Tuesday, March 5, 2013

Division Solver

I think, you are involved in the math division of numbers, so you need to do undertaking has of finding the quotient and the remainder in the division of two positive numbers. Do most of “quotients, remainders” and you bring to aptitude an image like this:

                                       6        
                          200 | 1220
                                   1200   
                                       20
 
In this example, we are solver dividing 1220 by 200 and we are find the quotient to be 6 and the remainder to be 20 using dividing 1220 by 200. The division problem has the dividend and the divisor as its given value; in the example, these are, in that order, 1220 and 200. Results have of the quotient and the remainder, which, in the example, are 6 and 20, in that order.

Think about the solver division of number are 27 % 5= 5 remainder 2. It may also be written as

                                   `27/5`=2+(`25/5`)

In solver division using algorithm, 27 is called the dividend, 5 the divisor, 5 the quotient, and 2 the remainder. The relation between these four quantities can also be representation as 27=5x5+2.

In fact, given any integers g and h (h not equal to 0) there exist only one of its kind integers q and r, where 0≤ r<h, such that                            g=hq+r

This solver division algorithm is referred to as the math division decimals or the division independence.
If you require to do divide g by h (b not equal to 0), we get `g/h`=q=`r/h`, which makes the solver  division algorithm almost clear.

When g is divided by h we get a quotient q and a remainder r, 0 ≤r<h, and this cannot be ended in more than one way (q and r are only one of its kind).

Division solver need to follow the step:


     Given: solver division positive numbers g and h.        
  
     Result: non-negative numbers q and r such that g=hq+r, and 0≤r<h.

Steps you need to do for division solver:

        Step 1: Begin by set Q=0 and R=g.

       Step 2: if R<h, write down, “The quotient is Q and the remainder is R” and stop; or else, go to do step 3.

       Step 3: If R≥h, take off b from R, boost Q by 1, and go back to step 2.

Math division problem  solver

Problems on Division Solver:


Problem 1:- Division problem solver 23 by 68

Solution:-


In following steps for how to do divide 23 by 68 

Step 1:-
        -------
    23| 68

In the above equation 23 is divisor and 68 is dividend. In the divisor has two decimal numbers put the value dividend of 23.

Step 2:-
         2
       -------
   23| 68
        46
      ---------
        22

In 23 x 2 = 46 the divisor number 23 is multiplied with 2 to get an answer 46. In 46 is less than from 68.So use the value then subtract the value and get 22. 

Step 3:-
         2.9
        -------
    23| 68
         46
       ---------
         220
         207
      ---------
          13

The value 22 has no more value in the right side. So put 0 to get 220 and put decimal point on the quotient. Then normal dividing 23x 9 = 207 the divisor number 23 is multiplied with 9 to get an answer 207. In 207 is less than from 220.So use the value then subtract the value we get 13 

Step 4:-
         2.95
        -------
    23| 68
         46
       ---------
        220
        207
      ---------
         130
         115
      ---------
           15 (continued)


The value 13 has no more value in the right side. So put 0 to get 130 and put decimal point on the quotient. Then normal dividing 23x 5 = 115 the divisor number 23 is multiplied with 5 to get an answer 115. In 115 is less than from 130.So use the value then subtract the value we get 2.95


Problem 2:- Division problem solver 96 by 4 Solution:-

In following steps for how to divide 96 by 4


Step 1:-
       -------
     4| 96

In the above equation 4 is divisor and 96 is dividend. In the divisor has two decimal numbers put the value dividend of 96.

Step 2:-
       2
     -------
   4| 96
      8
     ---------
      16

In  4 x 2 = 8 the divisor number 4 is multiplied with 2 to get an answer 16. In 8 is less than from 9.So use the value then subtract the value and get 1.

Step 3:-
       24
     -------
   4| 96
      8
    ---------
      16
      16
   ----------
       0
    ----------


In 4 x 4 = 16 the divisor number 4 is multiplied with 4 to get an answer 16. In 16 is equal to 16.So use the value then subtract the value and get remainder is 0.



Monday, March 4, 2013

solving shape area formulas

Area is nothing but a region bounded by a closed curve. Area is a quantity which expresses the 2D size of a defined part of a surface. In terms of differential geometry of surfaces, area is an important variant. In this article solving shape area formulas, we are going to discuss about solving the basic shape area formulas.


Solving shape area formulas types:


Area of a Rectangle.

The Formula for Area of a Rectangle is given below:

     Rectangle shape Area = Length x Breadth   ( A = LB )

Area of a triangle.

The formula for the area of a triangle is given below :

         Triangle shape Area = ½ x Base x Height

                                    A = ½ BH

Area of a Trapezium.

A Trapezium is closed shape which has  two sides that are parallel and two sides that are not parallel.

Now we are going to find a formula for the area of the trapezium.

    Trapezium shape Area = A1 + ( A2 + A3 )

                              Area =  b x h + ½ x (a - b) x h

                               Area = bh + ½ h(a - b)

                               Area = bh + ½ ah – ½ bh

                               Area = ½ ah + ½ bh

                               Area = ½ h ( a + b )

The Area of a Circle.

The area of a circle with the radius r is given by the formula                

                              Area = `pi` r2.


Examples for solving shape area formulas:


Example 1:

Find the area of a triangle with the base length of 20 mm and a height of 6 mm.

Solution:

               Area of a triangle =  ½ b h

                                        =  ½ (20) (6)

                                        =  60 mm2  

Example 2:


Find the area of rectangle given the length is 10 cm and width is 7 cm.

Solution:  

         Area of a Rectangle  =  l * w

                                       = 10 * 7

                                       = 70 cm2

Example 3:

Find the area of a circle given the radius is 44 inches

Solution:

                 Area of  Circle = `pi` r2

                                      =  3.14 (44)2

                                      =  3.14 (1936)

                                      =  6079.04 in2

Friday, March 1, 2013

Coefficient Matrix

Introduction for Matrix:

A matrix is a rectangular array or arrangement of entries or elements displayed in rows and columns put within a square bracket or parenthesis. The entries or elements may be any kind of numbers (real or complex), polynomials or other expressions. Matrices are denoted by the capital letters like A, B, C…

A = [ai, j] m * n

i, j represent the numbers of m, n.

i, j, m, n all represented in the suffix of the considered terms.

A = `[[a11,b12],[c21,d22]]`

order of above matrix 2 * 2

Definition for Coefficient matrix:


The coefficient matrix is formed from the linear equations. There can be any number of linear equations. In the linear equation we are taking the coefficient of the variables in the linear equation to forms the coefficient matrix. Consider  linear equation from it we are going to form a coefficient matrix. The general linear equation as follows:

a11x1 + a12x2 + . . . +a1nxn = b1
a21 x1 + a22x2 + . . . +a2nxn = b2
a31x1 + a32x2 + . . . +a3nxn = b3
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
am1x1 + am2x2 + . . . +amnxn = bn

The coefficient matrix for the linear equation will be represented as:

A = `[[a11,a12,. . .,a1n],[a21,a22,. . .,a2n],[a31,a32,. . .,a3n],[.,.,. . .,.],[am1,am2,. . .,amn]]`

m * n

The coefficient matrix is formed from the linear equations.

Order or size of a coefficient matrix:

The order or size of number of Row Matrix and the number of columns that are present in a matrix.


Example for coefficient matrix:


The coefficient matrix is a resultant from the linear equations.

Linear equation as follows as:

x + 2y +3z = 4
2x + 3y + 4z = 5
3x + 4y +5z = 6

The coefficient equation of the above linear equation as follows:

A = `[[1,2,3],[2,3,4],[3,4,5]]`
3 * 3

The coefficient matrix is formed from the set of linear equations.


Thursday, February 28, 2013

Study Online Factors

In online study on factors, it is essential to know the definition of factors.The set of numbers which produce the remainder zero by dividing a particular number. These sets of numbers are called as factors. We can express a number by the multiples of another two numbers called as factors.

For Example,

                   10= 2 x 5

                   32=4 x 8

     Here 2, 5 are the factors of 10 and 4, 8 are the factors of 32.

     Types of Factors and Sample problems:


For the online study on factors, knowing the types of factors is an essential one. The types of factors for online study are as follows:

There are two types of factors,

Prime Factors
Composite factors

Online study on Prime Factors:
     The numbers that can be expressed as the multiple of one and that number itself are called as prime numbers. The factors of prime numbers are called as prime factors.

Consider the following Examples,

3= 1 x 3 (1, 3 are the prime factors of 3)

5= 1 x 5 (1, 5 are the prime factors of 5)

7= 1 x 7 (1, 7 are the prime factors of 7)

Online study on Composite Factors:

     The factors that are not a prime numbers are called as composite factors.

Consider the following example,

24=4 x 6

Here the numbers 4, 6 are not a prime number. Therefore, 4, 6 are called as composite factors of 24.

Example:

Find the factors of 130.
Solution:

130= 1 x  130

130= 2 x  65

130= 5 x  26

130= 10 x 13

So the factors of 130 =1, 2,5,10,13,26,65,130.

Important note: We can express all the numbers except “1” as a product of prime numbers are called as prime factorization.

Consider the following Example,

24 = 4 x 6

     = (2 x 2) x (2 x 3)

24 = 23 x 3

Here 2, 3 are the prime numbers. Hence, we conclude that all the numbers can be expressed as a product of prime numbers.

Prime factorization tree:

     By using the prime factorization tree, we can get all the prime factors of the given number.

Example:

Find the prime Factors of 124
Solution:

                                       124

                                         /  \

                                     2     62

                                             /  \ 

                                          2   31

                            124 = 2 x 2 x 31


Practice Problems on factors:


Following are the practice problems given for online study on factors.

1. Find the factors of 524.

2. Find the Prime factors of 100

3. Find the composite factors of 1056.

Wednesday, February 27, 2013

Histogram Calculation

A histogram is a graphical representation of frequencies of a variable. The variable range is equally divided and is scaled on the x axis and is continuous. The frequencies of the variable in each range is plotted on the y-axis and a rectangle is drawn  for each interval with the height of the rectangle equal to the frequency of the range and the width representing the range. The width of the rectangles in each range will be equal since total range is equally divided into intervals. The walls of adjacent intervals share the same line.The height of the histogram make the interpretation of the frequencies of each interval easier compared to a tabular representation. The more the height of the rectangle in an interval the more is the frequency within the interval.


Parts of Histogram:


Title:

The title section in the histogram briefly explains the information about the variable that is used in the graph.

Bars:

The bars are explained by thier height and width. The height represents the frequency of observations falling into the interval. The width represents the interval.

Legend:

The legend provides extra information about the relation to the documents where the data came from and how the dimensions were gathered.

Horizontal X-Axis:

The horizontal X-axis provide the scale value, which represent the dimension that fit into the data. These dimensions were usually recognized to the periods. Plot the horizontal X-axis points with in the bar chart which respect the values of Vertical Y-axis.The dimension determine the interval to be fixed.

Vertical Y-Axis:

The vertical Y axis represent the scale of frequencies and is optimized to represent the data on the graph. The units are acquiesced and is linear starting from zero.

Histogram calculation - Conditions in Histograms:



The scale should be supposed to have all the data values. The scale divides the range into equal parts.


Steps to construct histograms:
  • Classify the data of the given histogram
  • Identify the time period for the data
  • Tabulate the data for the given histogram.
  • Establish the range of the given data
  • come to a decision for the number of height and width of each bar
  • Count the number of items in each bar.
  • Make a bar chart using the data given.

Histogram calculation - Example Problems:


Histogram calculation - Problem 1:

Calculate the histogram for the given data.

5    10    15    20    25    30    35    40    45    50    55    60
2      4      7    10      5      7      7      4      4    10      7      9



Histogram calculation - Problem 2:

calculate the histogram for the following given data.

100-200    200-300    300-400    400-500    500-600    600-700
45             34             89              23            67               98



Histogram calculation - Problem 3:

calculate the histogram for the given data set.

1   2      3      4      5    6      7      8      9    10
7    3    32    56    15    4    78    34    45    56

Tuesday, February 26, 2013

Frequency Distribution Tables

Frequency distribution:

The frequency distribution represents the number of observations with in the interval These are  graphically or tabular format.But the intervals must be mutually exclusive and exhaustive,and these are used with in a statistical context.The frequency distribution is a table it contains classes and its representing frequency.The class means quantitative or qualitative type in which the placed of raw data.The data is two types .1)Primary data 2)Secondary data.Primary data is collected by who are the investigator,some times an investigator uses another investigator of primary data.This type of data is called secondary data.The secondary data grouping and presenting in form of table.These type of tables are called Frequency  distribution tables.The data form is in the table shows below.

Data Range:

It is Highest value-lowest value

Class width

Range/ desired number of classes

Upper/lower class limit – upper/lower class Limit of next class

Upper class boundary – lower class Boundary

Class midpoint

Xm   = ( Lower bound + Upper bound)/2

Or

Xm = (Lower Limit + Upper Limit) /2


Frequency Distribution table:


.We can represents The frequency distribution table in number of ways.

1)Group frequency table or graph(polygon,chart)

2)Regular frequency table or Bar graph(Histogram)

When the data is from nominal or ordinary scale then we use Bar graph.

When the data measurements consists more categories than the listed in regular table then we use Group frequency distribution.


Important Notes:


1)The grouped frequency distribution table must use when the range of scores is large, causing a regular frequency table to have too many entries in the score categories (X column). The guidelines for a group frequency table include   approximately 10 rows in the table

2)  The Interval width of 2,5,10,20,50,100 should be used  it depends on the number of rows chosen

3)  Each interval of the  first (lowest) value of should be a multiple of the interval width

4) Note all intervals without missing any, The top interval must contain the highest observed X value and the bottom interval should contain the lowest observed X value.

Example:

For  the given data below into a frequency distribution table and show percentage of each category.
8, 9, 8, 7, 10, 9, 6, 4, 9, 8,
7, 8, 10, 9, 8, 6, 9, 7, 8, 8



x    f    ρ
10    2    0.1
9    5    0.25
8    7    0.35
7    3    0.15
6    2    0.10
5    0    0
4    1    0.05

Monday, February 25, 2013

Solving Irrational

solving irrational numbers:

Irrational numbers in difference to rational numbers aren’t presented a fraction of the shape: m / n,  where m and n are integers. There are numbers of a new type, which are calculated with any accuracy, but can’t be changed by a rational number. They can appear as outcome of geometrical measurements,

for example:

- a ratio of a square diagonal duration to its side length is equal to √2.

- a ratio of a circumference duration to its diameter length is an irrational number  Pi



Where can you find special irrational numbers?(solving irrational)


The answer to this depends on what you consider 'special'.  Mathematicians have proved that definite special numbers are irrational, for example Pi and e.  The number e is the base of natural logarithms.   It is irrational, just like Pi, and has the value 2.718281828459045235306....

It's not easy to just "come up" with such special numbers.  But you can easily discover more irrational numbers after you've found that most square roots are irrational.  For example, what do you think of √2 + 1?  Is the result of that addition a rational or an irrational number?  How can you know?  What about other sums where you add one irrational number and one rational number, for example √5 + 1/4?

You can also add two irrational numbers, and the amount will be many times irrational.  Not always though; for example, e + (-e) = 0, and 0 is rational even though both e and -e are irrational.  Or, take 1 + √3 and 1 - √3 and add these two irrational numbers - what do you obtain?

Or, increase/separate an irrational number by a rational number, and you get an irrational number.  For example, √7/10000 is an irrational number that is moderately close to zero.  Yet another possibility to discover irrational numbers is to multiply square roots or other irrational numbers.  Sometimes that outcome in a rational number though (when?).  Mathematicians have also calculated what happens if you raise an irrational number to a rational or irrational power.

Yet more irrational numbers begin when you take logarithms, or calculate sines, cosines, and tangents.  They don't have any particular names, but are just called "sine of 70 degrees" or "base 10 logarithm of 5" etc.  Your calculator will give you decimal approximation to these.

Examples of Irrational Number


`Pi`,  √10 Are few examples of irrational numbers.

Solved Example on Irrational Number

Identify the irrational number.


Choices:
A. 0.3
B. 3 / 5
C. √6
D. √25
Correct Answer: C

Solution:
Step 1: The value of  is 2.4494897427831780981972840747059...
Step 2: The value of  is 5.
Step 3: The value of  is 0.6.
Step 4: Among the choices given, only  is an irrational number