Math Solution Sentence

Introduction Math Solution Sentence

The expression with equal sign is said to be as math sentence. Thus the expression means equation where the left side is equal to right side or vice versa. Example:  (5+5=10). LHS is the sum of 5 and 5 which is equal to RHS. Math solution for sentence is to find the unknown term by using known term from the expression. Example: 7+x=14. by using known term of 7 and 14 we can find the unknown term x. Please express your views of this topic Solve Radical Expressions by commenting on blog.


Example Problems - Math Solution Sentence:


Addition math solution sentence

Example 1: What is the solution for the math sentence 80 + x = 140?

Solution:

Given:  80 + x = 140

Step 1: Subtract both sides by 80

80 + x - 80 = 140 - 80

0 + x = 60

Step 2: x = 60

Check the answer:

Step 1: By substituting value of x in the expression 80 + x = 140

80 + 60 = 140

140 = 140,

Answer: Thus the value of x = 60 is the correct solution for the math sentence

Subtraction math solution sentence

Example 2:

What is the solution for the math sentence x - 25 = 50?

Solution:

Given: x - 25 = 50

Step 1: Add both sides by 25

x - 25 + 25 = 50 + 25

x - 0 = 75

Step 2: x = 75

Check the answer:

Step 1: By substituting the value of x in the expression x – 25 = 50

75 - 25 = 50

50 = 50

Answer: Thus the value of x = 75 is the correct solution for the math sentence.

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Practice Problems - Math Solution Sentence:


Problem 1: What is the solution for the math sentence 15 + x = 45?

Answer: 30

Problem 2: What is the solution for the math sentence 220 + x = 440?

Answer: 220

Problem 3: What is the solution for the math sentence x - 55 = 45?

Answer: 100

Problem 4: What is the solution for the math sentence x - 450 = 110?

Answer: 560

Math Equation for 3 of 520

Introduction to math equation for  3 of  520:

Percentage calculation is one of the most important calculation which, every student must be aware of. Finding percentage is a calculation performed to find out the amount of portion or amount of consumption is done. Percentage calculation is said as a very important aspect because, they are used in our day to day life, almost in every field. The percentage is expressed in two forms of equations in math which is explained in the following sections. Examples to solve percentage problems, is illustrated in the following sections. I like to share this Reciprocal Definition with you all through my article.


Math equation for 3 of 520


Finding percentage in math is a calculation performed to find out the amount of portion or amount of consumption is done by a parameter of the other. As said earlier percentage calculation equation is of two types. For example: The problem, solve 3 of 520 can be expressed in two forms of equations as shown below.

Equation to solve what percent is 3 in  520 == > `(x%)/100` * 520 = 3
Equation to find 3% of 520. ==> `3/100 ` *520 = ?
The calculation of the above two formats is explained in the next section.

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Basic equation for percentage calculation:


The basic math equation for the calculation of percentage is as follows,

===>        x * `y/100` = z

where,

'x' is the whole amount

'y' is the percentage

'z' is the percentage value

Example math problems:


Here are few examples explaining the calculation of percentage using the above mentioned math equations,

Example 1:

Solve 3 of 520

Solution:

Lets assume the question in this format,

Solve what percent is 3 of 520

So the percent value = 3

The whole amount is 520

So substituting in the equation,

x * `y/100 ` = z

520 * `y/100 ` = 3

therefore,

`y/100` = `3/520` ,

y = `(3*100)/(520)`

y = `300/520`

y = 0.57%

Example 2:

Solve 3 of 520

Solution:

Lets assume the question in this format,

Solve what is 3 percent  520

So the percentage is given = 3

The whole amount is 520

So substituting in the formula,

x * `y/100 ` = z

520 * `3/100 ` = z

Therefore,

`1560/100` = z

z = `(156)/(10)`

z =` 15.6`

Therefore, 3% 0f 520 is 15.6

Properties in Math

Introduction of properties in math:

Math is the learning of measure, structure, space and change. Math is progressed from counting, calculation, measurement, and systematic learning of the shapes and motions of physical entities by the use of abstraction and logical reasoning. Math is used in the world as an important tool in various fields, such as natural science, engineering, medicine and the social sciences. Today all are working is based on mathematics. I like to share this Statistical Probability with you all through my article.


Properties in math:


Let we see about properties of math. All these properties are already defined by the mathematical experts it could not be changed. It is useful for all kinds of math.

Let us take x, y, z are real numbers, + = addition, - =subtraction, * = multiplication, / = division.

Associative Property:

Associative property refers that grouping of element within the parenthesis. It is performed for addition and multiplication and more than three values involved in it.

Associative property is defined as,

Addition: x+(y+z) = (x+y)+z

Multiplication: x*(y*z) = (x*y)*z

Example:

Find the value of 3+(6+10) and 3(6*10) using associative property.

Solution:

Given 3+(6+10)
Associative property: (3+6)+10

=9+10

=19

Given 3(6*10)
Associative property: (3*6)10

= 18*10

= 180

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Commutative Property:

It refers the changing the order of the element but does not change the result.

It is defined as,

Addition: a+b =b+a

Multiplication: a*b = b*a

Example:

Find the value of 12+98 and prove the commutative property value is equal.

Solution:

Given 12+98

=12+98= 110

Commutative property: 98+12=110

Hence, two results are equal.

Distributive property:

It defines distributing some elements. It is defined as,

Addition: a*(b+c) = ab+ac

Subtraction: a*(b-c) = ab – ac

Example:

Find the value of 5*(2+3) using distributive property.

Solution:

Given 5*(2+3)

Distributive property: (5*2) + (5*3)

= 10 + 15

= 15

Additive Identity Property:

Zero is called identity. Any value that is added with 0 it gives the same result. It is defined as,

x + 0 = x and 0 +  x = x

Multiplicative Identity Property:

Any value that is multiplied with 0 it gives the result as zero. It is defined as

x * 0 = 0 and 0 *  x = 0

Additive Inverse Property:

Any value that is added with inverse of the same value the result is zero. It is defined as

x + (-x) = 0

Multiplicative Inverse Property:

Any value that is multiplied with inverse of the same value the result is one.

x * (1/x) = 1

Now all are clear about  properties of math. Now see some more properties.


Some more properties in math:


Reflexive Property of Equality:

It is defined as result is same as question, that is x=x.

Symmetrical Property of Equal:

It is defined as x=y then y=x

Transitive Property of Equal:

It is defined as If x = y and y = z, then z = a

Substitution Property:

If x = y, then y can replace x in any equation.

Definition of Subtraction:

x - y = x + (-y)

Definition of Division:

0 / x = 0, x / x = 1, x / 0 = infinity

Now all are understood the properties of math.

Introduction Matrices Math

Introduction to matrices math:

Let us see introduction of matrices math. Matrices are the plural expression of matrix. An item in matrix is specified as specified as element. In matrix the numbers are represented by either row or column. Matrices are one of the key apparatus in math linear algebra. It is also used to represents the linear transformations.

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Definition of matrices:


The matrix is a rectangular array of numbers. It is a prearranged set of numbers. The math matrices are represented within square braces.  This is the introduction of basis matrices.

Let consider the matrix,

A=`[[2,3],[6,8]]`

The matrix A contains 2 rows and 2 columns. So it is simply called as 2 x 2 matrixes. If it contains 3 rows and 3 columns it is called as 3 x 3 matrices. There are many types of matrices in math.

Types of matrices:

There are 11 types of matrices in the introduction of math.

Type 1: Square matrices.

Type 2: oblique matrices.

Type 3: Row matrices.

Type 4: Column matrices.

Type 5: Matrices of same kind.

Type 6: Transpose of matrices.

Type 7: Zero matrices.

Type 8: Identity matrices.

Type 9: Scalar matrices.

Type 10: symmetric matrices.

Type 11: Skew-symmetric matrices.

Operations in matrices:

There are four operations in matrices. The introduction of operations is following below:

Operation 1: Addition of matrices.

Operation 2: Subtraction of matrices.

Operation 3: Multiplication of matrices.

Operation 4: Division of matrices.

Properties of matrices:

There are five properties in matrices. The introduction of properties is following below.

Property 1: Transpose of matrices.

Property 2: Inverse of matrices.

Property 3: Commutative of matrices.

Property 4: Associative of matrices.

Property 5: Distributive of matrices.

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Matrices example problem:


Let us see some introduction examples of matrices.

Problem 1:

Multiply two matrices, where the matrices are

A= `[[3,7],[5,2]]`     B = `[[6,2],[3,8]]` .

Solution:

The matrix multiplication is following below:

N = `[[3,7],[5,2]]`  * `[[6,2],[3,8]]` .

=`[[18+21,6+56],[30+6,10+16]]`

= `[[39,62],[36,26]]` .

This is the solution for the given matrices.

Problem 2:

Find the inverse matrices of given matrix.

A= `[[7,9],[3,5]]`

`Solution:`

Inverse matrices is the process of alternating the rows as columns and columns as rows.

So, A = `[[7,3],[9,5]]` .

This is the inverse matrices of given problem.

Problem 3:

Add the matrices with unit matrices. The matrix is A=`[[3,5],[7,8]]`

Solution:

The unit matrix is = `[[1,0],[0,1]]`

The addition  is  = `[[3,5],[7,8]] + [[1,0],[0,1]]`

= `[[3+1,5+0],[7+0,8+1]]` .

= `[[4,5],[7,9]]`

This is the addition of matrices.

Math Terms Product

Introduction:

Math tern Product means nothing but a multiplication of two numbers is called Math term product.Product or multiplication is one of the arithmetic operations. Multiplication operation is used in all fields.Math term of product defined simply repeated addition of given terms.For example 10 X4 means nothing but a 4 times of 10 is the meaning for Math terms of product.From the given example 4 times of 10 mean 10+10+10+10=40.This math terms is also used to solve the word problems in arithmetic.I like to share this Arithmetic Mean Formula with you all through my article.


Notation for math terms product


Evaluation of product notation:

Product notations are dot(.),(*),()(),(x)

These all are symbols are using product of two numners.

dot  (•)

It is symbol of Dot used to find the product of two variables or numbers

Star(*)

It is a symbol of star used to find the products

Parentheses ( )( )

It is a symbol for Parentheses Used for finding the multiplication of sign numbers.It is a special Symbol for only signed numbers

cross (x)

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Example problems Math term Product:


Example 1:

Multiply 81 by 12

Solution:

81 and 12(it is nothing but 12 times of 81

It can written as like

=two times of 81+1 times of 81

=972

Answer =972

Example 2:

(a) Solve: 14x10= 14 times 10=140

(b) Solve: 5x5=5  times 5 = 25

(c)Solve:5x8 =5 times 8 =40

(d) Solve: 1000*14 =1000times 14 = 14000

(e) Solve: (13).(13)=13 times 13 = 169

Example : 3

A  cost of  one bags are 2 dollars. Find the  the price of 20 bags?

Solution:

Price of 1 bag  = 2 dollars

Price of 20 bags = 20x 2

Price of 20 bags = $40

Example 4:

There are 10 boys and 16 girls in the class.All boys are having individualy 2 pencil’s find the total no of pencils boys having?

solution:

Total Number of boys = 10

Total Number of girls = 16

Each boy having 2 pencils

Total no of pencils=10* 2=20

What Does Range Mean in Math

Introduction:

In math, plenty of terms are available. One of the notable terms in math is the range. Range comprises of several meanings. The meaning of range is the set of all the output values, which are produced by a function. Another common meaning for range is the value that is obtained as a result of maximum and minimum value in a given set of numbers. This article mainly focuses on finding the range value in a given set of numbers. In this article, we are going to discuss the steps involved in finding the range of given set of numbers and few example problems are given based on finding the range value. In addition, few practice problems are given for the students, which helps to understand what does the math term 'range' really meant for.


Step-by-step explanation for finding range in math:


The following steps are essential for finding the range value for given set of numbers.

Step 1: Position the numbers from ascending to descending order.

Step 2: Find the maximum value

Step 3: Find the minimum value

Step 4: Find out the difference between the given maximum and minimum value


Worked examples for finding range in math:


Example 1:

Find the range value for the given set of numbers:

24, 36, 46, 59, 34, 43, 17, 20

Solution:

Maximum value is 59

Minimum value is 17

Range     =  Maximum value - Minimum value

=  59 - 17

=  42

Hence, the range value is 42.

Example 2:

Find the range value for the given data set:

{ 67, 56, 45, 10, 24 }

Solution:

Maximum value is 56

Minimum value is 10

Range     =  Maximum value - Minimum value

=  56 - 10

=  46

Hence, the range value is 46.

Practice problems for range:

Practice problem 1:

Find the range value for the given set of numbers:

90,160,260, 50, 320, 243, 217

Answer: Range value is 270.

Practice problem 2:

Find the range value for the given data set:

{ 4, 8, 16, 64 }

Answer: Range value is 60.

Range In Math

Introduction to range in math:

In math, Data set is a collection of data, which is usually presented, in tabular form. Each column represents a variable. In math, Range is generally defined as the value we obtained as a result of difference between a greater value and a smaller value.
In other words, range is defined as the difference between a maximum and minimum value. I like to share this Domain and Range Calculator with you all through my article.

Steps to learn the range in math:


In order to learn the range of data set the following steps are necessary.

Step 1: Arrange the numbers from ascending to descending order.

Step 2: Identify the greater value in the given set

Step 3: Identify the smaller value in the given set

Step 4: Find the difference between the greater value and the smaller value to identify the range of the given data set.


Worked Examples for range in math:


Example 1:

Find the range of the data set given below:

8 , 15 , 13 , 7 , 24 , 37 , 6.

Step 1: Arranging the numbers given in data set from least to greatest.

6 , 7 , 8 , 13 , 15 , 24 , 37.

Step 2: Identify the greater value in the given set

From the given set, we can identify 37 as the greater value.

Step 3: Identify the smaller value in the given set

From the given set, we can identify  6 as the smaller value.

Step 4: Find the Range.

Range     =   Greater value – Smaller value

=   37 - 6

=  31

Hence, the range of the given data set is 31.

Example 2:

Find the range of the data set shown below:

33 , 12 , 79 , 24 , 34 , 53 , 27 , 61

Step 1: Arranging the numbers given in data set from least to greatest.

12 , 24 , 27 , 33 , 34 , 53 , 61 , 79.

Step 2: Identify the greater value in the given set

From the given set, we can identify 79 as the greater value.

Step 3: Identify the smaller value in the given set

From the given set, we can identify  12 as the smaller value.

Step 4: Find the Range.

Range    =   Greater value – Smaller value

=   79 - 12

=   67

Hence, the range of the given data set is 67.

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Practice problems for range in math:


1) Find the range of the data set shown below:

7 , 9 , 19 , 31 , 37 , 43 , 6 , 37

Answer: 37

2) Find the range of the data set shown below:

14 , 11 , 32 , 10 , 32 , 77 , 27 , 43

Answer: 67