Study Online Elementary Matrices

Introduction to study online elementary matrices:

The online studying process of the elementary matrices represents the different learning way in its element representation and in operations by which the elements act under the corresponding operation. The operations in the matrices generally involve addition, subtraction, multiplication, division, inverse operations, etc.. In this article we are going to see the matrices operation with the elementary operation.

consider the matrix H =  ` [[-7,197,7],[-97,97,197]]`    It have the dimension of 2 x 3 order.

Total elements calculation 2 x 3 = 6 elements.

consider H =  ` [[-7,197,7]]`   It have the dimension of 1 x 3 order.

Total elements calculation 1 x 3 = 3 elements

Study online elementary matrices with examples


Online studying for the elementary matrices with the help
`[[12,13,14,15],[21,22,23,24],[25,26,27,28]]`   = `[[12,13,14,15],[21,22,23,6x],[25,26,27,28]]`


Solution:

Here the matrices present on the left side and the right side are equal in the dimension of 3 x 3.

Y =  `[[Y_11,Y_12 ,Y_13,Y_14 ],[Y_21 ,Y_22 ,Y_23,Y_24 ],[Y_31 ,Y_32 ,Y_33,Y_34 ]]`  =`[[12,13,14,15],[21,22,23,24],[25,26,27,28]]`

Y11 = 12              Y12 = 13                  Y13 = 14                Y14 = 15

Y21 =21                Y 22 =22                Y23 = 23                 Y24 =24

Y31 = 25               Y32 = 26                Y33 = 27                Y34 = 28

And   R =  `[[R_11,R_12 ,R_13,R_14 ],[R_21 ,R_22 ,R_23,R_24 ],[R_31 ,R_32 ,R_33,R_34 ]]`  =`[[12,13,14,15],[21,22,23,6x],[25,26,27,28]]`

R11 = 12              R12 = 13                R13 = 14                R14 = 15

R21 =21                R22 =22                R23 = 23                R24 =6x

R31 = 25               R32 = 26               R33 = 27                R34 = 28

In the given problem the similarity exists in the matrices

Y24 = 24   and    R24 = 6x

The similar matrices having the elements same

Y24 =  R24

6x = 24

And therefore the constant x = 4 is the answer.

Understanding Elementary Row Operations is always challenging for me but thanks to all math help websites to help me out.

Problems to study online elementary matrices


Online studying for the elementary matrices with the help
`[[12,13,14,15],[21,22,23,24]]`   = `[[12,13,14,15],[21,22,23,6x]]`


Solution:

Here the matrices present on the left side and the right side are equal in the dimension of 3 x 3.

Y =  `[[Y_11,Y_12 ,Y_13,Y_14 ],[Y_21 ,Y_22 ,Y_23,Y_24 ]]`  =`[[12,13,14,15],[21,22,23,24]]`

Y11 = 12              Y12 = 13                  Y13 = 14                Y14 = 15

Y21 =21                Y 22 =22                Y23 = 23                 Y24 =24

And   R =  `[[R_11,R_12 ,R_13,R_14 ],[R_21 ,R_22 ,R_23,R_24 ]]`  =`[[12,13,14,15],[21,22,23,6x]`

R11 = 12              R12 = 13                R13 = 14                R14 = 15

R21 =21                R22 =22                R23 = 23                R24 =6x

In the given problem the similarity exists in the matrices

Y24 = 24   and    R24 = 6x

The similar matrices having the elements same

Y24 =  R24

6x = 24

And therefore the constant x = 4 is the answer.

Elementary Multiplication

Introduction to elementary multiplication:

Here we are going to see the elementary multiplication, generally multiplication is called as the repeated addition, suppose if we are combine the same 9 groups with 5 objects in each group means it will be written in multiplication format of 5*9 = 45, we get the same answer in addition also, it will be shown below 9 +9+9+9+9+9 = 45. Let us see about elementary multiplication in the given below article.


Multiplication as repeated addition using elementary multiplication:

Multiplication is continuous addition of same number to some extent.  So we can say increase as immediate adding (repeated addition).

For example,

By add 2 for 4 times we result obtain 8.

2+2+2+2=8

Directly multiplying 2 with 4 also we can get 8.

4`xx` 2=8


Example Problem for elementary multiplication


Example 1

Multiplying two numbers 10 and 3

Solution:

The given two numbers 10 and 3

We need to find the product of two numbers

By multiple 10 and 3

We get 30

So the answer is 30

Example 2

Multiplying two numbers 35 and 5

Solution:

The given two numbers 35 and 5

We need to find the product of two numbers

By multiplying 35 and 5

We get 175

So the answer is 175

Example 3

Multiplying two numbers 33 and 44

Solution:

The given two numbers 33 and 44

We need to find the product of two numbers

By multiplying 33 and 44

We get 1452

So the answer is 1452

Example 4

Multiplying two numbers 50 and 60

Solution:

The given two numbers 50 and 60

We need to find the product of two numbers

By multiplying 50 and 60

We get 3000

So the answer is 3000

Example 5

Multiplying two numbers 120 and 70

Solution:

The given two numbers 120 and 70

We need to find the product of two numbers

By multiplying 120 and 70

We get 8400

So the answer is 8400

Example 6

Multiplying two numbers 92 and 87

Solution:

The given two numbers 92 and 87

We need to find the product of two numbers

By multiplying 92 and 87

We get 8004

So the answer is 8004

Example7

Multiplying two numbers 23 and 17

Solution:

The given two numbers 23 and 17

We need to find the product of two numbers

By multiplying 23 and 17

We get 391

So the answer is 391.

Solving Fractions Elementary

Introduction for Solving Fractions Elementary:

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.

In this article we shall discuss about the how to solve fractions in elementary level

Is this topic Improper Fractions to Mixed Numbers hard for you? Watch out for my coming posts.

Solving Fractions Elementary – Addition:


The following examples of addition problems show the fractions for elementary.

Addition of fractions: `1/10 + 1/10` .

Solution:

Denominators are same so we go to next step.

Add the numerators and denominator as same.

= `1/10+1/10`

= `(1+1)/10`

By simplifying we get

= `2/10`

= `1/5` is the solution.

Addition of fractions: `2/32 + 2/32` .

Solution:

Denominators are same so we go to next step.

Add the numerators and denominator as same.

= `2/32+2/32`

= `(2+2)/32`

By simplifying we get

= `4/32`

= `1/8` is the solution.

Addition of fractions: `3/54 + 3/54` .

Solution:

Denominators are same so we go to next step.

Add the numerators and denominator as same.

= `3/54+3/54`

= `(3+3)/54`

By simplifying we get

= ` 6/54`

= `1/9` is the solution.

Having problem with math problems 6th grade keep reading my upcoming posts, i will try to help you.

Solving Fractions Elementary – Subtraction:

The following examples of subtraction problems show the fractions for elementary.

Subtraction of fractions: `1/10 - 2/10` .

Solution:

Denominators are same so we go to next step.

Subtract the numerators and denominator as same.

= `1/10-2/10`

=` (1-2)/10`

By simplifying we get

= `-1/10` is the solution.

Subtraction of fractions: `2/32 - 4/32` .

Solution:

Denominators are same so we go to next step.

Subtract the numerators and denominator as same.

= `2/32-4/32`

= `(2-4)/32`

By simplifying we get

= `-2/32`

= `-1/16` is the solution.

Subtraction of fractions: `5/40 - 10/40` .

Solution:

Denominators are same so we go to next step.

Subtract the numerators and put the denominator as same.

= `5/40-10/40`

= `(5-10)/40`

By simplifying we get

= `-5/40`

= `-1/8 ` is the solution.

Elementary Math Word Problem

Introduction to elementary math word problem:

In mathematics education, the term solving word problem is often used to refer to any mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. As word problems often involve a narrative of some sort, they are occasionally also referred to as story problems and may vary in the amount of language used. In this article we shall discuss elementary math word problems. (Source: Wikipedia)

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

Elementary math word problem examples


Here we are going to solve elementary math word problem with detailed solutions.

Example:

In an office there are 90 employees work. If the number of gents employees is 37, frame the equations and find how many number of ladies work in office.

Solution:

Let the number of ladies work in office be x.

The number of gents works 37.

Total number of worker 90.

Therefore simple equation is x+37 = 90

x =90 - 37

x = 53 ladies in office.

Example:

The 12 orange costs is `$` 125, find the total cost of 16 orange.

Solution:

Step 1:

Consider the given problem as If the 12 orange costs is 125. Find the cost of 16 orange?

Step 2:

12 orange cost =125

16 orange cost = `16/12 ` x125

=167

Answer:

Therefore the cost of 16 orange is `$ ` 167

Problem:

In a class room there are 60 students taking a math exam. 20 students get an average score of 70. The left over students get an average score of 75. Find the average score of the entire class?

Solution:

To find the average score of the entire class, we need to follow the following steps these steps very helpful to find the average.

Step 1:

First we need to find the sum of weighted terms and multiply each average value by the number of students in the entire class had that average and sums.

70 × 20 + 75 × 40 = 1400 + 3000 = 4400

Step 2:

Number of total terms = Number of students in the entire class = 60

Step 3:

Here we need using the formula for weighted average formula to find the average

Average = sum of average terms
Total number of term

=` 4400/60`

= 73.3

Answer:

The average mark of the entire class is 73.3


Understanding math problems for 3rd grade is always challenging for me but thanks to all math help websites to help me out.

Elementary practice math word problem


Problem:

In an office there are 70 employees work. If the number of gents employees is 27, frame the equations and find how many number of ladies work in office.

Answer:

43 ladies in an office

Problem:

The 13 orange costs is `$ `130, find the total cost of 17 orange.

Answer:

The cost of 17 orange is` $` 170

Solving Elementary Math Test

Introduction to solving elementary math test:

Mathematics is used for throughout the entire world used in many areas like, engineering, science, and medicine. In elementary school the students receive first level of education is called as primary education. Elementary mathematics includes topics from algebra, arithmetic, number system and geometry etc. In this article we shall discuss solving elementary math test example problem.

Having problem with Slope of Horizontal Line keep reading my upcoming posts, i will try to help you.

Solving elementary math test example problem


Here we are going to solving the elementary math test example problem with detailed solutions. It is very helpful for elementary math students.

Example:

Solving the equation: x-15 = 35

Solution:

Given x-15= 35

x = 35 + 15 (-15 in the LHS becomes +15 when it comes to the RHS)

Therefore y = 50

Example:

The cost of 20 pens is `$` 420. Find the cost of each pen.

Solution:

Consider the cost of one pen be x

Therefore the cost of 20 pen is 20 × x = 20x

But the cost of 20 pen            = `$` 420

The simple equation is 20x         = $420

To get the cost of one pen, solving the equation

20x = 420

x = 420 x 1/20

= 21

The cost of each pen is `$` 21

Example:

Solving the equation 6x – 4 = 26

Solution:

Given 6x – 4 =26

6x = 26 +4

6x = 30

x = 30 x `1/6`

Therefore x = 5

Example:

Solve the expression 12x + 5y - 4 + 6x + 6y + 8

Solution:

Find the like terms in the expression and then group and combine like terms:

• +12x and +6x are like terms, and combined to get +18x,

• +5y and +6y combine all like terms to get +11y, and

• -4 and +8 combine all like term and get +4.

So after simplify, the expression:

18x + 11y + 4

Example:

The sum of two numbers is 25. If one number is 14, find the other number.

Solution:

Consider the unknown number be x.

The sum of two numbers = 25

One number is 14.

Therefore the simple equation is            x = 25 - 14

x = 25 -14

x = 11

The other number is 11.

Is this topic math problem solver online hard for you? Watch out for my coming posts.

Elementary math test practice problem


Problem:

The cost of 25 pens is `$` 500. Find the cost of each pen.

Answer:

The cost of each pen is `$` 20

Problem:

Solving the expression 8x + 6y - 5 + 6x + 6y + 10

Answer:

14x + 12y + 5

Problem:

The sum of two numbers is 22. If one number is 10, find the other number.

Answer:

The other number is 12.

4th Grade Math Expressions

Introduction to 4th grade math expressions:

4th grade math expressions deals with the simple  format of expressions containing variable, the variables are in the form of alphabetic, such as x, y, z, m, n… Using this we can create and expressions which is in the equation form and find the value of variables.

Addition, subtraction, division, and multiplication are called basic arithmetic operations of mathematics which are performed on 4th grade math expressions. This article shows the different operations performed on 4th grade math expressions.

I like to share this Dividing Rational Expressions with you all through my article.

Examples problem for 4th grade math expressions:


1. Find the x value for given expression, x + 7.

Solution:

Given expression is,

x + 7 = 0

Both sides subtracting by -7,

x + 7 – 7 = -7

Simplify the values,

Then we get the answer is,

x = -7

The answer to variable x is -7.

2. Find the z value for given expression, z + 3.

Solution:

Given expression is,

z + 3 = 0

Both sides subtracting by -3,

z + 3 – 3 = -3

Simplify the values,

Then we get the answer is,

z = -3

The answer to variable z is -3.

3. Find the y value for given expression, y +17.

Solution:

Given expression is,

y + 17 = 0

Both sides subtracting by –17,

y + 17 – 17 = -17

Simplify the values,

Then we get the answer is,

y = -17

The answer to variable y is -17.


More examples problem for 4th grade math expressions:

4. Find the x value for given expression, x - 5 -13 + 4.

Solution:

Given expression is,

x - 5 -13 + 4 = 0

First combine the integers,

x - 5 -13 + 4 = 0                          (-5 -13 + 4 = -14)

x -14 = 0

Both sides adding by 14,

x - 14 + 14 = 14

Simplify the values,

Then we get the answer is,

x = 14

The answer to variable x is 14.

5. Find the y value for given expression, y - 2 - 3 + 4.

Solution:

Given expression is,

y - 2 - 3 + 4 = 0

First combine the integers,

y - 2 - 3 + 4 = 0                          (-2 -3 + 4 = -1)

y -1 = 0

Both sides adding by 1,

y - 1 + 1 = 1

Simplify the values,

Then we get the answer is,

y = 1

The answer to variable y is 1.

More examples problem for 4th grade math expressions:


6. Find the z value for given expression, z - 4 -10 + 24.

Solution:

Given expression is,

z - 4 -10 + 24 = 0

First combine the integers,

z - 4 -10 + 24 = 0                          (-4 -10 + 24 = 10)

z +10 = 0

Both sides adding by -10,

z + 10 - 10 = -10

Simplify the values,

Then we get the answer is,

z = -10

The answer to variable z is -10.

7. Find the x value for given expression, x - 25 -10 + 20.

Solution:

Given expression is,

x - 25 -10 + 20 = 0

First combine the integers,

x - 25 -10 + 20 = 0                          (-25 -10 + 20 = -15)

x -15 = 0

Both sides adding by 15,

x - 15 + 15 = 15

Simplify the values,

Then we get the answer is,

x = 15

The answer to variable x is 15.

Free 3rd Grade Math

Introduction for free 3rd grade math:

In algebra basic arithmetic operation (addition, subtraction, multiplication, and division) generally used in day to day life. In these articles we are going to discuss about free 3rd grade math. Addition (+) defined as adding the two numbers. Subtraction (-) defined as the inverse of addition.Addition is a mathematical process so as to represent combine collection of objects as one into a better collection. It is signifying by the plus sign (+). For example, there is 6 + 5 apple, 6 + 5 = 11. Subtraction is a mathematical process so as to inverse of addition. 6 – 3 apples, 6 – 3 = 3 apples (Source: Wikipedia)

Please express your views of this topic Calculus Inverse Functions by commenting on blog.

Free 3rd grade math - Addition and subtraction example problems:


Free 3rd grade math – Addition example problems:

Example 1:

Adding the given values

89775 – 16654

Solution:

89775

16654   (+)

-----------

106429

----------

So, the final answer is 106429

Example 2:

If there are 192 tickets in a box and Joshua puts 49 more tickets inside, how many tickets are in the box?

Solution:

If there are 192 tickets in a box and Joshua puts 49 more tickets inside,

= 192 + 49

= 241 tickets

241 tickets are in the box.

Example 3:

Evelyn has 187 apples. Marvin has 125 apples. If Marvin gives all of his apples to Evelyn, how many apples will Evelyn have?

Solution:

Evelyn has 187 apples. Marvin has 125 apples. If Marvin gives all of his apples to Evelyn,

= 187 + 125

187

125   (+)

--------

312

----------

312 apples will Evelyn have,

Free 3rd grade math – Subtraction example problems:


Example 1:

Subtracting the given values

67484 – 45867

Solution:

67484

45867    (-)

-----------

21617

-----------

So, the final answer is 21617.

Example 2:

James reading a chapter book that has 872 pages. He has already read 246 pages. How many pages does he have left to read?

Solution:

James reading a chapter book that has 872 pages. He has already read 246 pages.

872

246   (-)

----------

626

----------

626 pages does he have left to read.

Example 3:

There are 659 employees working in an office building. 368 of them are about to leave to go home. How many employees will be left in the building?

Solution:

There are 659 employees working in an office building.

368 of them are about to leave to go home.

659

368   (-)

---------

291

---------

291 employees will be left in the building.

Elementary Math Area

Introduction For elementary Math Area:

Elementary math area consist of area for square, rectangle ,triangle it is a menstruation part it is interesting in finding area of shapes and measuring length for given shapes. In menstruation area is an essential part for measuring the shape length. Measurement math consists also volume, surface area such as in higher grade for elementary math we have only fundamental shapes.

Please express your views of this topic Formula for Area of a Square by commenting on blog.

Elementary Math Area For Square:


Area of a Square:
We know  square is a like rectangle in which its Length = Breadth.
The area of the square
= Length `xx ` Length
= (Length)2 = (Side)2
= a × a
= a^2

Example 1:
Find area of a square whose side is 12 cm.

Solution :
Side of the square, a = 12 cm
Area of the square, A = a^2
= a × a
= 12 × 12
= 144 sq.cm (or 144 cm2)
Example 2:
Find area of a square whose side is 14 cm.

Solution :
Side of the square, a = 14 cm
Area of the square, A = a^2
= a × a
= 14 × 14
= 196 sq.cm (or 196 cm2)

Area of Rectangle:
Length `xx` Breadth

Example 1 :
Length and breadth of a rectangle are 15 cms and 13 cms respectively. find its area.

Solution:
= Length `xx` Breadth
= l `xx` b
= 15 cm. `xx` 13 cm.
= 195 Sq. cm.

Example 2:
Find the area  of a rectangle whose length is 2m and breadth is 70 cm.

Solution :
Length of the rectangle, l = 2 m or 200 cm
Breadth of the rectangle, b = 70 cm
Area of the rectangle, A = l × b
= 200 cm × 70 cm
Area = 14000 sq.cm.

Is this topic how to solve proportion problems hard for you? Watch out for my coming posts.

Elementary Math Area For Triangle:


Area of a  triangle:
`1/2` × base × height

Example 1 :
In a triangle the length of sides containing  angles are 20 cm and 21 cm. Find its area.

Solution :
Let b = 20 cm and h = 21 cm
Area of the right triangle, A =1/2 bh
= `1/2` × 20 cm × 21 cm
= 210 sq.cm

Example 2 :
In a right triangle the length of sides containing the right angles are 15 cm and 20 cm. Find its area.

Solution :
Let b = 15 cm and h = 20cm
Area of the right triangle, A = `1/2` bh
=`1/2` × 15 cm × 20 cm
= 150 sq.cm

Rules for Elementary Algebra

Introduction to rules for elementary algebra:

Algebra is a system of written calculations that help us reason about numbers. At the very first, we should realize that algebra is a skill. The initial thing to note is that, in algebra, we use letters as well as numbers.  But the letters represent numbers.  And the rules of algebra match to the rules of arithmetic, but we write those rules using letters. Rules for elementary algebra is very basic in algebra, Now we are going to see about the rules for elementary algebra.

Please express your views of this topic Transitive Property of Equality by commenting on blog.

Rules for elementary algebra part - I:


Property of zero

0 · x = 0
0 + x = x

Property of One

1 + x = 1
1. x = x

Identity Property

x · x = x
x + x = x

Redundancy Property

x · ( x + y ) = x
x + ( x · y ) = x

Commutative property

x · y = y · x
x + y = y + x

Associate Property

x · ( y · z ) = ( x · y ) · z
x + ( y + z ) = ( x + y ) + z

Distributive Property

x · ( y + z ) = ( x · y ) + ( x · z )
x + ( y · z ) = ( x + y ) · ( x + z )


Rules for elementary algebra part - II:


Properties of negation

a ( -1 ) = -a

-( -a ) = a

( -a ) b = - ( ab ) = a ( -b )

( -a ) ( -b ) = ab

-( a + b ) = ( -a ) + ( -b )

Properties of equality

If a + c = b + c, then a = b

Word Problems Elementary Level

Introduction:

The term word problem refers to the math exercise which has information about the problem in words rather than text. It is hard to translate the words into mathematical expression or equations. When it is done, then it is easy to solve those problems. But translation of those words to mathematical symbols or equation is hard. Understanding the given condition or situation in the word problem is more important than solving it. Without understanding the math word problems the solving work can’t be done. Elementary level word problems are easy to solve. The elementary level word problems involve basic arithmetic operations only. Those elementary level problems are not much complicated.

I like to share this Elementary Row Operations with you all through my article.

Elementary level Word problems:


Example 1:

A fish tank contains 30 fish of which 5 are stationary. How many fish in the tank are moving?

Solution:

Here the total number of fish = 30

Number of stationary fish = 5

Numbers of moving fish = 30 – 5

= 25 fish

The answer is 25 fish.



Example 2:

A zoo has 18 Thailand elephants and 6 Indian elephants. How many elephants are there in the zoo?

Solution:

Number of Thailand elephants = 18

Number of Indian elephants = 6

Total number of elephants = 18 + 6

= 24 elephants.

The answer is 24 elephants.



Example 3:

Raja sent invitations to 60 relatives for a family get-together. Only 35 relatives came to the function. How many relatives did not come?

Solution:

Total number of invitations send = 60

Number of relatives came to function = 35

Number of relatives did not come = 60 – 35

= 25

The answer is 25.

More elementary level word problems:


Example 4:

Lokesh had brought 17 flowers from a Park last time. His mom wants Lokesh to bring 4 times as many this time. How many flowers will Lokesh bring this time?

Solution:

Number of flowers Lokesh bought last time = 17

He bought 4 times as many flowers this time,

Hence,

Number of flowers Lokesh bought this time = 17*4

= 68

The answer is 68 flowers.



Example 5:

There are 60 apple trees planted in 5 rows. How many apple trees are there in each row?

Solution:

Total number of trees planted = 60

Total number of rows = 5

Number of apple trees peer row = 60/5

= 12 trees

The answer is 12 trees.

5th Grade Math Variables

Introduction to 5th grade math variables:

In mathematics, 5th grade math variables are using addition and subtraction operation with variables. Single-symbol are called for variables are the normal, with x, y, and z being most common using in variables problem. Constants are generally denoted as a, b, c. In mathematics, constants and variables are usually set in an italic typeface.

Specific branches and applications of mathematics regularly have specific naming conventions for variables.

Meanings or variables with similar roles are regularly assigned consecutive letters. For example, x, y, and z is the three axes in 3D coordinates space are conventionally.

Having problem with Simplify Radicals with Variables keep reading my upcoming posts, i will try to help you.

Examples problems for 5th grade math variables:


1. Find the x value, for the given for single variable expressions.

18x + 2 = 38

Solution:

18x + 2 = 38

Subtract (2) with both sides,

18x + 2 – 2 = 38 – 2

18x = 36

Divide (18) with both sides,

18x / 18 = 36 / 18

x = 2.

The solution to the given expression in single variable x = 2.

2. Find the y value, for the given for single variable expressions.

4y + 4 = 20

Solution:

4y + 4 = 20

Subtract (4) with both sides,

4y + 4 – 4 = 20 – 4

4y = 16

Divide (4) with both sides,

4y / 4 = 16 / 4

y = 4.

The solution to the given expression in single variable y = 4.


More examples problems for 5th grade math variables:


3. Find the z value, for the given for single variable expressions.

5z + 5 = 30

Solution:

5z + 5 = 30

Subtract (5) with both sides,

5z + 5 – 5 = 30 – 5

5z = 25

Divide (5) with both sides,

5z / 5 = 25 / 5

z = 5.

The solution to the given expression in single variable z = 5.

More examples problems for 5th grade math variables:


4. Find the x value, for the given for single variable expressions.

6x - 2 = -38

Solution:

6x - 2 = -38

Add (2) with both sides,

6x - 2 + 2 = -38 + 2

6x = -36

Divide (6) with both sides,

6x / 6 = -36 / 6

x = -6.

The solution to the given expression in single variable x = -6.

Elementary Set Theory

Introduction to elementary set theory:

A set theory is a collection of elements or the items can be considered as a whole. If the set contains only a few items or elements, then the set can be defined by listing them in braces. For example: A = {1,2,3}. Now we are going to see about the elementary set theory.

Please express your views of this topic Set Theory Notation by commenting on blog.

Elementary set theory:


Now we are going to see about the elementary set theory as follows,

Set and Sample Space:

The sets are the important part and the basic concepts in mathematics and probability. Sets are usually consists of collection of some elements.

Example of sample spaces:

Pick a card from a pack of 52 cards:

Sample space = {1, 2 ...52}, which is a infinite sample space.

Subset:

A subset is can be defined by some property of its elements.

For example, let P = {1,2,3,4}, and let Q = {2,}. Then Q can be defined as the set of all elements of P which are even, or in symbols:

Q ={x  `in` A |  x is even}.

The operation properties are given as follows,

The intersection operation has the properties are given as,

Commutative: A `nn` B = B `nn` A.

Associative: (A `nn` B) `nn` C = A `nn` (B `nn` C).

The union operation has several properties

Commutative: A `uu` B = B `uu` A.

Associative: (A `uu` B) `uu` C = A `uu` (B `uu`C).

Ordered pairs:

An ordered pair contains set of two elements that are arranged in a specified order. An ordered pair is usually written as (x, y).

Relations:

A relation R is on a set A, where A is simply a set of ordered pair of element of A.

Functions:

A function ‘f’ from the set X to the set Y is a rule given any element x of A, This concept is often expressed symbolically as f: X--->Y

Problems for elementary set theory:


Example 1:

A = {1, 2, 3, 4, 5, 6, 7, 8, 11, 12} B = {9, 10, 11, 12, 13). Determine the union and intersection of set A and B.

Solution:

The union of set is nothing but including both the set elements in a single set

(B `uu` C) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, (B ∩ C) = {11, 12}.

Example 2:

P = {f, g, h, i, j, k, l} Q = {g, j, l, m, n}. Determine (P – Q) and compliment of C related to Q.

Solution:

The difference of the two sets P and Q are given as,

(P – Q) = {f, h, I, k}, Cc = {m, n}

Study Elementary Probability

Introduction to study elementary probability:

The elementary probability theory condition for all probability mass function (pmf) there is functions which give the probability in a divide random variable which is accurately corresponding to some of the value recognized. A pmf differs as of a common probability density function (pdf) in the values of a pdf, defined for the permanent random variables and not the probabilities as such desired.


How to study elementary probability:


The study of elementary probability function always defines as known in the relationship among the two such variables in a probability distribution function which is named as the "Probability Function". An elementary probability function assumes that the "variable" which indicates the values within the given range of such a random variable at its independent variable and "probability" defined as the dependent variable.

Is this topic Significant Figures Calculator hard for you? Watch out for my coming posts.

Study the representation of probability function for elementary type:


An elementary probability function which relates the break up random variable is recognized as the "Probability Mass Function". In the sequence of a random variable the value of "X" assumes that the distinct set of values `x_1, x_2, x_3, ... x_n,` then the function "f" is defined by the f(xi) = P(X = xi) and that is called as the "Probability Function" or "Probability Mass Function". The pmf assigns a value for the required probability [P(X = xi)] in each of the possible values [xi] of the variable.

That gives the study of elementary probability value and the variable which represents the sequence of the distinct random variable which equals to some value. A study of discrete probability function f(x) defines the following properties.

f (xi) ≥ 0 is given by the probability for the variable to carryover a particular value which is always a positive real number.

Σ f (xi) = 1 [i = 1, 2, 3, ... ∞] The sum of the corresponding probabilities of all the given possible values and that suits the variable which represents the range of all the discrete random variable which may carry the value equal to One.

Solve Elementary Statistics Problems

Introduction of elementary statistics problem:

Data is a word in a plural form of the Latin word datum. Every part of our lives utilizes data in one form or the other. This extraction of significant information is study in a branch of mathematics called statistics. A step additionally by studying certain numerical representatives of the ungrouped data, also called measures of central tendency, namely, mean, median, mode and also range are under the elementary statistics only.

I like to share this How to Find the Mean Median and Mode with you all through my article.

About Elementary statistics


Elementary statistics is deals with the basic static calculations of data’s for finding the mean values etc... The word ‘statistics’ appears to have been taken from the Latin word ‘status’ meaning ‘a state (related to a political)’... Statistics deals with collection, organization, analysis, and Interpretation of data. ‘Statistics’ has held different meanings in different contexts, so that the calculation process is based on the meaning and data. Elementary statistics problems are mainly deals with the mean, median, mode, and range.

Example for elementary statistics problems


Let us see about the basic elementary stastistics problem below,
Example for Mean: what is the mean of 3, 8 and 5?
Add the numbers: 6 + 8 + 4 = 16
divide by how many numbers (i.e. we added 3 numbers): 18 ÷ 3 = 6
so the Mean is 6
Example for Median: Find the Median of {12, 3 and 5}. Put them in order: {3, 5, 12}, the middle number is 5, so the median is 5.
Special Case: If there are two middle numbers (as happens when there are an even amount of numbers) then average those two numbers.
Find the Median of {12, 3, 5 and 2}. Put them in order: {2, 3, 5, 12}, the middle numbers are 3 and 5, the average of 3 and 5 is 4, so the median is 4.
Example for Mode: The number, which appears mostly, repeated in a set of numbers. In Set {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6.
Example for Range: is nothing but the difference between the lower and higher values.
In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9-3 equals 6.
Range can also mean all the output values of a function.

Patterns in Elementary Algebra

Introduction of Patterns in algebra:

Numeric patterns in algebra are patterns made from numbers.

The numbers can be in a list. Any math operation (addition, subtraction, multiplication, or division) can be used to make the pattern.

Many of the patterns in algebra you see will use addition. The same number will be added to each number in the list to make the next number in the list.

Example

2,5,8,11,14,17…

The pattern in algebra is to add 3 every time. The next number is 20, then 23.

I like to share this how to solve algebra 2 problems with you all through my article.

Example for patterns in algebra:


Example 1:

2,4,6,8,10,12,…

Solution:

The rule here is counting by 2 using even number, so next term are 14 and 16.

Example 2:

1,3,5,6,9,11,13,15,…

Solution:

If you guessed that the rule is counting by 2 using odd numbers, you are correct.

Example 3:

1,1,2,3,5,8,13,21,34,55,…

Solution:

Look carefully and think!!!

If you concluded that the answer to this pattern in algebra is that you need to add number together to get the next number in line, you are correct.

1+1=2,2+1=3,3+2=5,5+3=8,…

This is a famous pattern in algebra or sequence known as the Fibonacci sequence.

Example 4:

A store gives a door prize to its third customer and to every fifth customer after that. Which of the following customers will get a door prize?

The 62nd

The 71st

The 79th

The 98th

Solution:

Whenever you see a problem like this one, do not just stare at it hoping to see the pattern in algebra. Start working out the problem on paper, and after a few steps, you should be able to see the pattern in algebra. If the third customer gets a prize, as does every fifty customer who follows, the list of customer who will get prizes should be numbers.

3,8,13,18,23,28,33,…

Therefore, every number that ends in a 3 or an 8 will get a prize. Of the choices listed, only D ends with 3 or an 8, so it must be the answer.

Understanding Permutations Definition is always challenging for me but thanks to all math help websites to help me out.

Practices problem for patterns in algebra:


Problem 1:

Which of the following best describes the pattern in algebra of these numbers?

5/2,3,7/2,4.

Answer:          Each number is one-half more than the number before it.

Problem 2:

Consider the pattern in algebra of numbers given.

Row 1:                  2

Row 2:                  4                6

Row 3:                  8               10                    12

Row 4:                  14             16                    18                    20

What will be the sum of the number is Row 7?

Answer: 350

Linear Elementary Algebra

Introduction to linear elementary algebra:

A linear elementary algebra  equation is constructed by constants and one or more variables by using only the arithmetic operations like, addition, subtraction, multiplication and division.

The linear equations are most often used in linear elementary algebra.

A general form with two variables x and y is

y= mx +c

Where, m and b values are constants.


Example problem for linear elementary algebra 1


Example problem for linear elementary algebra 1 is given below:

Find four different solutions of the linear equation x + 2y = 6.

Solution:

x = 2, y = 2 is a solution because for x = 2, y=2

x + 2y = 6, 2 + 2(2) = 6, 2+4=6, 6=6.

Now, let us choose x = 0. With this value of x, the specified equation reduces to 2y = 6, which has the unique solution y = 3.

So x = 0, y = 3 is also a solution of x + 2y = 6.

Similarly, plug y = 0, the given equation reduces to x = 6.

So, x = 6, y = 0 is a solution of x + 2y = 6 as well.

Finally, let us take y = 1.

The given equation now reduces to x + 2 = 6, whose solution is given by x = 4. Then, (4, 1) is also a solution of the given equation so four of the infinitely many solutions of the given linear equation are:

(2, 2), (0, 3), (6, 0) and (4, 1).

Example problem for linear elementary algebra 2:


Example problem for linear elementary algebra 2 is given below:

The price of 2 pencils and 3 erasers is Rs 9 and the price of 4 pencils and 6 erasers is Rs 18. Find the price of each pencil and each eraser.

Solution:

The pair of linear equations formed was:

2x + 3y = 9 ……………..… (1)

4x + 6y = 18 …………….... (2)

We first write the value of x in terms of y from the equation

2x + 3y =9, to get x = (9-3y)/2 ………………. (3)

Now we plug this value of x in Equation (2),

4(9-3y)/2+ 6y = 18

18 – 6y + 6y = 18

18 = 18

This statement is true for all values of y.

However, there is no specific value for y as a solution.

Therefore, we cannot get a specific value of x.

Therefore, Equations (1) and (2) have infinitely lots of solutions.

Here an exact cost of a pencil and an eraser  can't be found, because there are many common solutions, to the given situation.

Elementary Geometry Definitions

Introduction to learning elementary geometry definitions:

Learning elementary geometry definitions,

In learning elementary geometry definitions, the word geometry can be defined as the system of concepts, in which a few ideas were initialized to derive the big ones. It is said to be Deductive systems. Geometry tells you the deduction concepts and consequence logic's, which can be applied throughout your life time. By learning this article, you can learn about the elementary definitions of geometry. I like to share this Find the Volume of a Cube with you all through my article.


Learning Elementary Definitions of Geometry:

Let we see elementary definitions of geometry,

Point: A Point can be defined as the basic object of geometry. A point has no dimensions, denote position.

Line: A line is connection of many points. The line having one dimension, i.e., length.

Concurrent lines: By learning geometry, if three lines are said to be a concurrent lines, then the three lines should pass through common point.

Intersecting Lines: If two lines are not parallel, then they will intersect each other at a common point.

Collinear points: Collinear Points are the points, which lie on the same line.

Plane: By learning, a Plane is an infinite set of points combined to form a flat surface.

Understanding algebra 2 formulas list is always challenging for me but thanks to all math help websites to help me out.

Learning Elementary Shapes and their Definitions in Geometry :


Let we see elementary shapes of geometry and their definitions,

Square: A Square can be defined as a regular quadrilateral. All the four sides of the square are equal.

Rectangle: A Rectangle is a four sided geometrical figure. The opposite sides of a rectangle are equal.

Triangle: In geometry, triangle is one of the basic shapes. It consists of three sides. It belongs to polygon family.

Circle: A circle is a geometric figure, formed by a locus of points equidistant from a common point.

Midpoint: A midpoint is point, which separates a line segment from both the end points.

Ray: A line having one fixed end point and an infinite extension on other end.

Angles: An angle can be formed by two rays having common end point.

Right angle: If an angle is 90°, it is said to be  right angle.

Obtuse angle: If an angle is more than 90° but less than 180°, it is said to be an obtuse angle.

Straight angle: If an angle is 180°, it is said to be straight angle.

By learning the geometry, many elementary shapes are found and their definitions are known.

Elementary Linear Algebra 8th Solution Kolman

Introduction of elementary linear algebra 8th solution kolman:

Algebra is a part of mathematics, which deals with the study of operations and relations. Algebra also includes the equations and polynomials. Algebra also performs topologies, number theory, addition, equation solving, etc can be done. Algebra derived from Arabic language al-jabr. Algebra consists of simultaneous equation, partial fractions, factorization, rational expressions, square root, etc. Let us see about elementary linear algebra koulman.  For example,

5+3 = 3+5 is same as a+b = b+a.

Please express your views of this topic Elementary Row Operations by commenting on blog.

Examples for elementary linear algebra 8th solution kolman:


Problem 1 for elementary linear algebra 8th solution Kolman:

Find the value of the expressions 3x+7, if x=5.

Solution for elementary linear algebra 8th solution Kolman:

sub, x=5 in the given expression 3x+7

3x+7 = 3(5) +7

=15 + 7

= 22

Therefore the value of expression 3x + 7 is 22.

Problem 2 for elementary linear algebra 8th solution Kolman:

Solve 7x-5 =79

Solution for elementary linear algebra 8th solution Kolman:

7x-5 = 79

7x = 79 +5 from rule(2)

7x = 84

x= 84 *1/7 from rule(3)

x = 84 / 7

x = 12

Value of x is 12.

Problem 3 for elementary linear algebra 8th solution Kolman:

The perimeter (p) of a rectangle is twice the sum of its length (l) and breath(b).

1. Frame a formula to find the perimeter

2. Find b when p=34 and l=10cm

Solution for elementary linear algebra 8th solution Kolman:

From the given statement

Perimeter = 2[length +breadth]

I.e p=2[l+b]

p=2[l+b]

2[l+b] = p

l+b = ½ *p

b = (p/ 2)-l

then sub, p=34 and l=10 in above step,

b = (34/2)-10

=17-10 =7

b = 7cm

Practice Problems for Elementary Linear Algebra 8th Solution Koulman:


Q 1.  6x + 40 = 94.Find x?

Answer: x = 9

Q 2.  Solve 2x+7y = 11, -3x+5y=-1

Answer: x=2,y=1

Q 3.  Solve for x 3x + 10 = 8x + 5

Answer: x = 1

Elementary Statistics Homework

Introduction to elementary statistics homework:

Our world is flattering more and more information oriented. Every part of our lives utilizes data in one form or the other. So, it becomes necessary for us to know how to extract meaningful information from such data. This taking out of meaningful information had studied in a branch of mathematics called Statistics.


elementary statistics homework Problems of find median:


Statistics example:

The points scored by a Tennis team in a series of matches are as

Follows:

20, 5, 10, 30, 18, 8, 17, 11, 14, 27, 51, 13, 11, 10, 21, 31

Find the median of the points scored by the team.

Statistics solution:

To arrange the given points in ascending order, we get

5, 8, 10, 10, 11, 11, 13, 14, 17, 18, 20, 21, 27, 30, 31, 51

There are 16 terms. Therefore, there are two middle terms.

That is, (16/2)th term and ((16/2)+1)th term. Therefore, these are the 8th and 9th terms.

Hence, the median is the average values of the 8th and 9th terms.

Median (14+17)/2=15.5

Therefore, the medial point scored by the Tennis team is 15.5.

I have recently faced lot of problem while learning What Does Mean Median and Mode Mean, But thank to online resources of math which helped me to learn myself easily on net.

elementary statistics homework Problems of find mode:


Statistics example 1:

Find the mode of the following numbers (out of 10) obtained by 20 peoples:

4, 6, 5, 8, 3, 2, 7, 7, 6, 5, 4, 8, 10, 10, 3, 4, 7, 6, 8, 8

Statistics solution:

We arrange this data in the following form:

2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 10, 10

Here 8 occur most frequently, i.e., four times. Therefore, the mode is 8.

Statistics example 2:

A team in a series of 10 matches given below scored the number of goals:

2, 5, 4, 3, 0, 1, 5, 5, 4, 5

Find the mode of these scores.

Statistics solution:

We arrange this data in the following form:

0, 1, 2, 3, 4, 4, 5, 5, 5, 5

Here 5 occur most frequently, i.e., four times. Therefore, the mode is 5.

These are some of the homework problem on elementary statistics.

Elementary Algebra

Introduction to elementary Algebra

In elementary level the childrens would reading the lessons and solve their  algebra math problems with help of  simple arithmetic functions like addition,subtraction,division and multiplications and these can be denoted by (+ ,`xx` ,`-` ,÷ ).This elementary level of reading the algebra is the growing stage for the childrens in their  education field.Let we see about the problem based on elementary algebra. I like to share this help with algebra 2 problems with you all through my article.



Elementary Algebra solved problems

Problem 1:

Solve the given problem 20x - 6 = 12
Solution:

Step 1: Given that 20x - 6 =12

Step 2: Here we are going to add the 6 on both the sides

Step 3: 20x  - 6 + 6  = 12+ 6

Step 4 : 20x =18

Step 5: X = `18/20`

X = 0.9

So the solution foe x  is  0.9

Problem 2:

Calculate and simplify the given problem
6d2 + 48da

Solution:

Step 1: 6d2 + 48d

Step 2: We will take the 8a as common from 6d2 and 48d

Step 3: Then the expression become as,

6d (d + 8)

The answer: 6d2 + 48d = 6a (a + 8)

Problem 3:

solve  ` (3/2)` + `(6/2)`

Solution:

Step 1: Take LCM as 2
Step 2: = ` (3/2)` + `(6/2)`

Step 3:  Add the above terms.
= `(12+6) / 2`
= `18/2`

The answer is = `18/2`


One more solved problemsElementary Algebra


Problem 4:

Calculate and find the  system of equation 8x + 10y = 12, y = 2
Solution:

Given that:

Step 1: 8x + 10y = 12, y = 2

In the problem the y value is mentioned as 2 ,So apply the y value in 8x + 10y = 12

Step 2: 8x + 10y = 12

Step 3: 8x + 10(2) = 12

Step 4: 8x + 20 = 12

x =1

We get a variables as x =1 and y = 2.

So the answer is x =1 and y = 2.

The above solved problems done in basic elementary algebra for the childrens used in elementary. Please express your views of this topic How to Rationalize the Denominator by commenting on blog.


Practice problems in Elementary Algebra


Problem 1:

Solve the given problem 30x - 8 = 12
Answer:  X = 0.66

Problem 2:

Calculate and simplify the given problem
5d2 + 45da

Answer: 5a (a + 9)

Problem 3:

solve  ` (6/2)` + `(5/2)`

Answer:  = `22/2`

Elementary Algebraic Expressions

Elementary Algebraic expressions of addition, subtraction, and multiplication: .
Thus, ax + by and axx + bx + c are common algebraic expressions. Exponential notation is used to avoid repeating the same term in a product, so that x2 for xx and y3 for yyy. Expressions is built up in the way from the real and complex numbers, the algebraic quantities a, b, c, …, x, y, z, and ... Arithmetic numbers and arithmetical operations (such as +, −, ×, ÷) occur, in algebra can also uses symbols (such as x and y, or a and b) to denote numbers. Elementary Algebra be distinguished from abstract algebra, a more advanced field of study.

In elementary algebraic expressions, an "expression" contain numbers, variables and arithmetical operations. These are written (by convention) with 'higher-power' terms on the left (see polynomial); a few examples are:

An equation is the claim that two algebraic expressions are equal. The equations are true values involved variables (such as a + b = b + a); such equations are called identities. Conditional equations are true for some values of the involved variables: x2 − 1 = 4.


Generalizations of elementary algebraic expressions.


The symbols are denoted a number is called variables, It is used in algebra to make generalizations mathematics.

• It allows arithmetical equations to be stated as laws (such as a + b = b + a for all a and b), and the first step to the systematic study of the properties of the real number system.

• It allows reference to numbers which are not known. In this of a problem, a variable may represent a certain value is not yet known, but which may be found through the formulation and manipulation the equations.

• It allows the exploration of the mathematical relationships between quantities (such as "if you sell x tickets, then your profit will be 3x − 10 dollars").

These three are the main strands of elementary algebraic expressions.

The operation of addition...
It has an inverse operation called subtraction: (a + b) − b = a, which is the same as adding a negative     number, a − b = a + (−b);
The operation of multiplication...
Means repeated addition: a × n = a + a +...+ a (n number of times);
Has an inverse operation is said to be division that works for non-zero numbers: (ab)/b = a, which is the same as multiplying by a reciprocal, a/b = a(1/b);
Distributes over addition: (a + b)c = ac + bc
Is abbreviated by juxtaposition: a × b ≡ ab
The operation of exponentiation...
Means repeated multiplication: an = a × a ×...× a (n number of times);
Has an inverse operation, called the logarithm: alogab = b = logaab;
Distributes over multiplication: (ab)c = acbc
C an be written in terms of n-th roots: am/n ≡ (n√a)m and thus even roots of negative numbers do not exist in the real number system. (See: complex number system)
Has the property: abac = ab + c;
Has the property: (ab)c = abc.
In general ab ≠ ba and (ab)c ≠ a(bc);

I like to share this Algebraic Properties of Equality with you all through my article.

elementary algebraic expressions


It is important of expression is always computed the same way. it is necessary to compute the parts of an expression in the particular order, known as the order of operations. The order of operations is expressed in the following:

parenthesis
exponents and roots
multiplication and division
addition and subtraction

Essentials of Elementary Algebra

Introduction: Essentials of elementary algebra:

Algebra is a branch of mathematics is use to construct the mathematical model of the real-world situations and to handle the problems that we could not solve the problems using the simple arithmetic. Using the words, algebra uses symbols to make statements.

Algebra includes real numbers, complex numbers, matrices, vectors etc. In algebra, we are frequently using the letters for represents the numbers in mathematics.  Algebra is using the symbols as arithmetic operations for adding, subtracting, dividing and multiplying. I like to share this Distributive Property Definition with you all through my article.



Properties used in elementary algebra.


1. Commutative Property of Addition in algebra

The two numbers are adding any order (a, b or b, a), the sum value is the same.

a + b = b + a

2. Commutative Property of Multiplication in algebra

The two numbers are multiplying any order (a, b or b, a), the sum value is the same.

a * b = b * a

3. Associative Property of Addition in algebra

The associative property will take up three or more numbers. The parenthesis indicates the terms that are measured one unit. Hence, the numbers are 'associated' jointly. In multiplication, the product is at all times the same anyway of their grouping.

(a + b) + c = a + (b + c)

4. Associative Property of Multiplication

The associative property will take up three or more numbers. The parenthesis indicates the terms that are measured one unit. Hence, the numbers are 'associated' jointly. In addition, the sum is at all times the same anyway of their grouping.

(a * b) * c = a * (b * c)

Understanding Multiplying with Decimals is always challenging for me but thanks to all math help websites to help me out.

Example Algebraic Problem:


Example on elementary algebra:

-3(x + 7) = x + 7

Solution:
multiply factors in left term

-3x - 21 = x + 7

add 21 to both sides

-3x - 21 + 21 = x + 7 + 21

Group like terms

-3x = x + 28

subtract x to both sides

-3x - x = x + 28 -x

Group like terms

-4x = 28

multiply both sides by -1/4

x = -7

Check the solution

Left side:-3(-7 +7) = 0
right side:-7 + 7 = 0

Conclusion

x = -7 is the correct solution for the given algebraic  equation.

Elementary Algebra Made Easy

Introduction to elementary algebra made easy:

Algebra is the branch of mathematics deals with the study of rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. It deals with the general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. Looking out for more help on What is a Common Factor in algebra by visiting listed websites.

Elementary algebraic expressions made easy:

An expression in an elementary algebra is a grouping of numbers, variables, constants, operators and parentheses or grouping brackets that are stated as an entity. An equation consists of an expression on each area of the equals sign. Some expressions are made up of sub-expressions. Much of an elementary algebra concerns simplify expressions to facilitate the solution of equations.


Steps for simplify elementary algebra expressions made easy:


Step 1: Group the terms containing the same variable together in algebra expressions.

Step 2: Perform the operation inside the parentheses for the variable and other.

Step 3: Rewrite the expressions and simplifying the algebra expressions.

Step 4: To check the equation, if there is able to simplify the expression, then repeat the step 1 to 4.

Introduction for elementary algebra equation:

An algebra equation is a mathematical statement that asserts the equality of two expressions. Elementary algebra equations consist of the expressions that are to be equal on opposite sides of an equal sign, as in

x+3=5

One use of an elementary algebra equation is in mathematical identities, assertions that are true independent of the values of any variables contained within them. Between, if you have problem on these topics What is an Dependent Variable, please browse expert math related websites for more help on cbse 11 syllabus.


Fundamental Laws of addition in elementary algebra made easy:


For the addition of positive and negative number, the following rules, established in the First Course, apply make easy to solve the an elementary algebra equation:

A number represented by a letter is called a literal number, and any number expression in which one or more number symbols are letter is called a literal expression.

Laws for addition in elementary algebra made easy:

1) To add two numbers with like signs, find the sum of their absolute values, and prefix the sign common to both.

2) To add two numbers with unlike signs, find the difference of their absolute values, and prefix the sign of the one with the greater absolute value.

Elementary Probability Problems

Introduction :

The measure of how possible it is that a number of event will occur; a number expressing the ratio of favorable cases to the whole number of cases possible  the quality of being probable; a probable event or the most probable event; "for a while mutiny seemed a probability"; "going by past experience there was a high probability that the visitors were lost"


Problems of Elementary Probability


Example:

At a car park there are 100 vehicles, 60 of which are cars, 30 are vans and the remainder are Lorries. If every vehicle is equally possible to depart, find the probability of:

a) Van leaving first.

b) Lorry leaving first.

c) Car leave-taking second if either a lorry or van had left first.

Solution:

a) Let S be the sample space and A be the event of a van leaving first.

n(S) = 100

n(A) = 30

Probability of a van leaving first:

P(A) = 30 / 100

P(A) = 3 / 10

b) Let B be the event of a lorry leaving first.

N(B) = 100 – 60 – 30 = 10

Probability of a lorry leaving first:

P(B) = 10 / 100

P(B)= 1 / 10

c) If either a lorry or van had left first, then there would be 99 vehicles remaining, 60 of which are cars. Let T be the sample space and C be the event of a car leaving.

n(T) = 99

n(C) = 60

Probability of a car leave-taking behind a lorry or van has left:

P(C) = 60 / 99

= 20 / 33

P ( C ) =  20 / 33

2. A die is roll, find the probability that an even number is obtain.

Solution:

Let us 1st write the sample space S of the experimentation.

S = {1,2,3,4,5,6}

Let E be the event "an even number is obtain" and write it down.

E = {2,4,6}

We now use the formula of the standard probability.

P(E) = n(E) / n(S)

= 3 / 6

= 1 / 2

Answer : P(E) = 1 / 2

3 . 2 coins are tossed, find the probability that 2 heads are obtained.

Solution :

The sample space S is given by.

S = {(H,T), (H,H), (T,H), (T,T)}

Let E be the event "two heads are obtained".

E = {(H,H)}

We use the formula of the standard probability.

P(E) = n(E) / n(S)

= 1 / 4

Answer : P(E) = 1 / 4

Elementary Probability

Introduction to elementary probability:

          The elementary probability started with gambling, The probability mostly used in the field of physical science, commerce, biology science, medical science, weather forecasting , etc., An experiment having more than one possible outcome is called statistical experiment. A statistical experiment is also known as a trial. Tossing a coin whether it results in a head or a tail is a trial. Certain statements implying more than one possible situation can also be termed as trials.


Elementary probability of an event

In a random experiment, let S be the sample space and E `sube` S. Then E is an event.

The elementary probability of occurrence of E is defined as

            P (E)= number of outcomes favorable to occurrence of E
                         number of all possible outcomes

                        = number of distinct element in E
                                number of distinct element in S

                        = n (E)
                           n (S)

                        Therefore P (E) = n(E)
                                                  n(S)


Elementary probability example problem

Example 1:

A coin is tossed once. Find the probability of getting a head?

Solution:

When a coin is tossed once, the sample space is given by S= {H, T},

Let E be the event of getting a head.

Then, E = {H}.

Therefore n(E)=1 and n(S)=2.

P (getting a head)= p(E)= n(E) / n(S) = 1 / 2.

Example 2:

Two coins are tossed once. Find the probability of

(i)Getting 2 heads

(ii)Getting a least 1 head

(iii)Getting no head

(iv)Getting 1 tail and 1 tail

Solution:

Where 2 coins are tossed once, the sample space is given by S= {HH, HT, TH, TT} and, therefore, n(S)=4.

(i)Getting 2 head

Let E1 = event of getting 2 heads. Then,

E1= {HH} and, therefore, n (E1) =1.

Therefore P (getting 2 heads) = P(E1) =  n(E1) / n(S) = 1 / 4

(ii)Getting at least 1 head

Let E2 = event of getting at least 1 head. Then,

E2= {HT, TH, HH} and, therefore, n (E2) =3.

Therefore P (getting at least 1 head) = P (E2) = n(E2) / n(S) = 3 / 4

(iii)Getting no head

Let E3 = event of getting no head. Then,

E3= {TT} and, therefore, n (E3) =1.

Therefore P (getting no head) = P (E3) = n(E3) / n(S) = 1 / 4

(iv)Getting 1 head and 1 tail

Let E4 = event of getting 1 head and 1 tail. Then,

E4= {HT, TH} and, therefore, n (E4) =2.

Therefore P (getting 1 head and 1 tail) = P (E4) = n(E4) / n(S) = 2 / 4 = 1 / 2.

Elementary Algebra Homework

Introduction for elementary algebra homework:

Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. The elementary algebra covers that the four basic operations such as addition, subtraction, multiplication and division In Algebra, besides numerals we use symbols and alphabets in place of unknown numbers to make a statement. Hence, elementary algebra  homework covers may be as they regarded as in extension of Arithmetic Understanding One-step Linear Equations is always challenging for me but thanks to all math help websites to help me out.


Basic rules and properties of elementary algebra homework:


•     Variables

Algebraic variables are the alphabetical characters which can be used for assigning the value. While solving the algebraic equation value of that variable will be changed. Widely used variables are x, y, z

•     Constant

An algebraic constants are the value whose value are never to be changed during the solving the algebraic equation. In 2y + 5, the value 5 is the constant.

•     Expressions

An algebraic Expression is the combination of that variables, constant, coefficients, exponents, terms which are combined by the following arithmetic operations Addition, subtraction, multiplication and division. The example of an algebraic expression is given below

2y + 5

•     Term

Terms of the algebraic expression is concatenated to the form of a algebraic expression by the arithmetic operations such as addition, subtraction, multiplication and division. In the following example 3n2 + 2n the terms 3n2, 2n are combined to form the algebraic expression 3n2 + 2n by the addition operation (+)

•     Coefficient

The coefficient of an algebraic expression has the value will present just before the terms. From the following example, 3n2 + 2n the coefficient of 3n2 is 3 and 2n is 2

•     Equations

An algebraic equation equals the numbers or expressions. Most probably algebraic equation is used for that an value of the variable. The example of the equation is given below

2y + 5=0

In elementary algebra, we list out the fundamental rules and properties of pre-algebra and give examples on they may be used.

Suppose that the a, b and c are variables or pre-algebraic expressions.

Suppose that the a, b and c are variables or pre-algebraic expressions.

1. Commutative Property of Addition In elementary algebra.

a + b = b + a

Examples:

1. real numbers

2 + 3 = 3 + 2

2. pre-algebra expressions

x 2 + x = x + x 2

2. Commutative Property of Multiplication In the elementary algebra.

a * b = b * a

Examples:

1. real numbers

5 * 7 = 7 * 5

2. pre-algebra expressions

(x 3 - 2) * x = x * (x 3 - 2)

3. Associative Property of Addition In elementary algebra.

(a + b) + c = a + (b + c)

Having problem with Variables and Expressions keep reading my upcoming posts, i will try to help you.


Order of the operation for elementary algebra homework


1. Reduce whatever inside the parentheses.

2. Reduce the exponents.

3. Multiplication or division.

4. Finally, perform Addition or Subtraction.

Examples of elementary algebra home work

Elementary algebra homework problem1:

5*(10+5)

Solution:

5*(10+5) = 5*10+5*5

=50+25

=75

Elementary algebra homework problem 2:

2+(4+6)

Solution:

2+(4+6)=2+10

=12

Elementary algebra homework problem 3: Find the value for the below expression if a=6

3(a-9)

Solution:

= 3(a-9) (evaluate the expression at inside the parenthesis)

= 3(6-9)

= 3(-3) which is equal to 3 * -3

= -9

Elementary algebra homework problem 4:

Simplify the following expression 4*(44÷2)

Solution:

= 4*(44÷2) (evaluate the expression inside the parenthesis)

= 4*(22)

= 88

Elementary algebra homework problem5:

Simplify the following expression 3*(27÷9)+5

Solution:

= 3*(27÷9)+5 (evaluate the expression inside the parenthesis)

= (3*3) +5

= 9+5

= 14

Math Questions and Answers

Introduction to math questions and answers:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". In this article we shall discuss about  math questions and answers.


Math questions and answers:


Some of the important math Questions and Answers are given below ,

Example 1:

Solve the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Answer:

Given the equation

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Multiply factors.

-15x - 10 - x + 3 = -16x - 20 +13

Group like terms

-16x - 7 = -16x - 7

Add 16x + 7 to both sides

0 = 0

Example 2:

Find the average marks obtained by john in his 5 test.

92, 86,90,94,96

Solution:

Number of test = 5

Marks obtained by john = 92, 86, 90, 94, 96

Average marks obtained by john in 5 test = ` (92+86+90+94+96)/5`

Average =  91.6.

Example 3:

Solve 9x2 + 6x - 3 = 0 for x.

Solution:  Factor:  (9x - 3)(x + 1) = 0

9x - 3 = 0, x + 1 = 0

9x = 3 ,      x = -1

x = (1 / 3) ,   x = -1

x = -1,(1/3)


Example 4:


Surface area of a right circular cylinder of height 30 cm is 112 cm^2. find the radius of the base.

Solution:

Curved surface area = (2?r h) = 112 cm^2

2*(22/7)* r *30 = 112

r = (7*112)/(2*22*30)

= 784/1320.

= 0.5939 cm

Hence, radius of the base = 0.5939 cm.

Example 5:

Find the median of the following set of points:

17, 16, 12, 8, 12, 9, 18, 14

Solution:

Step 1:

First arrange the given numbers in ascending or descending order.

8, 9, 12, 12, 14, 16, 17, 18

Step 2:

Here 4th and 5th number of the given observation are 12, 14

So 12 and 14 are the middle observation

Step 3:

So median of the even observation = average of the middle two numbers

Median = `(12+14)/2`

= 26/2

= 13

So the median is 13.

Elementary Math Geometry

Introduction to elementary math geometry :

Geometry plays their important part in the mathematics in which it deals with the shapes like cone, circle, square, rectangle and their positions in the spaces and the measurement of the shapes using parameters like area, volume and perimeter.  Elementary geometry problems includes solving simple basic level math problems. Here we will solve some elementary math problems. In this article we will brief about elementary math geometry. I like to share this Equation Parabola with you all through my article.
 
Elementary Math Geometry:

Elementary math geometry involves in preparing geometry math problems. Here we will see some sample problems as below,
Example problem 1- Elementary math geometry

What is the area of the square whose sides measures 7cm?

Solution:

Area of the square = side 2

= 7 2

= 49

Area of the square = 49 cm 2

Example problem 2:

Find out the diagonal of the rectangle whose length is l =15 cm and breadth is b = 6 cm?

Solution:

Diagonal of the rectangle  = `sqrt(l^(2) + b^(2))`

= `sqrt(15^(2) + 6^(2))`

= `sqrt(225+ 36)`

= `sqrt(261)`

= 16.15

Diagonal of the rectangle = 16.15 cm

Example problem 3:

What is the area of the trapezoid whose side measures a = 9 cm and b = 7 cm and height measures h =6 cm?

Solution:

In the trapezoid, consists of  4 sides; out of the four sides 2 sides are parallel.

Area of the trapezoid = `1 / 2` (a + b) * h

= `1 / 2` (9 + 7) * 6

= `1 / 2(` (16) * 6

= 8 * 6

Area of the trapezoid = 48 cm2

Example problem 5:

The angle of a triangle is 120. Then what is the measure of its supplementary angle?

Solution:

Supplementary angle is 180.

Given angle of the triangle is 120.

Supplementary angle to measure for 120= 180 – 120

= 60


Understanding Math Help Geometry is always challenging for me but thanks to all math help websites to help me out.

Practice Problem: Elementary Math Geometry

Practice problem 1 - Elementary math geometry
What is the area of the square whose sides measures 8cm?

Answer: 64cm 2

Practice problem 2 - Elementary math geometry

The angle of a triangle is 160. Then what is the measure of its supplementary angle?

Answer: 20

Two Hundred Forty

Introduction to two hundred forty:

In this article we shall discuss the finding two hundred forty. The below given are the various place values. The number two hundred forty (240) is a natural number. In this article we shall discuss about factors solving problems related to two hundred forty (240). It is three (3) digits number with,

0 is once place,

4 is tens place,

2 is hundreds places,

The numbers

Two hundred forty numbers is between 239 and 241. Please express your views of this topic Math Median by commenting on blog

Factors of Numbers Two Hundred Forty:

The factors two hundred forty:

The factors two hundred forty are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.

The numbers two hundred forty factor pairs are:

1 x 240,

2 x 120,

3 x 80,

4 x 60,

5 x 48,

6 x 40,

8 x 30,

10 x 24,

12 x 20,

15 x 16,

20 x 12,

24 x 10

30 x 8,

40 x 6,

48 x 5,

60 x 4,

80 x 3,

120 x 2,

and 240 x 1.

Is this topic List Odd Numbers hard for you? Watch out for my coming posts.

Example Problems for Two Hundred Forty:

Example 1:

Add 200 to two hundred forty.

Solution:

The given things are 200 + 240.

By adding this two we get 200+ 240.

440.

So the sum of 240 and 200 is 440.

Example 2:

Find the value of 2402?

Solution:

We need to find the value of 2402.

2402 = 240 x 240.

The product of 240 x 240 is 57600

Example 3:

Find the value of 240 +240 =?

Solution:

We need to find the value of 240 + 240.

The product of 240 + 240 is 480.

Example 4:

Find the value of 240 + 240 + 240 =?

Solution:

We need to find the value of 240 + 240 + 240.

240 + 240 + 240= 720

The product of 240 + 240 + 240 is 720.

Example 5:

Find the reciprocal of the number 240

Solution:

The given element is 240 we need to find the reciprocal of the element.

The basic syntax that finds the reciprocal of the element y is ` 1/y`

Here the number is 240.

By plugging in the given values in to the formula we get

240= `1/240`

So the reciprocal of the number 240 is `1/240`

Example 6:

Find the reciprocal of the number `50/240`

Solution:

The given number is `50/240` we need to find the reciprocal of the number.

The basic syntax that finds the reciprocal of the element` x/y`  is `y/x.`

Here the number is `50/240` .

By plugging in the given values in to the formula we get

`50/240` =`240/50`

So the reciprocal of the number `50/240` is `240/50` .

The simplify reciprocal solution is 4.8

The Math Term for Conjecture

Introduction to math term conjecture:

The term conjecture in math refers a statement or assumptions that are not proved. It is like a theorem, but they have not proved. For example the kite area conjecture states that the area of kite is equal to half the product lengths of two diagonals. The term Conjecture can be also mean as rules or conditions. In this article we shall some math conjectures and example problems.

Math Term for Conjecture – Formulas:

Rectangle area conjecture:

Area of rectangle (A) = b x h square units

Where,

A – Area of rectangle

b – Length of the base

h – Height of the rectangle

Trapezoid area conjecture:

The diagram of trapezoid is shown in below.

Area of trapezoid (A) = `1/2` x h x (a + b) square units

Where,

A – Area of trapezoid

h – Height

a, b – length of two parallel sides

Circle area conjecture:

The diagram of circle is shown in below

Area of the circle (A) = pr2 square units

Where,

A – Area of circle

r – Radius of circle

Having problem with Cube Root Formula keep reading my upcoming posts, i will try to help you.

Math Term for Conjecture – Example Problems:

1. The rectangle has base length 10.5 cm and height 5.5 cm. solve for area of rectangle.

Solution:

Given:

Base Length (b) = 10.5 cm,

Height (h) = 5.5 cm

Solving area:

Rectangle area conjecture:

Area of rectangle = b x h square unit.

= 10.5 x 5.5

Area of rectangle = 57.75 cm^2

2.      Find the area of trapezoid whose height 13.5 cm, side a= 7.5 cm and side b= 9.5 cm

Solution:

Given:

Height (h) = 13.5 cm

Side a= 7.5 cm;            b= 9.5 cm

Formula:

Area of trapezoid (A) = `1/2` x h x (a + b) square units

=`1/2` x 13.5 x (7.5 + 9.5)

=`1/2` x 13.5 x 17

=`1/2` x 229.5

= `229.5 / 2`

= 114.75

Area of trapezoid (A) = 114.75 cm^2

3. The radius of a circle is 8.5 cm. Find the area of that circle?

Solution:

Given:

r = 8.5 cm

Formula:

Area of the circle = p x r^2

p = 3.14

A = 3.14 x (8.5)^2

=3.14 x 72.25

Area of circle = 226.86 cm^2

Definition of Exercise in Math

Introduction for Math Exercise:

Collection of practice problem is known as exercise. If a student wants some definition in math exercise with problems, they can refer to the below examples. In this we can see some of the math exercise in statistics with example problems as shown. Let us see some of the general math exercise in statistics such as mean, median and mode with examples and practice problems as follows.

Definition of Exercise in Math – Definitions for Exercise:

In this following we can see some math definition for statistics exercise.

Mean:

It is a set of data which can find the average in dividing by sum of numbers with total numbers in the given data.

Median:

It is a set of numbers which can find the middle numbers and arrange the numbers in order to select the middle number.

Mode:

It is a set of numbers that can occur frequently in a set of data and no number can occur more than once.

Definition of Exercise in Math – Examples and Practice Problems:

In this following we can see some math definition for statistics exercise with example and practice problems.

Math Definition for Exercise 1:

Find the mean of weights for 6 peoples in kilograms are 4, 1, 9, 2, 11, and 3.

Solution:

Sum of numbers
Mean = ------------------------------
Total number

= `(4+1+9+2+11+3)/6`

= `30/6`

= 5

Math Definition for Exercise 2:

Find the median of 16, 1, 15, 13, 20, and 8.

Solution:

Arrange the data in ascending order as 1, 8, 13, 15, 16 and 20.

N = 6

Since n is even, median = `1 / 2` [`(nth)/2` item value + (`n / 2` + 1)th item value]

= `1 / 2` [6th item value + (`6/2` + 1)th item value]

= `1 / 2` [3rd item value + 4th item value]

= `1 / 2` [13 + 15]

= `1 / 2` * 28

= 14

Math Definition for Exercise 3:

Find the mode of 23, 19, 28, 13, and 28.

Solution:

28 are repeated twice.

Mode = 28

Practice Problems:

Find the mean of weights for 6 peoples in kilograms are 8, 1, 10, 2, 7, and 3.

Solution:

= 5.16

Find the median of 19, 14, 6, 8, 3, and 12.

Solution:

= 10

Find the mode of 17, 19, 16, 24, and 19.

Solution:

= 19