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.

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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

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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.

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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)

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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


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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.

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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.

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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.

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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)

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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.