, 9, 13, 17, 21, 25, 29.

Online number pattern solver is used to find the pattern or rule between the numbers.


Online Number Pattern Solver - Example Problems


Online number pattern solver.

Steps to find the pattern are:

1. Enter the numbers in the boxes

2. Click the button 'solve' to know the pattern(s).

Buttons:

1. Insert - Add the box(es).

2. Delete - Remove the box(es).

3. Left - Shift '?' to the left.

4. Right - Shift '?' to the right.

5. Clear - Clear the numbers in the boxes

Example 1: 1, 9, 25, 49, 81, __?. Find the pattern and next number of the given sequence.

Solution:

Answer: 1, 9, 25, 49, 81, 121.

Example 2: 1, 32, 81, 64, 25, __?. Find the pattern and next number of the given sequence.

Solution:

Explanation: 16 = 1, 25 = 32, 34 = 81, 43 = 64, 52 = 25

So, 61 = 6.

Answer: 1, 32, 81, 64, 25, 6.

Example 3: 3, 9, 27, 81, 343, __?. Find the pattern and next number of the given sequence.

Solution:

Explanation: Multiplicative difference between numbers (i.e.power of x)

3 x 3 = 9, 9 x 3 = 27, 27 x 3 = 81, 81 x 3 = 343.

So, 343 x 3 = 1029.

Answer: 3, 9, 27, 81, 343, 1029.

Example 4: 625, 575, 475, 325,  __, -125?. Find the pattern and next number of the given sequence.

Solution:

Explanation: 625 - 50 = 575, 575 - 100 = 475, 475 - 150 = 325.

So, 325 - 200 = 125.

Answer: 625, 575, 475, 325, 125, -125.


Online Number Pattern Solver - Practice Problems


Solve these following practice problems using online number pattern solver.

Problem 1: 1, 6, 36, 216, 1296, __?. Find the pattern and next number of the given sequence.

Problem 2: 10, 20, 35, 55, 80, __?. Find the pattern and next number of the given sequence.

Problem 3: 3, 9, 21, 39, __, 93, 129?. Find the pattern and next number of the given sequence.

Problem 4: 256, 244, 220, 172, 76, __?. Find the pattern and next number of the given sequence.

Answer: 1) 7776 2) 110 3) 63 4) -116

X and Y Table Solver

Introduction :
Solver:

A solver is a generic term indicating a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. (source : Wikipedia)

x and y table solver:

The solver that used to solve the system of linear equations called as x and y table solver.

In this article we are going to see some sample and practice problems on x and y table solver.


Solved problems on x and y table solver:

Problem 1:

Solve the following system of equation by using x and y table solver.

5x + 8y = -6

3x - 4y =14

Solution:

Given,   5x + 8y = -6

3x - 4y  =14

The given equations are system of linear equation.

We can solve these equations by using substitution method or elimination method.

Here we are going to solve these equations by using both methods.

5x+8y = -6 --------- > 1

3x-4y=14  ---------- > 2

Multiply the equation 2 by 2,

2(3x-4y) = 2(14)

6x - 8y = 28 ----------- > 3

Add the equation 1 and 3,

5x+8y = -6

(+)6x - 8y = 28

11x -0 = 22

11x = 22

Divided by 11 on both sides,

x =22/11

x = 2

Substitute x =2 in the equation 1,

5x+8y = -6

5(2)+8y = -6

10+8y = -6

Subtract 10 on both sides,

10 + 8y - 10 = -6 -10

8y = -16

Divide by 8 on both sides,

y = -16/8

y = -2

The solution of the system of linear equation is x =2 and y = -2

Answer: x = 2 , y = -2

Problem 2:

Solve the following system of equation by using x and y table solver.

x + y =10

8x- y = 8

Solution:

Given,   x + y =10

8x- y = 8

The given equations are system of linear equation.

We can solve these equations by using substitution method or elimination method.

Here we are going to solve these equations by using both methods.

x + y =10 --------- > 1

8x- y = 8  ---------- > 2

Add the equation 1 and equation 2,

x + y = 10

(+)   8x - y = 8

9x = 18

Divide by 9 on both sides,

9x/9 =18/9

x = 2

Substitute x = 2 in 1,

x + y =10

2 + y =10

Subtract 2 on both sides,

2 + y -2 = 10 -2

y = 8

The solution of the system of given linear equation is x =2 and y = 8

Answer: x = 2 , y =8

Practice problems on x and y table solver:


Problems:

1.Solve the following system of equation by using x and y table solver.

x + y = 150

x - y = - 50


2. Solve the following system of equation by using x and y table solver.

x + 3y = 36

3x + y =  44

Answer key:

1. x =50 and y =100

2. x =12 and y = 8

Online Arithmetic

Introduction :

Arithmetic is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers.

In online, we can learn more about arithmetic. We can learn arithmetic operations with lot of examples through online. It is very easy to learn arithmetic in online. Practice problems are also available in online which helps for conducting test for our self. In online, free arithmetic calculators are available which helps to do arithmetic operations. The different operations of arithmetic are explained below.

(Source: Wikipedia)


Learning arithmetic operations through online::


Arithmetic operations:

• Addition
• Subtraction
• Multiplication
• Division

Addition operation:

Addition operation is the basic operation in arithmetic.

It is denoted by the symbol ( + )

It produces the sum of two numbers. For example, 3 + 4 = 7

Subtraction operation:

Subtraction operation is opposite to the operation of addition.

It is denoted by the symbol ( - ).

It produces difference between the two numbers. For example, 7 - 6 = 1

Multiplication operation:

Multiplication operation is the second basic operation in arithmetic.

It is denoted by the symbols ( * ).

It produces the product of two numbers. For example, 2 * 3 = 6

Division operation:

Division operation is opposite to the operation of multiplication.

It is denoted by the symbol ( ÷ )

It produces quotient of two numbers.

The example problems for addition and subtraction operation are explained below in step by step.

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Online arithmetic example problems:


Example problem 1:

Add the numbers 234 and 456

Solutions:

Step 1: Given numbers

234 and 456

Step 2: Add first digit from left of the two numbers

4 + 6 = 10

Keep 0 as left most digit and keep 1 as carry

Step 3: Add second digit from left of the two numbers with carry

1 + 3 + 5 = 9

Step 4: : Add third digit from left of the two numbers

2 + 4 = 6

2            3            4

4            5            6

--------------------------------------

6             9             0

--------------------------------------

Step 5: Solution

234 + 456 = 690

Example problem 2:

Subtract 145 from 267

Solution:

Step 1: Given numbers

145 and 267

Step 2: Subtract first digit from left of the number 145 from 267 i.e.,

7 - 5 = 2

Step 3: Subtract second and third digit from left of the number 145 from 267 i.e.,

6 - 4 = 2

2 - 1 = 1

2        6        7

1        4        5   ( - )

-----------------------------

1       2          2

-----------------------------

Step 4: Solution

267 - 145 = 122

Online Calculus Notes

Introduction to online calculus notes:

Calculus is an important part in mathematics focused on limits, functions, derivatives integrals and infinite series. This subject constitutes a major section of modern mathematics education.  It has two major branches,

Differential calculus

Integral calculus

Both differential and integral calculus are associated to the fundamental theorem of calculus.

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Online calculus notes:


Here are the online notes for calculus which is available to everyone who wants to learn calculus from online notes.

This online note provides lot of examples to learn online calculus.

This notes will help the students who cant get clear idea in calculus class.

The material covered in this notes are derivatives, application of derivatives, integrals and application of integrals.

Derivatives and integrals are described below with its applications to show how online notes helpful to you.


Derivatives and its applications:


In derivatives, we will study the changes in the values of y corresponding to small changes in the values of x where y and x are related to each other by the equation y = f(x).

Application of derivatives:

Rate of change of quantities
Errors and approximation
Rolle's and Lagrange's theorem
Maxima and minima functions
Increasing function and decreasing functions
Tangents and normal
Optimization
Graph shape
Example problem:

Find the derivative of the function y = 7x^3 + 2x^2 + 6.

Solution:

Step 1: Given function

y = 7x^3 + 2x^2 + 6

Step 2: Differentiate the given function y = 7x^3 + 2x^2 + 6   with respect to ' x ', to get `(dy)/dx`

`(dy)/dx` = 21x^2 + 4x

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Integrals and its application:


Integration is the reverse process of that of differentiation and the process of finding derivative of the given function is called differentiation whereas finding the function whose derivative is known is called integration. This function is known as integral of the given function.

Application of integrals:

To find area under simple curves
To find areas of circles
To find areas of parabolas
To find areas of ellipses
To find area between the curves
Average function value
Volumes of solids of revolution
Example problem:

Find the integration of the function,  f(x) = 7x + 2.

Solution:

Step 1: Given function

f(x) =7x + 2

`int` f(x) dx = `int` 7x + 2 dx

Step 2:Separate the integral function

`int` 7x + 2 dx= `int` 7x dx + `int` 2 dx

Step 3: Integrate each function with respect to ' x',

`int` 7x + 2 = `(7x^2)/2` + 2x + C

Order of Operations Solve Online

Introduction :

In this online, The students will get understand about what is order of operations and step by step process of order of operations and how we are going to solve order of operations with solved problems.

The Order of Operation is PEMDAS which expands following,

P          - Parentheses ( )
E          - Exponents like `2^3`
M         - Multiplication like 5 x 4
D         - Division like  5 ÷ 5
A         - Addition like 4 + 6 and
S          - Subtraction like 9 - 6

Order of operations is very important in mathematics. Because we solve any equation in same way by using order of operations. Let us discuss about step by step process of order of operations in online.


Step by step process of solution using Order of Operations Online:


In online, we will teach the students very easily and more convenient. In online, We will teach order of operations with step by step explanations than textbook or class.

First step:

The arithmetic calculations should be finished from left to right for addition, subtraction, multiplication, division operation.

Second step:

First of all, We need to complete the operations inside a parenthesis.

Third step:

We need to complete the operations of  exponents if it is available.

Fourth step:

Now we do multiplication and division operation , from left to right sides.


Fifth step:

Next we do addition and subtraction operation  , from left to right sides.

These steps are followed while we are solving order of operations in online.

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Solved Problems on Order of operations in online:


Let us solve order of operations problems with step by step explanations in online.

Problem 1:

Solve this 9 + 4 x (4 + 9) ÷ 4 - 5 using the order of operations.

Sol:

Step 1:

Parentheses:       9 + 4 x (4 + 9) ÷ 4 - 5           =            9 + 4 x 13 ÷ 4 – 5

Step 2:

Multiplication:       9 + 4 x 13 ÷ 4 – 5                =            9 + 5^2 ÷ 4 – 5

Step 3:

Division:                9 + 5^2 ÷ 4 – 5                     =            9 + 13 – 5

Step 4:

Addition:                 9 + 13 - 5                          =            22 – 5

Step 5:

Subtraction:           22 - 5                                 =            17

The answer is 17.

Problem 2:

Solve this 5^2 + 4 x 3 ÷ ( 2 - 1 ) - 3 using order of operations.

Sol:

Step 1:

Parentheses:       5^2 + 4 x 3 ÷ ( 2 - 1 ) - 3           =            5^2 + 4 x 3 ÷ 1 - 3

Step 2:

Exponents:           5^2 + 4 x 3 ÷ 1 - 3                   =           25 + 4 x 3 ÷ 1 - 3

Step 3:

Multiplication:       25 + 4 x 3 ÷ 1 - 3                  =            25 + 12 ÷ 1 - 3

Step 4:

Division:                25 + 12 ÷ 1 - 3                      =            25 + 12  - 3

Step 5:

Addition:                 25 + 12  - 3                         =             37 - 3

Step 6:

Subtraction:             37 - 3                                 =            34

The answer is 34.

Online Geometry Course

Introduction to online geometry course:
Geometry is a special branch of mat emetics to study about the Shapes and size. Geometry contains group of objects. It used to make the object according to our given original measurement. Geometry are classified into more types. Online geometry course mean nothing but we study the relationship between shapes and sizes of all two-dimensional and three dimensional objects with real time examples.

Having problem with What is a Congruent Angle keep reading my upcoming posts, i will try to help you.

Types of geometry:

Major kinds of geometry:

Riemann geometry(Elliptic geometry)
Analytic geometry
Algebraic Geometry
Differential geometry
Descriptive Geometry
Projective geometry
Non Euclidean Geometry

Basic concepts of online geometry course and formulas:


Basic concepts of online geometry course

Types of line and angles in geometric:

Lines:

Intersecting line: The two lines are crossed together
Perpendicular line: One line stands vertically on horizontal line
Parallel line: Two line stands opposite with vertically


Angles:

Acute angle
Right angle
Obtuse angle
Straight angle
Reflex angle
Shapes in online geometry course:

Two-dimensional object:

Square
Rectangle
Triangle
Circle
Parallelogram
Trapezoid
Three dimensional object:

Cone
Sphere
Cylinder
Hemisphere
prism
Standard formulas of online geometry course objects::

Two dimensional objects:

Square:

Perimeter of square= 2*side
Area of square= side*side
Rectangle:

Area of rectangle= Length x width
Perimeter of rectangle=2(Length +Width)
Triangle

Area of triangle=1/2(Base* height)
Perimeter of triangle=(sum of three sides)
Parallelogram

Area of parallelogram = length × breadth
Circle problems:

Area of circle = p r2 Where r is the radius.
Circumference of Triangle = 2 * p * r
Diameter=2*Radius
Three dimensional objects:

Volume of cylinder = p*R2*h
Volume of a right circular cone = 1/3  * p  * R3
Volume of a sphere  = 4/3 * p * R3
Volume of a hemisphere = 2/3 * p * R3

Is this topic Discriminant Formula hard for you? Watch out for my coming posts.

Example problem in online geometry course:


Square problem:

Example 1:

Find the area and perimeter of square whose side length is 34cm?

Solution:

Area of square    = (side*side)

=34*34

=1156cm2

Perimeter of square= 4* side

=4*34

=136

Rectangle problem:

Example 2:

Find the area of rectangle with length 90cm and width 3 cm

Solution:

Area of rectangle = Length x width

= 90*3

=180cm2

Triangle problem

Example 3:

Find perimeter of Triangle whose side lengths are 100cm, 25cm, and 75cm?

Solution:

Perimeter=Sum of three side lengths (a+b+c)

a=100, b=25, c=75

= 100+25+75

=200cm

Circle problem:

Find the area of  the circle whose radius is 15cm?

Solution:

Area= Pi *Radius*Radius

Pi=3.14

=3.14*15*15

=706.2cm2

Learn Online Slope Form

Introduction to learning slope form - online

In mathematics, learning slope means the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.

The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points (x1,y1) and (x2,y2) on a line, the slope m of the line is

m = (y2 - y1)/(x2-x1)

Through differential calculus, one can calculate the slope of the tangent line to a curve at a point.

The concept of slope applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the grade m of a road is related to its angle of incline ? by. (Source: From Wikipedia)

Here we are going to learn about the slope form in online. Please express your views of this topic What is the Slope Formula by commenting on blog.


Learning formulas and examples for slope form:


General form of equation:

Y=mx+b

where:

Y and X are co-ordinates, b is a constant

Types of slope forms

Point slope form

Equation of line passing through a point (x1,y1) is

y-y1 = m(x-x1)

where:

X and Y are co-ordinates

X1, Y1 – point, M is slope

Online Example problem:

Ex 1:      Find the equation of the straight line with the purpose of has slope m = 4 and passes through the point (1, –6).

Sol :       The slope intercept form of an straight line is y,m,x and b is y-intercept. Slope and the value x and y from this particular point, solve for b.

y = mx + b

(–6) = (4)(1) + b

–6 = 4 + b

–2 = b

Then the line equation must be "y = 4x – 2"

Ex 2:  Find the equation of line passing through point (3,2) and slope -1/2 ?

Sol :   Given:       Point (3,2)

x1=3,y1=2

M= -1/2

Equation of line passing through point is

Y-y1 = m(x-x1)

Y-2= -1/2(x-3)

2(y-2) =-1(x-3)

2y-4 = -x+3

2y = -x+7

y = -x / 2+7 / 2

Ex 3:   Determine the equation of the line (write in slope- intercept form) passes through (1, 3) with a slope 1/4.

Sol :    y - y1 = m ( x - x1 )

It goes through the point (1,3) and has a slope of 1/4.  So appropriate this information to the point-slope formula gives:

y - 3 = 1/4(x - 1))
y - 3 = 1/4(x - 1)
y - 3 = x/4 - 1/4
y = x/4 - 1/4 + 3
y = x/4 - 1/4 + 12/4
y = x/4 + 11/4
The final equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

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Some practice problems for learning slope form


Q 1:   Find the slope of the line that passes through the points (-1, 2) and (4, 8).

Answer: y = 2x + 4

Q 2:   Find the equation of the straight line which have slope m = 4 and passes through the point (–2, –6).

Answer: y = 4x + 2

Q 3: . What is the slope of the line parallel to the line in which the equation is given by 5x – 6y = 3?

Answer: y = 5x / 6 – 1 / 2.

Study Online Linear

Introduction :

Online Linear equation is incorporated form an algebraic equation, for example y = 5x + 8 or 5x + 6y – 2z = 4. The degree of the variable of the linear equation is 1. If the Online linear equation has two variable, that  online  linear equation will give  the straight line on the graph. online is one of the best tool to study a lot of things.

Procedure to study online linear equation:


Step 1:  If we want to solve the equation for x, we  have to move the x to on side of the equal sign, which  is similar to,    10x+10+50=300

Step 2:Do the 'reverse operations.' This means we would want to add -50.  So we will get 10x+10=250

Step 3: Now we have to add -10 on both sides of the equation. So we will get 10x=240

Step 4: Now we have to divide both sided by 10. That is 10x/10=240/10. Therefore, x=24

Understanding Quadratic Equation Formulas is always challenging for me but thanks to all math help websites to help me out.

Examples to study online linear problems:


Ex:1

x - 4 = 10

Add 4 to both sides of the equation:

x = 14

The answer is x = 14

Ex:2

2x - 1 = 10

Add 1 to both sides of the equation:

2x = 11

Divide both sides by 2:

X = 5.5

The answer is x = 5.5

Ex::

x+y=9

-x+2y=0

Substitution method for linear equation:

x+y=9   ---------------------- equation 1
-x+2y=0---------------------- equation 2

If we add the equations 1 and 2, we will get

3y=9

3y/3 = 9/3 ( both sides are divided by 3 )

y = 3

Substitute y = 3 in the equation 1, so we will get

x +  3 = 9

x+3-3=9-3 ( -3 is added on both sides)

x=6

Elimination method for linear equation:

x+y=9   ---------------------- equation 1
-x+2y=0---------------------- equation 2

Take the equation 1

x+y=9

x+y-y=9-y ( -y is added on the both sides )

x=9-y

Substitute x=9-y  in the equation 2, we will get

-(9-y ) +y=0

-9+y+2y=0

-9+3y=0

-9+9+3y=0+9

3y=9

3y/3=9/-3 ( both sides are divided by 3)

Y=3

Substitute y=3 in the equation 1

X+3=9

X+3-3=9-3 ( Add -3 on the both sides)

X=6

Solving Online Simultaneous Equations

Introduction to online simultaneous Equation:

A set of linear equations having a common solution set is called a system of simultaneous linear equation. In solving simultaneous equation section we are going to learn how to solve the linear equations in three variables To find the values of three unknowns, we need to be given three linear equations on three unknown variables.In general online is defined as tutoring on internet. Thus the solving of  simultaneous equation which is taught on internet is known as solving online simultaneous equation.

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Procedure for solving three given linear equations with three variables x, y, z


Three equations are given.
Take any two, say the first two equations.
Eliminate one variable say z.
Similarly eliminate z from the second and the third (or first and the third equation).
We get two linear equations in x, y.
Solve them in the usual way learnt in early cases.
Substitute the values of x and y in any one of the three equations to get the value of z.
Thus the values of x, y and z are obtained.

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Example Problems on online simultaneous equation:


Example 1: Solve : x+ y = 3, y + z = –5, z + x = 2.

Solution: Let the equations be identified as

x + y = 3------------------- (1)

y + z = –5 ------------------(2)

z + x = 2 --------------------(3)

Adding all the three equations, we get

2x + 2y + 2z = 3 + (–5) + 2 or 2(x + y + z) = 0 or x + y + z = 0 (4)

Substituting y + z = –5 in equation (4) we get x + (–5) = 0 ∴x = 5.

Substituting z + x = 2 in equation (4) we get y + 2 = 0 ∴ y = –2.

Substituting x = 5 in equation (3) we get z + 5 = 2 or z = 2–5 = –3

The solution is x = 5, y = –2, z = –3.

Example 2: solve: x +3y = 4, x + 6y = 2.

Solution: Let the equation can be written as

X + 3y = 4 ------------(1)

X + 6y = 2 ------------(2)

Changing the sign      __-__-____-___

-3y   =  2

Y = -(2/3).

Sub y in (1) we get

X + 3{-(2/3)} = 4

X – 2 = 4

X = 6.

Solve Online Percentages

Introduction:

A ratio assessment of two quantities expressed by using 100 equal parts, or hundredths; symbolized %. There are three major uses of percent: division of a whole, rate, and comparison of any two quantities. In other words, One part in a hundred: The report states that 42 percent of the alumni contributed to the endowment. Also called per cent um.

Sample Problems: Percentage


Example : Imagine 15 red balls in a basket of 40 balls. If the ratio stays the same, how many red balls would there be in a basket of 100 balls?

To solve the proportion set up the equation:

Red balls 15 X Multiply the diagonal numbers. 15x100=1500

Total balls 40 100 Then divide by the remaining number. 1500)40=37.5

There would be 37.5 if there were 100 total in the basket

This says if we have 15 red balls out of 40 total there are 37.5 % red balls.

Fractions to Percents

Example : Imagine 24 green shirts in the shirt drawer. If the ratio of green shirts to total is 70 to 100, how many total shirts are in the drawer?

To solve the proportion set up the equation:

Green Shirts 24 70 Multiply the diagonal numbers. 24x100=2400

Total Shirts x 100 Then divide by the remaining number. 2400)70=34.29

There would be 34.29 total shirts. (One must have a large hole.)

Example : Write each fraction as a percent: ½,18/20,4/5

(1 / 2 )* 100 = 50 %

(18 / 20 ) * 100 =18 * 5 = 90 %

( 4 / 5 ) * 100 = 80

Decimal to Percentage


I have recently faced lot of problem while learning Simple Interest Rate Formula, But thank to online resources of math which helped me to learn myself easily on net.

Example:

On shopping, a certain item has increased from 75 cents per pound to 81 cents per pound. What is the percent increase in the cost of the item?

Percent change =( New value – Old Value) / Old Value * 100

Percent Change = ( ( 81-75 ) / 75) / 100 = ( 6 / 75 ) *100 = 0.08 * 100 = 8 %

There was an 8 % increase in the cost of the item

Easy Calculator Online

Introduction to easy calculator online:

In general, calculators are used to perform various operations. Mathematical calculators are used to perform various mathematical operations such as addition, subtraction, multiplication, division etc., The term easy calculator online refers to the online calculators performing easier operations such as  addition, subtraction, multiplication and  division. In this article of easy calculator online, we are going to discuss about easiest mathematical operations that can be performed using calculators.

Having problem with Antiderivative Calculator keep reading my upcoming posts, i will try to help you.

Online calculators for Addition and Subtraction:


Examples using addition calculator:

1) 43 + 27 = ?

Step 1: Enter the numbers 43

Step 2: Press the + sign

Step 3: Enter the numbers 27

Step 4: If we press = sign, the result can be obtained as 70.

2) 399 + 826 = ?

Step 1: Enter the numbers 399

Step 2: Press the + sign

Step 3: Enter the numbers 826

Step 4: If we press = sign, the result can be obtained as 1225.

Examples for subtraction calculator:

1) 150 - 80 = ?

Step 1: Enter the numbers 150

Step 2: Press the - sign

Step 3: Enter the numbers 80

Step 4: If we press = sign, the result can be obtained as 70.

2) 359 - 148 = ?

Step 1: Enter the numbers 359

Step 2: Press the - sign

Step 3: Enter the numbers 148

Step 4: If we press = sign, the result can be obtained as 211.

Is this topic Slope of a Horizontal Line hard for you? Watch out for my coming posts.

Online calculators for Multiplication and Division:


Examples for multiplication:

1) 18  * 37 = ?

Step 1: Enter the numbers 18

Step 2: Press the  *  sign

Step 3: Enter the numbers 37

Step 4: If we press = sign, the result can be obtained as 666.

2) 72  * 31 = ?

Step 1: Enter the numbers 72

Step 2: Press the  *  sign

Step 3: Enter the numbers 31

Step 4: If we press = sign, the result can be obtained as 2232.

Examples for Division:

1) 100 / 20 = ?

Step 1: Enter the numbers 100

Step 2: Press the  /   sign

Step 3: Enter the numbers 20

Step 4: If we press = sign, the result can be obtained as 5.

2) 82 / 5 = ?

Step 1: Enter the numbers 82

Step 2: Press the  /  sign

Step 3: Enter the number 5

Step 4: If we press = sign, the result can be obtained as 16.4.

Online Statistics

Introduction to online statistics:
Online statistics software provides the way to access statistical tools to analyze data and improve quality through online. This provides an interactive way of analyze and access data. Possess the software packages for various analyses and easy data access, some software’s offers analyzing of data at free of cost. Mainly used in statistical applications helpful for students and statistical analyzers.



I like to share this Correlation Coefficient Definition with you all through my article.

Explanation about online statistics:


Some commonly used online statistics software is brightstat, dataplot, statistics 101, and tetrad.

Statistical table’s calculator: This online statistics software is used to find out the probabilities, mean and all basic statistical analyzes.

Convert to Standard Scores: This online software is used to convert the individual values into statistics standard scores according to the conventional formula.

Data Transformation: This online statistics software uses some mathematical function to translate the data values, so that each transformed value is replaced with the transformed value. Transformed data value should be more close to assumption value.

Randomizer: This online software tool is used to perform random sampling.

Simple Graph Maker: This is used to draw graphs, graph functions. We can produce graphs with high quality accurately. We can produce our own graph.

Pocket Calculator: This online software tool is used to do simple arithmetic calculations.

Descriptive statistical software:  This online statistics software is used to find out average, mean, median, variability.

Mathematical Equation Plotter: This is used to plots mathematical equations, statistical distributions, derived functions, cumulative functions, and apply numerical integration.

Understanding 7th grade math problems with answers is always challenging for me but thanks to all math help websites to help me out.

Procedures involved in online statistics:


Procedures:

Entering of Data: Enter the input data in the given text field.
Importing of Data: Import any data or values either by copy or paste operations.
Data Check:  Check all the data values before submitting. If there is any error in data entry, the process will not be computed.When all values are entered, click convert buttons.
Exporting Results: The software will perform the computation process using various computational techniques and displays the results.The results are displayed in the displaying context area.

Rounding Solve Online

Introduction :

The rounding of a number for estimate the result of a problem. The rounding a number is must end with one or more ' 0'(zeros). The rounded operations of number are the nearest ten, hundred, thousand, million, etc. The rounded numbers are based on their size. It is avoids the inaccuracy of end of the answer.

I like to share this Consecutive Numbers with you all through my article.

Rules for solving Rounding a number online:


Following rules are used for solving rounding problems online:

If a number of right most digit is less than 5 then the last digit is neglected and the retained of the last digit is unchanged.
If a number of right most digit is greater than 5 then the last digit is neglected and the retained of the last digit is increased by one.

If  a number of right most digit is equal to 5 than the last digit is neglected and the retained of the last digit is unchanged, if it is even or increase the last retained digit by one if it is odd.


Solving Example for Rounding online:


Estimate the result of expression ( 476 + 354 - 125 + 435 - 289 + 231) by rounding to the nearest ten and hundred.

Solution:

Step 1 : To round the each number by nearest ten.

476 is rounding to 480.

354 is rounding to 350.

125 is rounding to 120.

435 is rounding to 440.

289 is rounding to 290.

231 is rounding to 230.

Step 2:       Estimation of rounding the expression:

480 + 350 - 120 + 440  - 290  + 230 = 1090

Step 3: To round the each number by nearest hundred.

476 is rounding to 500.

354 is rounding to 400.

125 is rounding to 100.

435 is rounding to 400.

289 is rounding to 300.

231 is rounding to 200.

Step 4:  Estimation of rounding the expression:

500 + 400 - 100 + 400  - 300  + 200 = 1100

Step 5: To check with real(actual) values.

476 + 354 - 125 + 435 - 289 + 231 = 1082.

Therefore, Rounding to the nearest hundred did not produce as good of an estimate as rounding to the nearest ten.

Progressions Solve Online

Introduction:

Solving online progression is very interesting since we can find the nth term of the particular sequence in much easier way. In this article we shall learn about steps involved in progressions solving. Moreover we will see in detail about different types involved in progression.

There are three types of Progression in math,

• Arithmetic progression
• Geometric progression
• Harmonic progression

Let us see these progression and their properties in the following section.

Arithmetic Progression


Definition:

It is a sequence of numbers in which each term except the first term can be calculated by adding constant number (common difference) to the immediately preceding number.

The General form of the arithmetic sequence is,

a, a+d, a+2d, a+3d………..

Here a is the first number and d is the common difference.

To find the nth term of an arithmetic progression we can use the following formula,

an=a+ (n-1) d

Properties of Arithmetic Progression:

When we add or subtract any constant number with all the terms of the sequence, the arithmetic sequence remains an arithmetic sequence.
Example:

5, 7, 9, 11, 13, 15, 17….. is an A.P with common difference 2.

Add 3 with all the terms,

8, 10, 12, 14, 16, 18, 20…. Is also an A.P with common difference 2.



When we multiply or divide by a non-zero constant with all the terms of the sequence, the arithmetic progression sequence remains an arithmetic progression.
Example:

10, 20, 30, 40, 50, 60, 70…. Is an A.P with common difference 10.

Multiply by 2 with all the terms,

20, 40, 60, 80, 100, 120, 140…. Is also an A.P with common difference 20.

Example Problem:

1. Find the 6th term of the following sequence, 7, 12,17,22,27…

Solution:

The common difference is 5.

nth term of the A.P is an= a+(n-1)d

6th term of the A.P  is a6 = 7+ (6-1)5

= 7+ 5 × 5

= 7 + 25

= 32

So the 6th term of the given sequence is 32.


Geometric Progression


Definition:

It is a sequence of numbers in which each term of the sequence except the first term can be calculated by multiplying the preceding term by means of a constant factor (common ratio).

The General form of the Geometric progress is,

a, ar,ar2,ar3,………

nth term of the geometric progression is,

an=ar (n-1)

Properties:

When we multiply or divide by a non-zero constant with all the terms of the sequence, the arithmetic progression sequence remains an arithmetic progression.
Ex:  2, 4, 8, 16, 32, 64…. is the geometric series with common ratio 2.

Multiply by 2,

4, 8,16, 32, 64, 128…. Is also the geometric series with common ratio 2.


Harmonic Progression:


Definition:

In mathematics, a harmonic progression is a progression formed by taking the reciprocals of an arithmetic progression.Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms.

The general form of the harmonic progression is ,

a ,   a      ,   a     ,     a    .............

1+d     1+2d    1+3d

Example:

10, 10/6 , 10/11 , 10/16....

Here a = 10 and d = 5.

Business Math Help Online

Introduction :
The business mathematics always deals with gain or  loss. The cost of a thing or materials are fixed by taking into consideration of its profit, margin, cash discount, trade discount, etc. The price that  marked in the article is called catalogue price or marked price. For trading, the producer makes a discount in the marked price to the buyer and the test questions to improve  their knowledge in business .Online is new process where a  good business adviser  will  help and share his knowledge through Internet and solves the customer problems more effectively with out any error.Let us see about the article called business math help in online.


Business math problems are solved with the help of online


Problem 1:

A capenter bought 158 wooden tables for the cost $1900. In the amount of  158 wooden tables 61are damaged . Then the capenter sold the remaining wooden tables for the cost185 for each. Calculate and find the profit or loss percent of his business.
Solution:

Cost Price of 158 wooden tables = 1900.

61 wooden tables are damaged

Remaining  wooden tables  = 158 – 61 = 97

Selling Price of wooden tables = 1900

Selling Price of 97  wooden tables = 97 × 1900 = $ 184300.

Here the sales  Price is greater than Cost Price.

Profit = Selling Price – Cost Price

= 184300 – 1900 = $ 182400

Profit % = `(profit)/(cost price)` × 100

`182400/1900 ` x 100
Profit percentage is =9600%

Problem 2:

In a ice cream shop  a employee  gets  salary  depends upon how he work for the day for 5 days and he gets salary Rs.20,80,250,320,340.calculate and find the profit  cost of his salary.
Solution:

Given that ,
Number of working days,n=5
The formula for average cost.
X=`sum``(X_ i) /n`

= `((20+80+250+320+340)/5) `

= `1010/5`

profit cost price  per day   = $.202

Is this topic Greatest Common Factor Calculator hard for you? Watch out for my coming posts.

One more business math problems are solved with the help of online


Problem 3:

A sports material producing company bought 779 cricket bats for the cost 250. Among the779 cricket bats 23 are damaged. Then the company sold the undamaged cricket bats for the cost 155 each. Calculate and find the profit or loss percent of the company business.
Solution:

Cost Price of 779 cricket bats = $250.

23 are damaged cricket bats

Remaining cricket bats = 779 – 23 = 756

Selling Price of one cricket bat is  = $250

Selling Price of 756  cricket bats = 756 × 250 = $189000.

Here the sales Price is greater than Cost Price.

Profit = Selling Price – Cost Price

= 189000 – 250 = $188750

Profit % = `(profit)/(cost price)` × 100

= `188750/250` × 100

Profit percentage is = 75500 %

Online Measurement Practice

Online measurement practice:

The quantities using to find lengths, capacities, weights of things etc are called measures. Many countries have their ownsystem of measures. But Metric System of dealings is very simple and easy to calculate. Hence most countries in the world use Metric System of measures

In Metric System:

The basic unit of length is meter (m)

The basic unit of weight is gram (g)

The basic unit of capacity is liter (l)

Metric system is also known as decimal system, like it has other sub units in powers of ten.


Online measurement practice-Example 1:


Convert 378.6 cm into meter.

Solution:

Here the conversion is from centimeter to meter. i.e. from lower unit to higher unit.

100cm = 1m.

Hence 378.6cm =378.6/100m

= 3.786 m (shifting the decimal two digits to the left)

Online measurement practice-Example 2:

Convert 40.1735 km into meter.

Solution:

Here the conversion is from higher to lower. Hence we have to shift the decimal point to the right.

1km = 1000 m

40.1735 km = 40.1735 × 1000 m

= 40173.5 m

Online measurement practice-Example 3:

Convert 6m into millimeter.

Solution:

Note: Here we are converting the unit meter into millimeter. i.e. from higher unit to lower unit.

The operation should be multiplication.

Solution:

1 m = 1000 mm

Hence 6 m = 6 × 1000 mm

= 6000 mm.


Online measurement practice-Example 4:


Express 8 kg 3 dag in grams

Solution:

1 kg = 1000 g

1 dag = 10 g

Hence 8 kg 3 dag = 8 × 1000 g + 3 × 10 g

= 8000 g + 30 g

= 8030 g

Online measurement practice-Example 5:

Convert 3 ton 7q 18 kg into kilograms.

Solution:

1 ton = 1000 kg

1 q = 100 kg

Hence 3 ton 7 q 18 kg = 3 × 1000 kg + 7 × 100 kg + 18 kg

= 3000 kg + 700 kg + 18 kg

= 3718 kg

Online measurement practice-Example 6:

Convert 25 k 37 into liters.

Solution:

1 k = 1000

Hence 25 k 37 = 25 × 1000l + 37

= 25000  + 37

= 25037

Online measurement practice-Problems:

Problem 1: Convert 478.6 cm into meter

Solution: 4.78600 meters

Problem 2: Convert 10m into millimeter.

Solution: 10000 mm.

Grade 4 Math Fractions

Grade 4 math fractions:
This article we are discussing about grade 4 math fractions. A part of a whole object is called fraction. Fractions can be consisting of minimum two digits. The numerator is specified as top digits. The denominator is specified as bottom digits.

Numerator
denominator

An arithmetical expression relating digits or two quantities, one divided by the other is called fraction. The digits may be whole numbers of this is a rational number.

For example, 3/3 is a fraction. The digit 3 is numerator and digit 3 is a denominator. Grade 4 math fractions are used to solve the simple addition fraction, multiplication fraction and subtraction fraction.

Please express your views of this topic Numerator Denominator by commenting on blog.

Examples problem for grade 4 math fractions:


Example 1:

Add the fractions for given two fraction,` 5/8` +`6/8`

Solution:

The given two fractions are `5/8 ` + `6/8`

The same denominators of the two fractions, so

= `5/8` + `6/8`

Add the numerators the 5 and 6 = 5+6 = 11.

The same denominator is 8.

= `11/8`

The addition fraction solution is `11/8`

Example 2:

Subtract the fractions for given two fractions, `15/8` – `6/8`

Solution:

The given two fractions are `15/8` – `6/8`

The same denominators of the two fractions, so

= `15/8 ` – `6/8`

Subtract the numerators the 15 and 6 = 15 - 6 = 9.

The same denominator is 8.

= `9/8`

The addition fraction solution is `9/8`

Example 3:

Multiply the fractions for given two fraction, `15/8` * `6/8`

Solution:

The given two fractions are `15/8` * `6/8`

The same denominators of the two fractions, so

= `15/8` * `6/8`

Multiply the numerators the 15 and 6 = 15*6 = 90.

Multiply the denominators the 8 and 8 = 8 *8= 64

= `90/64`

The addition fraction solution is `90/64`

Example 4:

Add the fractions for given two fraction `5/6` + `4/5`

Solution:

The denominator is different so we take a least common denominator (LCD)

LCD = 6*5 = 30

So multiply and divide by 4 in first term we get

`(5 *5) / (6 * 5)`

=`25/30`

Multiply and divide by 3 in second terms

= `(4*6) / (5*6)`

= `24/30`

The denominators are equals

So adding the numerator directly

=` (25+24)/30`

Simplify the above equation we get

= `49/30`

Therefore the final answer is `49/30`

I have recently faced lot of problem while learning Combining Like Terms, But thank to online resources of math which helped me to learn myself easily on net.

Practices problems for grade 4 math fractions:

Problem 1: Add the two fraction `11/10` +`10/10`

Solution: `21/10`

Problem 2: Subtract two fractions `11/10` – `10/10`

Solution: `1/10`

Problem 3: multiply two fractions `12/10` * `5/10`

Solution: `3/5`

Domain and Range and Math

Introduction :

In mathematics, the domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined. That’s provides an "output" or "value" for each member of the domain.Interval, also called a range; the range between minimum and maximum e.g. the range on 21 22 23 and 24 is 3.Range, the set of all output values produced by a function. (Source: Wikipedia)

Please express your views of this topic What is a Denominator by commenting on blog.

Example problems for domain and range and math:

Domain and range and math – Example problem: 1

In the function of f that can be expressed as f(x) = -1 / (x + 19). Solve the domain function.

Solution:

To find the domain equate denominator to zero

x + 19 = 0

x = -19

The domain function of f lies in the interval (-infinity, -19) U (-19, +infinity)

Domain and range and math – Example problem: 2

In the function of f that can be expressed as the f(x) = x ^2 + 52. Solve the domain function.

Solution:

The function f(x) = x ^2 + 52 is defined for all real values of x.

In the ‘x’ is the real value and f(x) is the domain function.

Since x ^2 is never negative, x ^2 + 52 is never less than 52

Domain and range and math – Example problem: 3

The function of f that can be expressed as f(t) = (1)/(t + 27). Solve the domain function.

Solution:

The function f(t) = (1)/(t + 27) is not defined for t = -27, as this value requires division by zero.

In all the real numbers that except by -27 and the domain function is f(t).

It has no matter how large or small t it becomes, f(t) will never be equal to zero

Domain and range and math – Example problem: 4

The function of f that can be expressed as f (x) = x 2 + 35. Solve the range function.

Solution:

The range of the function f that is the set of all values of f(x) in the interval (35, +infinity)

Domain and range and math – Example problem: 5

In the function of f that can be expressed as f (x) = x 2 + 39. Solve the range function.

Solution:

The range of function f lies in the interval (39, +infinity)


Practice problems for domain and range and math:


1. The function of f that can be defined as f(x) = `sqrt(-x + 59)` . Solve the domain function.

[Answer: The domain function of f that lies in the interval  (-infinity , 59) ]

2. The function of f that can be defined as f(x) = `sqrt( -x + 60) / ((x + 37)(x + 51))` . Solve the domain function.

[Answer: The domain function of f that lies in the interval  (-infinity , -51) U (-51 , -37) U (-37, 60 ) ]

3. The function of f that can be defined as f (x) = x 2 + 89. Solve the range function.

[Answer: The range of function f that lies in the interval (89, + infinity)]

Doing Fractions Online

Introduction for Fractions:

A fraction (from the Latin fractus, broken) is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ?, ¾, etc.) and which consist of a numerator and a denominator.

Source – Wikipedia.


Doing Fractions Online for Addition:


The followings are some of the examples in addition for fractions online.

Add the fractions: `3/8 + 4/8` .

Solution:

= `3/8+4/8`

= `(3+4)/8`

= `7/8`

Add the fractions: `2/6+3/4`

Solution:

In this the denominators are different in them.

Then we have to find a LCM for these denominators.

The LCM of 6, 4 = 24

So `(2*6)/(6*4)` = `12/24`

`(3*6)/(4*6)` = `18/24`

In this the denominators are equal so we can add the numerator in the fractions.

=`12/24 ` + `18/24`

=`(12+18)/24`

=`30/24` is the answer.

Add the fractions: `4/3+5/2`

Solution:

In this the denominators are different in them.

Then we have to find a LCM for these denominators.

The LCM of 3, 2 = 6

So `(4*2)/(3*2)` = `8/6`

`(5*3)/(2*3)` = `15/6`

In this the denominators are equal so we can add the numerator in the fractions.

=`8/6 ` + `15/6`

=`(15+8)/6`

=`23/6` is the answer.


Doing Fractions Online for Subtraction:


The followings are some of the examples in subtraction for fractions online.

Subtract the fractions:  `3/8-4/8` .

Solution:

= `3/8-4/8`

= `(3-4)/8`

= `-1/8`

Subtract the fractions: `3/4-2/5` .

Solution:

In this the denominators are different in them.

Then we have to find a LCM for these denominators.

The LCM of 4, 5 = 20

So `(3*5)/(4*5)` = `15/20`

`(2*4)/(5*4)` = `8/20`

In this the denominators are equal so we can add the numerator in the fractions.

=`15/20-8/20`

=`(15-8)/20`

=`7/20` is the answer.

Subtract the fractions: `2/6-3/4` .

Solution:

In this the denominators are different in them.

Then we have to find a LCM for these denominators.

The LCM of 6, 4 = 24

So `(2* 6)/(6*4)` = `12/24`

`(3*6)/(4*6)` = `18/24`

In this the denominators are equal so we can add the numerator in the fractions.

=`12/24-18/24`

=`(12-18)/24`

=`-6/24` is the answer.

These are the examples on doing fractions online.

Define Minimum Math

Introduction :

In math the minimum has different versions like find the minimum values from given data, find the minimum distance between two objects and minimum value of function in set theory. Define the minimum in math as least value in as given set of numbers. In set element the minimum value is find out by integration. I like to share this Example Data Sets with you all through my article.


Explanation for define a minimum in math


Define the steps for finding minimum value in math:

The given set of data are collected and arrange it by using comparison technique.
Arrange the numbers in ascending order and find the difference between the numbers.
Finally get the least number as minimum.


For example consider the set of elements 5, 8, 3, 7, 6, 10, 1. Arrange the numbers in ascending order by using comparison. The ascending order of elements is 1, 3, 5, 6, 7, 8, 10. Here the least value of given set of elements is 1.

Minima in math:

In function of math the minima is find out by using set operations. This is find the minimum value of set with optimization. The global minimum value is defined by real valued function. If f ( x* ) <= f (x ) means the global minimum is present at x*. In math the global minimum value is using the bounded value theorem.

In the minimum value of set is represented as A = { ai }N and the sorted first element is equal to this resultant value. The minimum is one type of order statistics. For example consider the set { 2, 8, 4, 9 }. Sort this set as { 2, 4, 8, 9 }. So the minimum value of this math set is 2.


Define the minimum with examples


Problem 1: Find the minimum value from the set of numbers 20, 15, 35, 75, 12, 28.

Answer:

Sort the set of numbers as 12, 15, 20, 28, 35, 75.

The minimum value is 12.

Problem 2: Find the minimum value from given set A = { 4, 8, 2, 10, 1 }.

Answer:

The sorted set is { 1, 2, 4, 8, 10 }.

The minimum value is 1.

Excercise for minimum term in math:

1. Find the minimum value from given set of numbers { 54, 35, 44, 78, 22 }.

Answer: The minimum value is 22.

2. Find the minimum value from set of numbers: 47, 56, 32, 66, 77.

Answer: The minimum value is 32.

Closure Property of Math

Introduction of closure property of math:

In math closure is a property which a group either includes or lacks with respect to a given process. A set is closed with respect to that process if the process can always be completed with elements in the set. For example, the set of even natural values, 2, 4, 6, 8,….., is closed by the addition because the sum of any two of them is another even natural value. The closed set that satisfies the closure property. Is this topic Conics Equations hard for you? Watch out for my coming posts.


Closed set:


A set is closed under a process if that operation gives a member of the set when evaluated on member of the set. Sometimes the condition that the process be valued in a set explicitly stated in which case it is called as the axiom of closure.

Consider the example, one may describe a group as a set along with binary product operator follow many rules, including a rule that the product of any two values of the group is again a value. But the modern explanation of an operation creates this rule unnecessary; an n-ary operator on A is just a subset of An+1.  In its very clarity, an operator on a set cannot contain values outside the set.

Yet, the closure property of an operator on a set yet contains few utility. Closure on a set does not essentially involve closure on all subsets. Therefore a subgroup of a group is a subset on which the binary product and the unary operation of inversion assure the closure axiom.


Binary relation for A closures in math:


In math concept of a closure property can be widespread for an arbitrary binary relation P ? T×T, and an arbitrary property A in the following form: the A closure of P is the least relation R  ? T×T that has P (i.e. P ? R) and for which property A fix.

I have recently faced lot of problem while learning dependent system of linear equations, But thank to online resources of math which helped me to learn myself easily on net.

Operator for closure property:


Given an operation on a set S, one can determine the closure C(A) of a subset A in S to be the smallest subset closed under that process that contains A as a subset.

Properties of every closure operations in math are:

The closure is increasing or growing: the closure of an entity contains the entity.

The closure is idempotent: the closure of the closure same as the closure.

The closure is monotone, i.e., if P is contained in Q, then also S(P) is contained in S(Q).

Geometry Calculator Online

Introduction to geometry calculator online:

Geometry "Earth-measuring" is the part of a mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. Initially in the  body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid .And now let us see about the online geometry calculator online problems.In this article we shall discuss about the geometry calculator online.


Problems in geometry online calculator


Online geometry calculator - Problem 1:

Calculate the volume of the cylinder which has the height is 14 centimeter and radius of 7 centimeter.

Solution:-

Given:-

Height = 14 centimeter.

Radius = 7centimeter.

The formula used to calculate the volume of the cylinder is  `pi`r 2h

Volume =  `pi`r 2h

r– radius of the cylinder

H – height of the cylinder.

By applying  the given values in to the formula we get =   `pi`(7)2x 14

The product of 49 and 14 is 686

So the volume of the given cylinder is 686  `pi`




Geometry calculator Online- Problem 2

Calculate the area of rectangle whose side’s measure 16 centimeters and 4 centimeters respectively.

Solution:-

Given

Length – 16 centimeter.

Breadth –4 centimeter.

The formula used to find the area of rectangle is length x  breadth.

Area = length x breadth.

By applying  the given values in to the formula.

We get,

Area   = 16 x  4

The product of 16 and 4 yields 64 so the area of the given rectangle is 64 square



Geometry calculator Online - Problem 3

Calculate the volume of the cube whose side measure 18 centimeter.

Solution:-

Given:-

Measure of cube length = 18.

The formula used to find the volume of the cube is .

By plugging the value in to formula we get the result as

Volume =  183 .

=  5832.

So the volume of given cube is 5832 cubic centimeters.


Practice Problems in geometry calculator Online-:


Problem 1

Calculate the volume of the cylinder which has the height is 6 centimeter and radius of 1 centimeter.

Answer:- 6`pi` .

Problem 2

Calculate the area of rectangle whose side’s measure 22 centimeters and 2 centimeters respectively.

Answer:- 44.

How to do Ratios in Math

Introduction to how to do ratios in math:

In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. Example: For every Spoon of sugar, you need 2 spoons of flour (1:2). (Source: Wikipedia).

Having problem with Math Ratio Problems keep reading my upcoming posts, i will try to help you.

Examples for how to do ratios in math:


Example 1 for how to do ratios in math:

Divide the number 270 in the ratio 3:7.

Solution:

The given ratio is 3:7.

The total ratio is 3+7 =10.

For the number 3, in the ratio

270x (3/10) = 27 x3

270x (3/10) = 81.

For the number 7, in the ratio

270x (7/10) = 27 x7

270x (7/10) = 189

For the ratio 3, the ratio of the number 270 is 81.

For the ratio 7, the ratio of the number 270 is 189.

Example 2 for how to do ratios in math:

Divide the number 1290 in the ratio1: 3: 6.

Solution:

The given ratio is 1:3:6.

The total ratio is 1+3+6 =10.

For the number 1, in the ratio

1290x (1/10) = 129 x1

1290x (1/10) = 129

For the number 3, in the ratio

1290x (3/10) = 129 x3

1290x (3/10) = 387

For the number 7, in the ratio

1290x (6/10) = 129 x6

1290x (6/10) = 774

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For the ratio 1, the ratio of the number 1290 is 129.

For the ratio 3, the ratio of the number 1290 is 387.

For the ratio 7, the ratio of the number 1290 is 774.

Example 3 for how to do ratios in math:

The members A: B: C starts a business by investing the amount Rs.1, 20,000, Rs. 1, 35, 000 and also 1, 50, 000 respectively. Their annual profit is Rs. 60,000. Find the share of each from their annual profit.

Solution:

The share of A, B, C is in the ratio 120000: 135000: 150000 = 8: 9:10.

The A’s share = (60,000 x 8/27) =17777

The B’s share = (60,000 x 9/27) =20000

The C’s share = (60,000 x 10/27) =22222


Practice problem for how to do ratios in math:


The mixture of alcohol with the water is in the ratio 3:8. The quantity of the alcohol is 4 liters. Find the quantity of the water.
Answer: 10.66 liters.

Learn Online Calculus BC

Introduction :-
Online learn Calculus BC is a senior placement calculus classes taken by high school students approximately the world, most of who learn at schools with an American curriculum. The course is conservatively taken after pre-calculus, otherwise known as Introduction to Analysis, and is the first calculus course offered at most schools. Online learn calculus BC is concerned with comparing quantities that differ in a non-linear way.


Ladder for learn calculus BC:-


•    Differential online learn calculus BC is use to determine the rate of change where the function is known.

•    Integral online learn calculus BC is use to determine function where we know the rate of change.

•    The College Board are deliberately schedules the BC online learn Calculus BC exam at the same time as the AP Calculus BC exam in order to make it not possible for a student to take both tests and receive college credit for both in the same academic year.

•    They do not, however the bar student from taking the two classes at the same time it is usually at the prudence of the individual school to label online learn Calculus BC as the pre-requisite class for online learn Calculus BC, although some schools do allow them as co-requisites for gifted students.

•    However, the popular of schools require pre calculus as a prerequisite to online Calculus BC.

•    In fact, the majority of these students taking Calculus AB have not taken online learn Calculus BC.

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Purposes of online learn calculus BC:-


It mainly online learns based process and then quality of calculus should be available through the internet.
Online learn Calculus BC can be existed as an AP course by any school that can organize a curriculum for students with the mathematical ability.

The students who take the BC learn Calculus course must do so with the intention of placing out of a similar college online calculus course.

Learn Online GCF

Introduction to learn online GCF

Greatest common factor (gcf)  of two (or) more non zero integers , is the largest positive integer that divides the numbers without a remainder . It is simply the largest of the common factors .GCF is also known as highest common factor ( hcf).

Greatest common factor is easily explained with three words

a)  Factors

b) common factors

c)  greatest of common factors

Let us go through each word

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Better understanding of what is GCF


a) Factor

Definition :  A number may be made by multiplying two or more numbers together .The numbers that are multiplied together are called factors of the Final number .

For example :the product of 2 and 6 is 12 ;   2 x 6 = 12

so 2 and 6 are called as factors of 12

to find all factors of 12 ;;   12 = 1 x 12 = 2 x 6 = 3 x 4   so the all factors of 12 are 1,2,3,4,6, and 12

B) Common factors ;

Let us find all the factors of any two numbers . Let the two numbers are 12 and 18

The all factors of 12 are 1,2,3,4,6, 12

The all factors of 18 are 1,2,3,6,9 , 18

so now the common factors are the numbers which are in common in both the factors . The common factors of 12 and 18 are 1,2,3,6

c) greatest of common factor :

From above the common factors we got for 12 and 18 are 1,2,3, 6

greatest common factor is the factor which is the greatest number of all common factors .

In the above example 6 is the greatest of all common factors of 12 and 18 . So 6 is the gcf of 12 and 18

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How to caluclate GCF of given numbers


1)  list out the prime factors of each number

2)multiply those factors which are common in both the numbers . If there are no common factors then the GCF is 1

For example ; Find the GCF of  18 and 24

The prime  factors of 18 =  2 x 3 x 3

the prime factors of 24   =  2 x 2 x 2 x 3

here we have 2 and 3 as common factors , so GCF is 2 x 3 = 6 . The GCF of 18 and 24 is 6

examples ;        Find the GCF of 60  and 160

60  =  2 x 2 x 3 x 5

160 =  2 x 2 x 2 x 2 x 2 x 5

the common factors are 2 and 5  . so the GCF is  2 x 5 = 10

Workout problems ;  1) Find the GCF of  45  and  75                         Ans) 15

2) find the GCF of 225  and 625                      Ans) 5

Learn Online Calculus

Introduction to online Calculus:

Calculus (Latin) is a branch in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, learn online differential calculus and learn integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

.(Source: Wikipedia)


Types of learn online calculus:

• Online Differential calculus
• Online Integral calculus

Differential calculus applications:

Differential calculus is used to find the differentiation for the given equations.

Differential calculus:

The applications of learn differential calculus are

(i) plane geometry process

(ii) theory of real functions in differentiation

(iii) optimization problems

Derivative as a rate measure:

If a quantity y depends on and varies with a quantity x then the rate of change of y with respect to x is

`dy / dx`

A rate of change with respect to time is usually called as ‘the rate of change’, the ‘with respect to time’ being assumed.

Integral calculus 1 applications:

Integral calculus 1 is used to find the integration of the given quadratic equation.

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Example problem for learn online calculus

Example 1:

Differentiate y = `x^3`

Solution:

y = `x^3`

`dy / dx` = 3x.

` dy / dx` = 3x.

Example 2:

Integrate `5x^3+2x^2`

Solution:

=  `x^3+2x^2`

= `5(x^4 / 4) + 2(x^3/3)+c` (answer)

Example 3:

Differentiate` x ^ 4 + x ^ 2+ x + 4`

Solution:

The given equation is `x ^ 4 + x ^ 2+ x + 4`

Differentiate the equation with respect to x we get `4 x^3 + 2 x +1`


Practice problem for learn online calculus:

Differentiate the quadratic equation x2+3x+2
Answer: 2x+3

Integrate the equation  6x+3
Answer :  3x2+ 3x

Online Data Collection

Introduction for learning online data collection:
Data collection is a term used to describe a process of preparing and collecting data
The purpose of data collection is to obtain information to keep on record, to make decisions about important issues, to pass information on to others. Primarily, data is collected to provide information regarding a specific topic.
Data collection usually takes place early on in an improvement project and often contains the following activity.
Pre collection activity – Agree goals, target data, definitions, methods
Collection – data collection
Present Findings – usually involves some form of sorting analysis and/or presentation.
Source Wikipedia

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Types for learning online Data collection:


There are mainly two types for learning online data collection:

1) Primary data collection

2) Secondary data collection

Primary data collection:

The data’s which are collected for the first time and those, which are original in character, is refer as primary data. There are several methods exists for primary data collection. Collections of primary data are obtained by either personal communication through interviews or by personal observation.

Secondary data collection:

The data’s that is already collect by some other person who undergone statistical processes are refer as secondary data. The secondary data’s may be published or unpublished. Sometimes, the data may be unsuitable. Therefore, it is necessary to handle those data’s carefully during the researches. Is this topic solving systems of linear equations by elimination hard for you? Watch out for my coming posts.


Methods for learning online data collection:


The Methods for learning online data collection are as follows:

Data collection by means of Observation:

In this method, data’s collected by means of observation. The observer can collect the data or he can collect the data by personally visiting the field.

Data collection by interviews:

The data’s can be collected by means of personal interviews or even by means of telephonic interviews.

Questionnaire method:

This is one of the popular methods of data collection. During enquiries, this method is mainly used.

Schedule method:

For solving social problems, this method of data collection is consider as an important one.

Data collection by means of case study:

The researchers can collect the data’s by taking one or more units for special study.

Survey method of data collection:

The data’s can be collect by means of undertaking surveys. This method is the most commonly used method for the collection of data’s.

Learn Online Intercept

Introduction to learn online intercept:

Intercept:

Intercept of a line can be defined as a point at which a line, curve, or surface intersects an axis.

Intercept is an intercepted segment of a line.

X – Intercept:

The x-intercept is defined as the point at which the line cuts the X-axis.

The x-intercept is given as (x, 0).

Y – Intercept:

The y-intercept is defined as the point at which the line cuts the Y-axis.

The  y-intercept is given as (0, y). Is this topic Segment of a Circle hard for you? Watch out for my coming posts.


Learn online intercept with examples:


A few example problems are given below to show how we can learn intercept through online.

Example: 1

Find x and y intercept of the equation 9x + 6y =18.

Solution

To find x intercept, plug y =0 in the equation and solve for x.

9x + 6y = 18

9x + 6(0) = 18

9x = 18

x = 18 / 9

x = 2

Therefore, the x-intercept = ( 2,0 ).

To find y intercept, plug x=0 in the equation and solve for y.

9x + 6y = 18

9(0) + 6y = 18

6y = 18

y = 18 /6

y = 3

Therefore, the y-intercept = (0, 3).

Example: 2

Find x and y intercept of the equation 3y = 6x + 24

Solution

To find x intercept, plug y =0 in the equation and solve for x.

3y = 6x + 24

3(0) = 6x + 24

0 = 6x + 24

-24 = 6x

-24 / 6 = x

-4 = x

x = -4

Therefore, the x-intercepts is (-4, 0)

To find y intercept, plug x=0 in the equation and solve for y.

3y = 6x + 24

3y = 6(0) + 24

3y = 0 + 24

3y = 24

y = 24/3

y = 8

Therefore, the y-intercepts is (0, 8)

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Homework problems to learn online intercept:


The following homework problems helpful to learn online intercept.

Find x and y intercept for the following equations,

y = 8x + 3
3x = -y + 9
y =x - 6
12y = -4x + 3
Solutions:

1) x intercept = (-3/8, 0)

y intercept =(0, 3)

2) x intercept = (3, 0)

y intercept = (0, 9)

3) x intercept = (6, 0)

y intercept = (0, -6)

4) x intercept = (3/4, 0)

y intercept = (0, 1/4)

Learn Online Calculating

Introduction :
Online calculating involves learning problems in all categories of mathematics. Here we are going to learn the problems in linear algebra which is to be solved in online and calculating the coefficients value. In online, the coefficient value for the given equation is showed automatically and it helps to learn step by step solution. Linear algebra is one of the branches of mathematics that deals with finding unknown variables with the known values. In online, linear algebra helps to learn problems with real numbers, complex numbers, matrices etc. Some of the example problems are discussed below in which it helps to learn the online calculating method.


Example problems for calculating online:


Example 1:

Calculate the ‘a’ value from the given equation   -3(a - 4) / 7 - (a - 2) / 2 = -2 a

Solution:

The given expression is
-3(a - 4) / 7 - (a - 2) / 2 = -2 a

From the above expression LCD = 7*2=14, multiplying the LCD on both sides.
14 * [-3 (a - 4) / 7 - (a - 2) / 2] = 14* [-2 a]

Solving the above term
-6(a - 4) - 7(a - 2) = -28a

Multiplying the integer terms and solves it.

-13a + 38 = -28a

Subtract 38 on both sides
-13a + 38 - 38 = -28a -38

Grouping the above terms
-13a = -28a - 38

Add 28x on both sides
-13a + 28a = -28a - 38 +28a

Grouping the terms
15a = -38

Multiply 15 on both sides
a = -38/15 is the solution.

Example 2:

Calculate ‘a’ value from the equation

(a - 1)(a + 1 / 2) = - a + 1

Solution:

The given function is

(a - 1) (a + 1 / 2) = - (a - 1)

Write the equation with the right side equal to zero.

(a - 1)(a + 1 / 2) + (a - 1) = 0

Take (a - 1) as common term

(a - 1)(a + 1 / 2 + 1) = 0

Solving the above equation to find a term
a - 1 = 0

a + 3 / 2 = 0

Solve for a
a = 1
or
a = - 3 / 2 is the solution.


Practice problems for calculating online:


1) Determine the Z value in the equation

1 – 2/ (a - 8) = 4

Answer: a =22/3 is the solution.

2)  Calculate the ‘a’ value in the equation

(a - 2)(a + 1) = - a + 2

Answer: a= -23

Online Adding Integers

Introduction:

The positive numbers (natural number) and negative numbers mutually with zero are called as the integer’s .The integers having three types. They are positive integers, negative integers and non negative integers. Integers like -5,-7, 0, 4, 5, 6….

For Example,

Set of Positive integer= (1, 2, 3, 4, 5, 6……)
Set of Negative integer= (-2,-3,-4……..)
Set of Non negative integer= (0, 1, 2, 4……)

Rules of learn online adding integers:

Addition of integer is performed by three different types of ways, they are following

Addition of two positive numbers
Addition of two negative numbers
Addition of one negative number and one positive number
Rules for adding integers with different signs

1. Find the difference of the numbers, ignore the signs

2. Write the answer as the sign of the large number

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Examples of learn online adding integers:


Ex: 1 (Addition of two positive integers)

Add the following integer values:  55+ (15)

Sol: of learn online adding integers:

Here, the both of two values are positive sign.

Now we add the given integers,

So,

55 + (15) = 70

Answer: 70

Ex: 2 (Addition of two negative numbers)

Add the following integer values: (- 34) + (- 25)

Sol: of learn online adding integers:

Here, the both of two values are negative sign.

Now we add the given integers,

So, we get

-34 + (-25)

-34 - 25

Answer: 69

Ex: 3 (Addition of one negative number and one positive number)

Add the following integer values: -14+23

Sol: of learn online adding integers:

Here the highest value of given two numbers -14, 23 is 23

The difference between numbers is (23 -14) =9

The sign of highest value is positive,

When a positive integer and a negative integer are added we get either a positive integer or a negative integer or zero

The answer: 9

Ex: 4 Add the following integer values: -30+30

Sol: of learn online adding integers:

Here the both integers are equal

So the difference between two integer is (30-30) =0

Therefore the answer is =0 (zero)

When a positive integer and a negative integer are added we get either a positive integer or a negative integer or zero.