Definition of Slides in Math

Introduction for Math Slides:

Math slides is a transformation which has a plane figure or move across a line. Moving a shape without rotating or flipping is known as slides (translation). A math slides is also known as translation. If any student wants to know about the definition of math slides, they can refer the below examples with definitions Let us see some of the definition and examples for math slides. I like to share this Properties of Exponents with you all through my article.

Definition of Slides in Math – Explanations:

These are the explanations of slides in math with definition and example figure.

Slides are one of the transformations which can translate the image from original direction A, B, C, D and E to other direction as shown.

This means, they can translate the same image to other side A', B', C', D', and E' as shown.

The image of the angle, length and size are not change in them.

The image of the figure translation is its mirror of the image or their translation plane.

Every point in the translation is same distance from the center of the line as shown.

This center line is known as the mirror line.

It has the same size and length from the original image.

The translating image in the opposite side will be always same as the original image as shown in the example figure.

Each point of translation can be marked in them to shows the image length and their sides.

We can show the translation from one place to another in the following example figure.


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Definition of Slides in Math – Example Figure:

These are the example figure for the definition of slides (translation) in math.

Slides in Math:

The example figure below shows the slides in math with the shape of an object.

Elementary Column Operations

Introduction on elementary column operations:

According to the term elementary Column operation are found to be one of the parts in matrix. Elementary is found be defined as Elementary matrix is found to be defined as a simple matrix where it represented in different identity matrix form. Elementary column operation is the operation that is done by post or right multiplication. I like to share this Complex Fractions with you all through my article.

Rules Based on Elementary Column Operations:

Rule 1: To find the sum given, of elementary column operator, the identity matrix operation is applied.

Rule 2: The post multiplication has to be done for carry out elementary column operations.

Rule 3: The column operator is created from multiplying “column * column"

Representation of Column in Matrix:

The column is represented in matrix as :  `[[a],[b],[c]]`

Example Problems Based on Elementary Column Operations:

Example 1:

Elementary column operation on the term “A”, where the identity used in matrix   `A= [[1,6], [4,1], [0,1]]` and identy matrix `x = [[1,0], [0 ,1]]`

Solution:

Given: Identity matrix `x = [[1,0], [0 ,1]]`

`A= [[1,6], [4,1], [0,1]]`

Step 1:  The given identity matrix x is interchanged of fist and second column and the finding result is named it   (x1).

Step 2: To do the elementary column operation on given `A= [[1,6], [4,1], [0,1]]`

Step 3: The operation in matrix is done by [row *column]

`X= [[1,0], [0,1]]`

The first and second column is interchanged and the result is,

`X1= [[0,1], [1,0]].`

Now, the found X1 is calculated with given “A”

`A= [[1,6], [4,1], [0,1]]`

`X1= [[0,1], [1,0]]`

`A*X1` for calculation elementary column operation on

`A*X1`

` [[1,6], [4,1], [0,1]] * [[0,1], [1,0]]`

` [[1*0+6*1 , 1*1+6*0],[4*0+1*1 , 4*1+1*0],[0*0+1*1, 0*1+1*0]]`

`[[0+6, 1+0], [0+1,4+1], [0+1, 0+0]]`

`[[6,1],[1,4],[1,0]]`

Hence ,the elmentary column operation for the given value `A=[[6,1],[1,4],[1,0]]`

Example 2:Based on elementary column operations

Elementary column operation on the term “D”, where `D= [[1,2],[1,1],[0,0]] ` the identity used in matrix   `"x= [[1,0],[0,1]] `

Solution:

Given: Identity matrix `x = [[1,0], [0 ,1]]`

`"D= [[1,2], [1,1],[0,0]], `

Step 1:  The given identity matrix x is interchanged of fist and second column and the finding result is named it   (x1).

Step 2: To do the elementary column operation on given `D=[[1,2],[1,1],[0,0]]`

Step 3: The operation in matrix is done by [row *column]

`X= [[1,0], [0,1]]`

The first and second column is interchanged and the result is,

`"X1= [[0,1],[1,0]]`

Now, the found X1 is calculated with given “A”

`D= [[1,2], [1,1], [0,0]]`

`X1= [[0,1], [1,0]]`

`D*X1` for calculation elementary column operation on

`D*X1`

`[[1,2], [1,1], [0,0]]*[[0,1], [1,0]]`

`[[1*0+2*1 , 1*1+2*0],[1*0+1*1 , 1*1+1*0],[0*0+0*1, 0*1+0*0]]`

`[[0+2, 1+0], [0+1,1+0], [0+0, 0+0]]`

`[[2,1],[1,1],[0,0]]`

Hence ,the elementary column operation for the given value `D=[[2,1],[1,1],[0,0]]`

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Problems to be Solved Based Elementary Column Operations:

Elementary column operation on the term “S”, where  `S ` =  `[[6,2],[2,1],[9,4]]` the identity used in matrix `X` =  `[[1,0],[0,1]] `
Answer: The elementary column operation of  `S` =`[[2,6],[1,2],[4,9]]`

Elementary column operation on the term “Z”, where `Z` =`[[2,1],[3,2],[6,3]]`   the identity used in matrix  `X` = `[[1,0],[0,1]] `

Answer: The elementary column operation of    `Z` =`[[1,2],[2,3],[3,6]]`

Elementary Math Estimation

Introduction to elementary math estimation:

In elementary number theory, integers are studied without use of techniques from other mathematical fields. Questions of divisibility, use of the Euclidean algorithm to compute greatest common divisors, integer factorizations into prime numbers, investigation of perfect numbers and congruence’s belong here. Several important discoveries of this field are Fermat's little theorem, Euler's theorem, the Chinese remainder theorem and the law of quadratic reciprocity. (Source: Wikipedia)

Types of Elementary Math Estimation:

There are four types of basic theory are mainly used in the elementary number theory; these types are classified according to the representation of the number. It will be shown as below,

Addition
Subtraction
Multiplying
Division
In elementary math to estimation it very easy to learning to study. And solve it easy. There are four steps are used in the elementary estimation of the math problems they are solved in the example problems in given below.

Example Problem for Elementary Math

Example 1:

Estimation the example of adding two numbers 163 and 13

Solution:

Let us write the given problem as 163 + 13.

Add the number 163 and 13 we get the sum as,

163 + 13 =176

Therefore, the solution for adding 163 + 13 is 176.

Example 2:

There are 56 peoples travelling in a bus. 17 of them left from the bus in one stopping. Estimation how many people will be left in the bus?

Solution:

Total number of peoples = 56

Number of peoples left from the bus in one stopping = 17

Number of peoples left in the bus = 56 - 17

= 39

Example 3

Estimation the multiplying two numbers 31 and 27

Solution:

The given two numbers 31 and 27

We need to find the product of two numbers

By multiplying 31 and 27

We get 837

So the answer is 837

Problem 4:

Estimation to divide 400 / 4

Solution:

100(quotient)

----

4)  400

400 -

---------

0(remainder)

---------

Practice Example Problem for Elementary Math

1. Estimation of adding 33 and 70

Key: 103

2. Estimation of Subtract 119 and 9

Key: 110

3. Estimation of Multiplying 29 by 20

Key: 580

4. Estimation of Divided 68 by 7

Key: 9.71

Sixth Grade Math Word Problems

Introduction to Sixth Grade math word problems:

Word problem is one of the best ways to turn up children’s towards solving, thinking and analyzing problems. Word problems will enhance this kind of attitude from the childhood stage itself. Sixth grade level includes real numbers,decimal,fraction,charts, graphs, money and basic mathematics like addition,subtraction,multiplication,division .Sixth Grade math word  problems is very essential for the children’s whose age lies between 8-13years old .It will be so fitful ,let us enjoy it, Let us deal about worked problems. Having problem with What is a Trinomial keep reading my upcoming posts, i will try to help you.

Example 1-sixth Grade Math Word Problems

One cat can kill a 10 rat. Then a  how many number of cat can kill  1000 rat?

Given:

1 cat=10 rat

?=1000 rat

Solution:

Step 1:

To find out the no of cat needed to kill a 1000 rat, we have to divide the total no of rat by the no of rat can be killed by single cat.

Step 2:

Division operation is used

The no of cat needed to kill a1000 rat=`1000/10=100 ` cat

Example 2 -Sixth Grade math word problems

One child makes a building with 250 bricks. How many no of bricks needed to make a 5 building?

Given:

1 Building needed=250 bricks

5 Building needed=?

Solution:

Step 1:

To find out the no of bricks needed to make a 5 building, we have to multiply the no of bricks needed to make a one building with 5

Step 2:

Use multiplication

No of bricks needed for to make 5 Building=`5xx25` =1250 bricks

No of bricks needed is 1250 bricks

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Example 3 - Sixth Grade Math Word Problems

A man travels 3 km per hour .So after 5 hour the distance traveled by him?

Given:

Man covered a distance per hour=3 km

Solution:

Step 1:

To find out the distance covered by him, we have to multiply the distance covered in 1 hour with 5

Step 2:

Use Multiplication

The total distance covered in 5hour=`5xx3=15km`

Example 4 - Sixth Grade math word problems

A child has 100 Chocolates and the dog grabbed 20% of it, from the child. How much number of chocolates dog has?

Given:

The number of chocolates Child has at first=100

Grabbed by the dog=20%

Solution:

Step 1:

To find out the 20% of chocolates, multiply the given percent with number of chocolates

=20%of100

Step 2:

Consider % as 1/100

` =(20/100)xx100`

=20

Finally, the dog has 20 chocolates

Univariate Data

Introduction to uni variate data:

Univariate means to equation, expression, polynomial or function of exactly one variable. This term is commonly used in statistics, mean, arithmetic mean to differentiate a distribution of one variable from the distribution of many other variables. Although it could be applied in many other ways as well. Since it is the simpler way to distribute the values. Correspondingly, the “multivariate time series” refers us to the changing values over the time of several quantities. I like to share this Two Way Table with you all through my article.

Properties of Univariate Analysis:

Univariate analysis is been used primarily in descriptive purposes to represent the quantitative analysis and the statistical analysis. It is the easiest method to identify the attributes and the single variable.

Univariate analysis contrasts with the bivariate analysis because it cannot analyse two variables simultaneously – or do multivariate analysis – the analysis of the multiple variables are been done simultaneously.

Univariate analysis is been commonly used in many fields like the scientific research, medical field and in simple hand calculations. Please express your views of this topic free math help online now by commenting on blog.

Data Set (univariate Data):

In our day to day life there may be many simple values that we go across. In those simple values twe can come across problems with only one variable and also with a single column of the data set, these are represented as a list. Mathematically, in the univariate data set there cannot be any repetition (i.e) because it cannot repeat multiple times. In general the order of the univariate data set does not be considered, but collection of those values may be considered to be a multi set rather than the (ordered) list.

Generally, the values might be of any of the kinds described as a level of the measurement. For every variable, the values will be normally of the same kind or similar.  Uni variate data can be as real numbers or the integers. For example, representation of a building's height using the meters. This could also be represented as a nominal data. However, there could also be "missing values", and those values need to be indicated in some representation.

Numerical Form

Introduction to numerical form:

Numerical form is nothing but the conversion of words into numbers. For example, one million can be expanded in numerical form as 1,000,000 or 106. Likewise, one billion can be expanded in numerical form as 1,000,000,000 or 109.  In this article numerical form, we are going to discuss about numerical form through example problems and practice problems. I like to share this Define Numerical Expression with you all through my article.

Example Problems for Numerical Form:

Example 1:

Write two and thirty five thousandths in numerical form.

Solution:

Step 1: thirty five thousandths can be written as .035

Step 2: Here, the whole number is two

Step 3: Hence, the numerical form is 2.035

Example 2:

Write thousand eight hundred million in numerical form.

Solution:

Step 1: one million is equal to 1000,000

Step 2: Thousand eight hundred million will be equal to 1,800,000,000

Step 3: Hence, the numerical form is 1,800,000,000

Example 3:

Write four and forty five thousandths in numerical form.

Solution:

Step 1: forty five thousandths can be written as .045

Step 2: Here, the whole number is four

Step 3: Hence, the numerical form is 4.045.

Example 4:

Write three thousand seven hundred million in numerical form.

Solution:

Step 1: one million is equal to 1000,000

Step 2: three thousand seven hundred million will be equal to 3,700,000,000

Step 3: Hence, the numerical form is 3,700,000,000

Example 5:

Write eight and eighty five thousandths in numerical form.

Solution:

Step 1: Eighty five thousandths can be written as .085

Step 2: Here, the whole number is eight.

Step 3: Hence, the numerical form is 8.085

Example 6:

Write two thousand four hundred billion in numerical form.

Solution:

Step 1: one billion is equal to 1000,000,000

Step 2: two thousand four hundred billion will be equal to 2,400,000,000,000

Step 3: Hence, the numerical form is 2,400,000,000,000


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Practice Problems for Numerical Form:

1) Write five and sixty five thousandths in numerical form.

Answer: Numerical form is 5.065

2) Write thousand hundred million in numerical form.

Answer: Numerical form is 1,100,000,000

3) Write four thousand five hundred billion in numerical form.

Answer: Numerical form is 4,500,000,000,000

Upper Limit Definition

Introduction to upper limit definition:

Real function: Let R be the set of all real numbers, and let X and Y be any two nonempty subsets of R.Then,a rule f which associates to each x ε X,a unique real number f(x) ε Y is called a real function from X to Y and we write, f : X ----> Y.f(x) is called the image of x or the value of the function at x.The sets X and Y are called the domain and co domain of f.Also,the set {f(x):x ε X} is called the range of f.

Limit : A function f(x) is said to tend to a limit L as x tends to 'a' if for every ε > 0,however small,there exists a corresponding positive  real number δ, such that

l f(x) − L l < ε, Whenever 0 < l x -a l < δ

This is denoted symbolically by        `lim_(x->a)` f (x) = L .

It implies that whenever the value of x lies in the open interval (a - δ , a + δ),for δ to be very small, then the value of the function f(x),lies in the open interval (L−ε , L+ε) on the y-axis.

Lower limit and Upper limit : In the limit of a function f(x), as x tends to a, x may approach a from lower side i.e, a < x or from upper side i.e, a > x.The limit of the function f(x),when 'x' tends to 'a' from lower side of a is called lower limit and when 'x' tends to 'a' from upper side of 'a' is called upper limit.

The upper limit and lower limit are represented as shown below.

Upper limit = `lim_(x->a+)` f(x),which implies that x tends to a from upper side of a,i.e, x > a.

lower limit = `lim_(x->a-)` f(x),which implies that x tends to a from lower side of a,i.e, x < a.

Fundamental Theorems of Limit Definition:

1) `lim_(x->a)` { f(x)+g(x)} = {`lim_(x->a)` f(x)} + {`lim_(x->a)` g(x)}.

2) `lim_(x->a)` { f(x)−g(x)} = {`lim_(x->a)` f(x)} − {`lim_(x->a)` g(x)}.

3) `lim_(x->a)` {c . f(x)}  = c. {`lim_(x->a)` f(x)}, where c is constant.

4) `lim_(x->a)` {f(x) . g(x)}  = {`lim_(x->a)` f(x)} . {`lim_(x->a)` g(x)}.

5) `lim_(x->a)` `(f(x))/(g(x))` = `(lim_(x->a)f(x))/(lim_(x->a)g(x))` , where `lim_(x->a)` g(x) ≠ 0.

6) If f(x)≤ g(x) for all x then `lim_(x->a)` f(x) ≤ `lim_(x->a)` g(x).

Example Problems of Upper Limit

Ex 1:  Find the upper limit of  `lim_(x->3 )` `(x^2-9)/(x-3) ` ?

Sol : `lim_(x->3+)` `(x^2-9)/(x-3)` = `lim_(x->3+)` `((x-3)(x+3))/(x-3)`

=  `lim_(x->3+)` `(x+3)`

= ` 6`

Ex 2:  Find the upper limit of `lim_(x->1)` `(x^2-4x+3)/(x-1)` ?

Sol : `lim_(x->1+)` `(x^2-4x+3)/(x-1)` = `lim_(x->1+)` `((x-1)(x-3))/(x-1)`

= `lim_(x->1+)` `(x-3)`

=   ` -2`


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Practice Problems of Upper Limit

Pro 1:  Evaluate `lim_(x->1+)` `(6x^2-4x+3)`

Ans: 5

Pro 2:  Evaluate `lim_(x->7+)` `(x^2-49)/(x-7)`

Ans:   14

Pro 3:  Evaluate `lim_(x->0+)``{(x-2)^2+6}`

Ans: 10