Group Identity Theory

Introduction about group theory

Group:            

    If a set is defined collectively with the binary o[operation  * then it is called a group. It is defined as the symbol G.If  x and y are the member of a set G and it related to  the binary operation * means then the g is said to be a Group. Here the binary operation should satisfy the certain Axioms.

Axioms of Group theory:

Closure
Associativity of an element
Identity of an element
Inverse of an element.

Properties of group theory


Closure property in group theory:

    If any two elements x ,y  in the group G, then the outcome of the product operation   (x.y) is also present in the group G.

Associativity property in Group theory:

        If any set of elements present in the group G then it satisfies the following condition

                      (x .y).z= x. (y .z).

 Inverse property in group theory:

   For each x is present in the group G , then there exist an element y is also present in  the group  G such that       x . y = y .x =e. here e is defined as an identity element. The outcome of combining element x with y   are not necessitate to acquiesce the same outcome as combining element y with x.

               x. y = y. as It is not always be true.

Identity of an element in the group theory:

If an element x is present in the group G and there exist an another element e in the group G then it satisfies the following,

                 e. x= x . e =x.Here we say that e is an identity element.

Identity of an element is the important axiom of group theory.


Applications of group identity theory:


It is used in the Galois Theory for describe the polynomial roots of symmetries.
The connection between the algebraic field extension and the group theory derived fro m the Galois fundamental theorem.
Another use of group theory is the Algebraic topology. Some of the topological invariants are defined by group.
Group theory is primarily used in the Cryptography and the Algebraic geometry.

Meaning of Integer

Introduction to Meaning of integer:

              The integers are the combination of negative number and non negative numbers. The integers are formed with the help of the natural numbers. The integer set is formed countable infinite set. The integer numbers are denoted with the help of alphabetic letter Z. the natural numbers including the 0. Denoted by 0,1,2,3,….

              Here we are going to understand the meaning of integer by solving some example problems.

Please express your views of this topic greatest integer function by commenting on blog.

Basic properties of an integers:


Now we see about the some basic properties of an integers.

1) Commutative property of addition of integer:

The commutative property is one of the property of integer addition .it tells that we can add numbers in any order.

For example: -7 + 8 = 8+ (-7)

2) Commutative property of multiplication of integer:

       The commutative property of multiplication is also one of the properties of an onteger that tells  we can multiply numbers in any order doesn’t change result.

For example: -8 x 5 = 5 x (-8).

3) Associative property of addition of integer:

       The associative property of Addition is one of the properties of an integer that tells  we can group together then we get the same result.

For example : (-4 + 3) + 2 = -4 + (3 + 2)

4) Associative property of multiplication of integer:

       The associative property of multiplication is fourth property of an integers that tells we can group together in a product then we get the same answer.

For example : -4(2) x 1 = -4( 2 x 1)

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Integer word problems:


Problem 1:

A team won 4 times as many matches as it lost. If it won 16 matches, how many games did it lose?

Solution:

Step 1: First we assign variable, A team won 4 time s as many matches as it lost.

            Let P be number of matches lost and

            4P is number of matches won.

            It won 16 matches

            So 4P = 16

Step 2: Solve the equation,

            Divide by 4 on both sides.

            We get `(4P)/4` = `16/4`

                              P = `16/4`

                              P = 4.

Answer: The team lost 4 games.

Problem 2:

          John and his friends were selling cookies. They sold 5 more boxes the third week than they did the second. On the fourth week, they doubled the sale of their third week.Altogether, they sold a total of 459 boxes. How many boxes did they sell in the fourth week?

Solution:

Step 1:

        They sold 5 more boxes the third week than they did the second. On the fourth week, they doubled the sale of their third week.

       Assign variables Let,   P be boxes sold in the second week 

                                       P + 5 boxes were sold in the third week 

                                       2(P + 5)  =   boxes sold in the third week

       John sold a total of 444 boxes.

       So, P + P + 5 + 2(P + 5) = 459

       Then remove brackets and combine like terms,

                   P + P + 5 + 2P + 10 = 459

                  4P + 15 = 459

       Subtract -15 on both sides

                4P + 15 – 15 = 459 -15

                    4P = 444

       Divide by 4 on both sides

                     `(4P) / 4` = `444 / 4`

                        P = 111

Step 2:  Plug P = 111 into 2(P+4)

             We get, 2(111 + 4)

                         = 222 + 8

                         = 230

Answer: In the fourth week, they sold 230 boxes.

Meaning of Geometry

Introduction for meaning of geometry:

                    The word “geometry” is derived from grouping of two Greek words “Geo” and “me tron”. The word “Geo” means “earth” and “me tron” means “measurement”. So the subject name is “earth measurement” . It was originally named as “geometry”.

                    Geometry is one of the main branch of mathematics, which involves the study of shapes, line equation, angles, and dimensions, relative position of diagrams etc. The basic diagram of geometry is point, line, square, rectangle, triangle, and circle. The geometry properties and example problems are given below.

Let us see properties and theorems of geometry meaning. And also see solved example problems using geometry meaning. I like to share this Ray Geometry with you all through my article.


Properties and theorems for geometry:


Property 1: If any two points on a plane, there is one and only one line containing them.

Property 2: Two distinct lines cannot have more than one point in common

Property 3: If a line and a point not on it, there is one and only one line that passes through the given point and is parallel to the given line.

Property 4: If the given two lines intersect, then the vertically opposite angles are equal.

Property 5: If a given transversal intersects two parallel lines, then any pair of corresponding angles are equal.

Property 6: If any two sides and the included angle of one triangle are equal to any two sides and the included angle of another triangle, then the two triangles are congruent

Theorem 1:

   The given two triangles are congruent if the three sides of one triangle are equal to the three sides of the other triangle.

             Draw a triangle ABC and a line XY parallel to the side BC (see Figure). Mark the point of intersection of line XY and the side AB as D, and the point of intersection of the line XY and the side AC as E. Since the side AB and the side AC are transversal of the parallel line segments XY and BC,

                               ∠D = ∠B, ∠E = ∠C

           The two triangles ABC and ADE have AAA property. However, they are not congruent since the corresponding sides are not equal. Hence, we conclude that AAA correspondence cannot be a criterion for congruency of triangles.

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Example Problems - Geometry:


Example problem 1:

     Find the supplement of the following angles:

      (i) 70° (ii) 45° (iii) 120° (iv) 155°

Solution:

    Since the sum of supplementary angles is 180°,

          (i) the supplement of 70° is 180° − 70° = 110°.

          (ii) the supplement of 45° is 180° − 45° = 135°.

          (iii) the supplement of 120° is 180° − 120° = 60°.

          (iv) the supplement of 155° is 180° − 155° = 25°.

Example problem 2:

   If the angles of a triangle are in the ratio 4 : 4 : 7, find them.

Solution:

    Let the angles be 4x, 4x, 7x.

    Then 4x + 4x + 7x = 180° or 15x = 180° or x = 12°.

    The angles are 4 × 12°, 4 × 12°, 7 × 12°, or 48°, 48°, 84°.

This is how problems solved using geometry meaning.

Geometry Hexagon

Geometry Hexagon

Hexagon is the two dimensional geometric closed figure with five sides.

Geometry Hexagon interior angle:

The angle that found inside the geometric figure is said to be interior angle of the Hexagon.

Geometry Hexagon Exterior angle:

The angle between any side of the Hexagon and the line extended from the next side is said to be exterior angle of the Hexagon.

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Formula:

Formula for calculating the exterior angle of the Hexagon:

Sum of the exterior angle of the Hexagon is 360 degrees.

Formula for calculating the interior angle of the Hexagon:

Sum of Interior angle of the Hexagon = (n-2) 180 degrees

Here n is the number of the Hexagon.

Regular Hexagons:

The regular Hexagon is the geometric figure  in which all sides are equal in length and all the angles are equal in degrees.

Interior angle of the regular Hexagon is `(((n-2) 180)/n)`

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Model Problems:

1.Find the sum of interior angle and each interior angle of the regular geometry Hexagon?

Solution:

To find the sum of the interior angle:

Here

Sum of the interior angle of Hexagon = (n-2) 180 degrees

Here n = 6 sides

= (6-2) 180

= (4) 180

Sum of the interior angle of Hexagon =720 degrees.

To find the each interior angle:

Here

Interior angle of the regular Hexagon =` (((n-2) 180)/n)`

= (((6-2)180)/5)

= (720/6)

Interior angle of the regular Hexagon = 120 degrees.

2. Find sixth interior angle of the Geometry Hexagon when first five angles are 108, 110, 106, 102, 104 degrees respectively?

Solution:

We know that sum of the interior angle of the Hexagon = 720 degrees

That is (angle 1+angle2+angle 3+angle 4+angle 5 +angle 6) = 720

(108+110+106+102+104+x) = 720

(530+x) = 720

x = 720-530

Sixth interior angle of the Hexagon x = 190 degrees

3. Find first interior angle of the Geometry Hexagon when last five angles are 108, 110, 108, 106, 104 degrees respectively?

Solution:

We know that sum of the interior angle of the Hexagon = 720 degrees

That is (angle 1+angle2+angle 3+angle 4+angle 5 +angle 6) = 720

(x+108+110+108+106+104) = 720

(x+536) = 720

x = 720-536

Sixth interior angle of the Hexagon x = 184 degrees

Fractionation Method

Introduction Fraction Method:

A fraction is a value that shows the number of equal parts taken of a whole quantity or unit. The denominator of a fraction is the number that shows how many equal parts are in the whole quantity. The numerator of a fraction is the number that shows how many equal parts of the, whose are taken.

The numerator and denominator are called the term of the fraction,

3 -(Numerator)
-------------------------
4-(Denominator)

A improper fraction is a fraction in which the numerator is larger than equal to the denominator, as in 3 / 2, 5 / 4, 11 / 8. A mixed number is a number composed of a whole number and a fraction, as examples 3 7/8, 7 1/2

A complex fraction is a fraction in which one or both of the terms are fraction or mixed number, as in example ¾ / 6.

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Fraction methods - Addition and Subtraction:


Steps for fraction method - addition:

To add algebraic fraction, follow these steps:

Write the given fraction and common denominator.
Added the numerators value.
Solution for the problem
Example:

`= (1 / 2) + (5 / 2)`

`= (1 + 5) / 2`

`= 6 / 2`

= 3

Steps for fraction method - subtraction:

To subtraction algebraic fraction, follow these steps:

Write the given fraction and common denominator.
Subtracted the numerators value.
Solution for the problem
Example:

` = (7 / 3) - (4 / 3)`

` = (7 - 3) / 3`

= `4 / 3`

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Fraction methods – Multiplication and Division:


Steps for fraction method - multiplication:

To multiply algebraic fraction, follow these steps:

Write the given fraction and cancel any common factors.
Multiply the numerators.
Multiply the denominators.

Example:

= `(3 / 7)xx (4 / 5)`

= `(3xx 4) / (7 xx5)`

= ` 12 / 35`

Steps for fraction method division:

To divide algebraic fraction, follow these steps:

Write the given fractions.
Change the division sign to a multiplication sign and invert the second fraction.
Write the given fraction and cancel any common factors.
Multiply the numerators.
Multiply the denominators.
Example:

= `( 1 / 6) / (3 / 4)` (divisor)

= `(1 /6)xx (4 / 3)`

=` (4 xx1) / (6xx 3)`

= `4 / 18`

= `2 / 9`

Solve One-to-one Function

Solve One-to-One Function

One-to-one function is a function, in which every element of the range of the function is corresponds to exactly one element of the domain of the function. One-to-one function is often written as 1–1 function.

Example:

Function: y = f(x) is a function, if it passes only the vertical line test.

One-to-function: y = f(x) is a one-to-one function, if it passes both the horizontal line test and the vertical line test.


Solve One-to-One Function – Example Problems


See these solved problems on one-to-one function.

Example 1: Show that the function f(x) = 4(x - 6)3 + 9 is one-to-one function.

Solution:

Let (x) = f(y)

4(x - 6)2 + 9 = 4(y - 6)3 + 9

Add -9 to both sides

4(x - 6)3 + 9 - 9 = 4(y - 6)3 + 9 - 9

4(x - 6)3 = 4(y - 6)3

Divide both sides by 4

(x - 6)3 = (y - 6)3

The above equation leads to two other equations

(x - 6) = (y - 6)

x = y

Therefore given function f(x) = 4(x - 6)2 + 9 is one-to-one function.

Example 2: Show that the rational function f(x) = `10 / (12x + 15)` is one-to-one function.

Solution:

Let f(x) = f(y)

`10 / (12x + 15)` = `10 / (12y + 15)`

Multiply both sides (12x + 15)(12y + 15) and simplify

12y + 15 = 12x + 15

Add -15 to both sides

12y = 12x

Divide both sides by 12

y = x

Therefore the given function f(x) = `10 / (12x + 15)` is one-to-one function.

Example 3: Show that the function f(x) = 15x + 18, is one-to-one function.

Solution:

Let f(x) = f(y) and show that this leads to x = y

15x + 18 = 15y + 18

Add -18 to both sides

15x = 15y

Divide both sides by 15

x = y

Therefore the given function f(x) = 15x + 18 is one-to-one.

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Solve One-to-One Function – Practice Problems


Solve these following practice problems

Problem 1: Show that the rational function f(x) = `7 / (11x + 6) ` is one-to-one function.

Problem 2: Show that the function f(x) = 5(x - 11)3 + 21 is one-to-one function.

Problem 3: Show that function f(x) = 19x + 4 is one-to-one function.

Exterior Angle Solve Online

Introduction - Exterior angle solve online:

In this article, we shall discuss about Exterior angle solve online. Online helps students to share their views as well as gather notes regarding their subject. In geometry, shapes play an important part. There are various kinds of shapes. Any plane figure which is formed at the vertex where two lines intersect are called angles. The angles formed at the outer part of each vertex are called as exterior angles. There are two methods to find the exterior angles.

Method 1:

Exterior angle = `360/n` ,

where n is the number of sides of the polygon.

Method 2:

Exterior angle = 180 - interior angle.

Now we shall solve some example problems regarding exterior angle solve online.


Example Problems - exterior angle solve online:


Example 1:

Solve for the exterior angle of a polygon whose interior angle is 108°. Also determine the number of sides of the polygon.

Solution:

Given, The interior angle of a polygon is 108°.

When the interior angle is given, the exterior angle of a polygon can be calculated by using the formula,

Exterior angle = 180 - Interior angle

Exterior angle = 180 - 108°

= 72°

The exterior angle of the polygon is 72°.

Now the number of sides of the polygon can be determined by using the formula,

Exterior angle = `360/n`

where n is the number of sides of the polygon.

We know that the exterior angle of the given polygon is 72°

72 = `360 / n`

Multiply by n on both sides,

`72 n = n[360/n]`

`72 n = 360`

Divide by 72 on both sides

`(72n) / 72 = 360/72`

`n = 5`

Therefore the number of sides of the polygon is 5.

Since n = 5, the name of the polygon is pentagon.

Example 2:

Solve for the exterior angle of a polygon whose number of sides is 8.

Solution:

When the number of sides of the polygon is given, the exterior angle can be calculated by using the formula,

Exterior angle = `360/n`

where n is the number of sides of the polygon.

By substituting n = 8 in the formula, we can obtain the exterior angle of the polygon.

Exterior angle = `360/8`

= 45°

Since n = 8, the name of the polygon is octagon.

Hence the exterior angle of octagon is 45°.

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Practice Problems - exterior angle solve online:


Problem 1:

Solve for the exterior angle of a polygon whose interior angle is 120°. Also determine the number of sides of the polygon.

Answer:

Exterior angle = 60°

Number of sides = 6

Problem 2:

Solve for the exterior angle of a polygon whose number of sides is 10.

Answer:

Exterior angle = 36°.

Third Grade Student

Introduction to Third grade student:

In this article we are going to discuss about third grade student math solving problems. Third grade student math solving problems are easy to understand and solve. The following topics are studied in the grade third.

Addition
Subtraction
Multiplication
Division
Place value
Third grade student math solving sheets examples and practice problems with solutions are given below.


Third grade student – Example problems:


Example 1:

Add the five digit numbers given 55649 + 21453

Solution:

5 5 6 4 9

2 1 4 5 3 +

-----------------

7 7 1 0 2

-----------------

The addition solution is 77102

Example 2:

Perform the subtraction of the given five digit number 81928 – 47256

Solution:

8 1 9 2 8

4 7 2 5 6 –

-------------

3 4 6 7 2

-------------

The subtracting solution is 34672

Example 3:

Add the given decimal digits given 45.35 + 21.32

Solution:

4 5.3 5

2 1.3 2 +

------------

6 6.6 7

------------

The adding decimal solution is 66.67

Example 4:

Subtract the decimal values given 78.98 – 52.65

Solution

7 8.9 8

5 2.6 5 –

---------------

2 6.3 3

----------------

The subtracting decimal solution is 26.33

Example 5:

Multiply 7.8 x 3.2

Solution:

7.8

3.2 x

-------

156

234   +

-------------

2 4.9 6

--------------

The multiplication solution is 24.96

Example 6:

Decimal multiplication: 0.07 by 1.2

Solution:

Primarily we start with 0.07 * 1.2

Multiplying without decimal points, we get 7 * 12 = 84

We place decimal places:

0.07 has the two decimal places

1.2 has one decimal place

Final answer has three decimal points are 0.084

The decimal multiplication solution is: 0.084


Third grade student – practice problems:


Problem 1: Add the given decimal digits given 75.32 + 31.58

Problem 2: Multiply 9.8 x 4.2

Problem 3: Perform the subtraction 45624 – 21983

Problem 4: Add 87123 + 12456

Problem 5: Subtract 97. 86 – 31.24

Problem 6: Decimal multiplication 0.08 * 10

Third grade student – answer key:

Problem 1: 106.90

Problem 2: 41.16

Problem 3: 23641

Problem 4: 99579

Problem 5: 66.62

Problem 6: 0.008

Solve Math Student Solutions

Introduction to solve math student solutions:

Mathematics is a vast area.Some of the main branches of mathematics are algebra, geometry, trigonometry and calculus. There are  number of math problems available under these branches for the students. In this article solve math student solutions, we are going to solve for some basic math solutions which are useful for the students. In addition, some practice problems are given to solve.

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Solved examples for math solutions:


Example 1:

Andrew bought a camera for `$` 100 and he sold it for `$` 110. Find the gain amount.

Solution:

cost price of camera  =  $ 100

selling price of camera  =  $ 110

Gain   =  selling price - cost price

=  110 - 100

=  $ 10

Example 2:

Find  the area of circle if the radius is 79 cm.

Solution:

Area of circle  =  `pi` r^2

=  3.14 (79)2

=  3.14 * 6241

=  19596.74 cm^2



Example 3:

Spears bought an ornament that costs `$` 1000. If the sales tax rate is 10%. What is the total amount she must pay for the ornament?

Solution:

Sales tax  =  10% of the price tax

=  10%  x  1000

=  0.10 x  1000

=  100

Final price  =  price before the tax + sales tax

=  1000+ 100

=  $ 1100

Example 4:

A basket contains 750 eggs. 680 were not broken. What percentage of the eggs were broken?

Solution:

Total number of eggs          =  750

Number of eggs not broken =  680

Number of eggs broken     =  750 - 680

= 70

Percentage of eggs broken   =  `<< 70/750>>`  x 100

=  `<< 7/75>>` x 100

=  9.3

Example 5:

Find the area and perimeter of rectangle, if the length is 35 m and breadth is 15 m.

Solution:

Area of rectangle  =  l * b

=  35 * 15

=  525 m^2

Perimeter of  rectangle  =  2 ( l + b )

=  2 ( 35 + 15 )

=  2 ( 50 )

=  100 m


Practice problems to solve:

1) Sarah bought a ring for `$` 1800 and she sold it for `$` 1880. Find the gain amount.

Answer: Gain =  `$` 80

2) Find  the area of circle if the radius is 16 cm.

Answer: Area =  803.84 cm^2

3) Mercy bought an ornament that costs `$` 1700. If the sales tax rate is 9%. What is the total amount she must pay for the ornament?

Answer: Amount = `$` 1853

4) A basket contains 200 eggs. 180 were not broken. What percentage of the eggs were broken?

Answer: Percentage = 10

5) Find the area and perimeter of rectangle, if the length is 28 m and breadth is 7 m.

Answer: Area = 196 m^2   Perimeter = 70 m

Student Teaching Requirements

Introduction to student teaching requirements:

Here given the student teaching requirements is the basic teaching requirements needed to students to practice as a teacher. Student teaching requirements are to make the students understand the concepts and help the students to learn in every concepts. Here for student teaching requirements we let us see problems solved by teachers for the given article student teaching requirements.


Student teaching requirements:


Basic algebra problems:

Example 1 :
What is the sum of 7 and 8? Express this statement by using place holder.
Solution :

We can write this statement, in short, as
7 + 8 = ?.

The answer for this problem would be 7 + 8 = 15.

Example 2 :
What number added to 10 will give 15?
Solution :
It is 10 + x = 15

Example 3 :
Rabi has 18 rupees. She buys vegetables for 8 rupees. Find the remaining amount she will have in her hands.
Solution :
We can write it as 18 – 8 = ?

The answer for this problem would be 18 - 8 = 10.

Example 4 :
Find the product of 5 and 12
Solution :
5 × 12 =?

The answer for this problem would be 5 × 12 = 60.

Example 5 :
When a number is multiplied by 4, the product is 116
Solution :
x × 4 = 116.

x = `116 / 4` = 29.


Student teaching requirements:


Example 6:
What is the sum of 9 and 10? Express this statement by using place holder.
Solution:

We can write this statement, in short, as
9 + 10 = ?.

The answer for this problem would be 9 + 10 = 19.

Example 7:
What number added to 12 will give 17?
Solution:
It is 12 + x = 17
The answer would be x = 17 - 12 = 5.

Example 8:
Rabi has 28 rupees. She buys vegetables for 12 rupees. Find the remaining amount she will have in her hands.
Solution:
We can write it as 28 – 12 = ?

The answer for this problem would be 28 - 12 = 16.

Example 9:
Find the product of 6 and 12
Solution:
6 × 12 =?

The answer for this problem would be 6 × 12 = 72.

Example 10:
When a number is multiplied by 4, the product is 84
Solution:
x × 4 = 84.

x = `84 / 4` = 21.

Student Learning Variables

Introduction to student learning variables:

A variable is some alphabet or combination of alphabet that has the stable value. For example, the weight of  the tables is variable. In arithmetics, one alphabet variables can be represented as a, b, c, and t. Variables with related position are state with following alphabets. The areas of triangle can be state as x, y, z. In this article, we are going to see about students learning variables.


Types of Variables in student learning variables:

Let us see about student learning variables,

There are several types of variables, to student to learn about variables.

Quantitative
Qualitative
Independent variables
Dependent variables

Explanation about student learning variables


Let us see about student learning variables,

Learning Quantitative:

Variables are important because they let quantitative interaction to be declared in a common way.
If we be required to use real values, then the relations would only affect in a more narrow set of situation.
For case:

Height, weight, age, and marks on an exam.

Learning Qualitative:

The qualitative variables do not contain the ordinary sense of ordering. It can be implicit to show numeric but their information are meaningless, as in true=1, false=2.
For Case:

Qualitative variables are hair color, religion, favorite movie, and so on.

The principles of a qualitative variable do not mean a numerical ordering.
Values of the variable "religion" vary qualitatively; no order of religions is indirect.
Qualitative variables are sometimes referred to as definite variables.
Values on qualitative variables do not mean order, they are simply category.
Learning Independent variables:

It is a variable in an expression, whose values create up the field.
In extra words, an independent variable in an expression may have its value generously select anyway the values of some other variable.
For Case:

In the equation x = 17y + 9, the independent variable is y. The variable y is not independent, for the reason that it depends on the value selected for y.

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Learning Dependent variables:

Variable whose value depends on the importance of one or more independent variables.
For Case:

In a = 19b, a is the dependent variable, as its value depends on the value of b.
In R = 9P2 – 7Q3, R is the dependent variable.

Free Fractions Study Guide

Free Fractions Study Guide:

These articles we are discussing about free fractions study guide solving problems. A fraction 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 (1/2, 5/8, 3/4 etc.) and which consist of a numerator and a denominator. (Source – Wikipedia)

Free fractions study guide problems solve for simple addition fraction, multiplication fraction, subtraction fraction and dividing fraction.


Free fractions study guide-Example problems:


Example 1:

Add the fractions `8/20` + `7/20`

Solution:

The given two fractions are `8/20 ` + `7/20`

Here both the fractions have equal denominators, so take the common denominator, here 20

= `8/20` + `7/20`

Add the numerators directly = 8+7 = 15.

= `15/20`

The addition fraction solution is `3/4` .

Example 2:

Subtract the fractions `4/5 ` – `3/4`

Solution:

The denominator is different so we have to take least common denominator (lcd).

LCD = 5 x 4 = 20

`(4 xx 4)/ (5 xx 4)` = `16/20` and `(3 xx 5)/ (4 xx 5)` =` 15/20`

`16/20` – `15/20`

The denominators are equals

So subtracting the numerator directly = `(16-15)/20`

Simplify the above equation we get =` 1/20`

Therefore the final answer is `1/20`

Example 3:

Multiply the fractions` 2/3` x `6/3`

Solution:

The given two fractions are `2/3` x `6/3`

Multiply the numerators; we get 2 x 6 = 12

Multiply the denominators; we get 3 x 3 = 9

= `12/9`

The multiply fraction solution is `4/3`

Example 4:

Dividing fraction:

`4/2` divides `2/4`

Solution:

First we have to take the reciprocal of the 2nd number, and then multiply with the second one

Reciprocal of `2/4` = `4/2`

`4/2` x `4/2`

Multiply the numerator and denominator

`(4 xx 4)/ (2 xx 2)`

Simplify the above equation we get

= `16/4`

Therefore the final answer is 4

Having problem with Fractions Calculator keep reading my upcoming posts, i will try to help you.

Free fractions study guide-practice problems:

Problem 1: Add the two fraction `6/15` +` 4/15`

Solution: `2/3`

Problem 2: Subtract two fractions `5/5` –` 2/5`

Solution: `3/5`

Problem 3: multiply two fractions` 3/4` x` 3/4`

Solution: `9/16`

Problem 4: Dividing two fractions` 3/2` and `4/2`

Solution:` 3/4`

Distance Measuring Devices

Introduction to distance measuring devices:Distance means that,  the length of two end points or distance between two objects. Distance measuring devices in a one of the instrument of finding length or distance. More devices are available to find the distance. Not only devices having standard formulas for finding the distance.


Concept for distance measuring devices:


Distance measuring devices:

Rulers (longer ruler, Shorter ruler)
Tapes
Distance formula
We have two standard formulas for finding the distance.

(1)   Finding the distance from two points

(2)   Finding distance from speed and Time

Finding the distance from two points:

Two points are (x1, y1) and (x 2, y2)

Distance, d = √ (x2-x1) + (y2-y1)

Finding distance from speed and Time:

If we have to know the speed and time, calculate the distance using formula

Distance, d = Speed * Time

Basic concepts of distance measuring devices:

Units for distance:

Millimeter.
Meter.
Centimeter.
Kilometer.
These all are measuring length of the distance.

I have recently faced lot of problem while learning Measure Circumference, But thank to online resources of math which helped me to learn myself easily on net.

Structure for distance measuring devices:


Ruler:


Ruler is a one of the distance measuring instrument used engineering sides, building construction sides, carpentry sides. More type of rulers is available .Desk ruler, shorter ruler, longer ruler. Desk ruler was mainly used for carpentry applications. Shorter and longer ruler is used to measuring the textiles fields, Student study for geometrical application.

Each and every Length of distance represented by the units. It may be meter, centimeter, kilometer. Each individual unit’s ruler are having for finding the distance. We can easily convert the units of distance from centimeter to meter, meter to kilometer.

Finding the distance between two objects using ruler:

1. In first we positioned the ruler on starting point of the object.

2. After then mark the ending point of the object and starting point of object.

3. Then measure the continues length of distance.

Tape:

Tape is a one of the distance measuring device, It should not having the straight edge instrument but ruler have the straight-line edge instrument.Tapes are mainly used for finding the length of fields ,clothes, walls .

How To Use Fractions in Math

Introduction for How to use Fractions in Math:
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.


How to use Fractions in Math -Type 1:

We can use the fractions in math by the following types.

Math -Example 1:

Addition of two fractions: `1/12+1/12` .

Solution:

Step 1:

From the given fractions the denominators are same.

Step 2:

Adding the numerators and use the same denominators.

= `1/12+1/12`

= `(1+1)/12`

Step 3:

By simplifying the fractions

= `2/12`

= `1/6` is the solution for them.

Math-Example 2:

Subtraction of two fractions: `5/24-10/13` .

Solution:

Step 1:

The LCD for the denominators 24, 13 is 312.

Step 2:

Multiplying and subtracting the numerators and use the same denominators.

= `(13*5)/312-(24*10)/312`

= `(65-240)/312`

Step 3:

By simplifying the fractions

=` -175/312` is the solution for them.

Math-Example 3:

Simplify the two fractions: `(23x)/13-(29x)/18` .

Solution:

Step 1:

LCD for the denominators 13 and 18 is 234.

=` (18*23x)/234-(13*29x)/234`

= `(414x)/234-(377x)/234`

Step 2:

Simplify the numerators.

= `(414x-377x)/234`

Step 3:

Subtract the numerators.

= `(37x)/234` is the solution.

I have recently faced lot of problem while learning Equivalent Fractions Definition, But thank to online resources of math which helped me to learn myself easily on net.

How to use Fractions in Math - Type 2:


Example 1:

Compare two fractions which are smaller: `11/9` or `23/17` ?

Solution:

Step 1:

LCD for the given denominators 9, 17 is 153.

Step 2:

Multiply the fractions as `(17*11)/153` and `(9*23)/153` .
Step 3:

The solutions for them as

`187/153` and` 207/153`

When comparing two fractions `11/9` is smaller.

Example 2:

Compare two fractions which are greater: `26/12` or `32/15` ?

Solution:

Step 1:

We can convert the given fractions in to decimal form.

Step 2:

Divide the fractions as (26÷12) and (32÷15).

Step 3:

Now we get the solutions for the given fractions.

`26/12` = 2.166 and `32/15` = 2.133

When comparing two fractions `26/12` is greater.

Verbal Expressions in Math

Introduction to verbal expression in math:

In math, An algebraic expression is an expression containing symbols, variables and constants together. In math, Verbal expression is a sentence forming from an algebraic expression. Some of the verbal phrases for arithmetic operation is given below. Using these, we can frame the verbal expression for given an algebraic expression.

Let us see brief about verbal expression in math.


Verbal expression in math:


The verbal expression for an algebraic expression a + b may write as following,

a plus b , a added to b, a is increased by b, the sum of a and b, b is added to a, b more than a.

The verbal expression for an algebraic expression a - b may write as following,

a minus b , a is decreased by b,  b subtracted from a, b less than a, a diminished by b, a reduced by b, the difference between a and b.

The verbal expression for an algebraic expression a x b may write as following,

a times b , the product of a and b, b is multiplied by a.

The verbal expression for an algebraic expression a ÷ b may write as following,

The quotient of a and b, a is divided by b.

Let us learn about how to translate algebraic expression into verbal expression.

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Example Problems of verbal expression in math:


Problem 1:

Translate this algebraic expression into verbal expression: 3 + b

Solution:

We can write it as,

b more than 3, 3 plus b, 3 added to b, b is increased by 3.

Problem 2:

Translate this algebraic expression into verbal expression: 3 - b

Solution:

We can write it as,

b less than 3, 3 minus b, b subtracted  from 3, b is decreased by 3.

Problem 3:

Translate this algebraic expression into verbal expression: 10ab

Solution:

We can write it as,

The product of 10a and b, 10 times a times b, 10a is multiplied by b.

Problem 4:

Translate this algebraic expression into verbal expression: 3x – 5 .

Solution:

We can write it as,

Thrice x, decreased by 5,

The difference between 4x and 5.

Problem 5:

Translate this algebraic expression into verbal expression: 5n3

Solution:

We can write it as,

The product of 5 and n to the third power.

Problem 6:

Translate this algebraic expression into verbal expression: b^2 + 30c

Solution:

We can write it as,

The sum of b squared and 30 times c.

Problem 7:

Translate this algebraic expression into verbal expression: `1/2` b^2

Solution:

We can write it as,

b to the power 3 divided by 2.

Extra Math Problems Geometry

Introduction to extra math problems geometry:

Extra math problems geometry means that we have to solve some extra geometry problems to students. Geometry is a one of the fundamental concepts of mathematics .geometry having the concept of of shapes and structures of two dimensional and three dimensional like square rectangle, circle, triangle, cone ,cylinder, cube .In this article extra math problems geometry, we see about some geometry problems with answers.


Extra Example math problems in geometry:


Rectangle  Example math problems in geometry:

Example 1:

A rectangle garden is 11.8cm and 13.8cm dimensions find the area of the rectangle?

Solution:

Given data: Dimensions of data

Length =11.8cm

Width=13.8cm

Area of the rectangle= Length * Width

Area of the rectangle= 11.8* 13.8

=162.84cm^2

Square Example math problems in geometry:

Example 2:

Find area and perimeter of the is the square its side length is 19.3m?

Solution:

Given data: Side length of the side=19.3m

Area of the square= side* side (a2)

Area= 19.3*19.3

Area=372.49m2

Perimeter of the square= 4*side

=4* 19.3

=77.2m

Example: 3

Find the perimeter of the triangle which side length is 21cm,13.5cm,16.7cm?

Solution:

Given data: three side length of the triangle

A=21cm

B=13.5cm

C=16.7cm

Perimeter of the triangle= (sum of three sides)(A+B+C)

Perimeter of the triangle=21+13.5+16.7

Perimeter=51.2cm

Example 4:

Find the volume of the sphere its radius is 16.7m?

Solution:

Given data :

Radius of the sphere=16.7m

Volume of the sphere=4/3*p*r3

Substitute pi= 3.14 and r=16.7m

Volume of the sphere= 4/3*3.14*16.73

Volume=19450.49m3

Having problem with math problems 3rd grade keep reading my upcoming posts, i will try to help you.

Extra Example math problems in geometry:


Cone ,cylinder, triangle extra Example math problems in geometry:

Example 5:

Find the area of the of the triangle Which base length is 14.6cm and height is 16cm?

Solution:

Given data: base length is 14.6cm

Height is  16cm

Area of the triangle=1/2*Base*Height

Area of the triangle=1/2*(14.6)*(16)

Area= 116.8cm^2

Example 6:

Find volume of the cone its radius is 5.8 and height of the cone is 9.7?

Solution:

Given data radius of the cone=5.8

Height of the cone=9.7

Volume of the cone=1/3*p*r2*h

Substitute p=3.14,r=5.8,h=9.7

Volume of the cone=1/3*3.14*5.8*5.8*9.7

Volume of the cone=341.5

Example 7:

Given that length of base = 4.6 cm, height  = 6.7 cm Find the area of parallelogram?

Solution:

Area of the parallelogram = b × h

= 4.6 cm × 6.7 cm

= 30.82 cm^2

Example 8:

Diameter of the base of a right circular cylinder is 13 cm. If its height is 17.5 cm, find its volume.?

Solution:

Since the diameter of the base is 13 cm, its radius r = 6.5cm. Also, h = 17.5cm,

Volume of a right circular cylinder:

V = (Area of the base) × (Height) = *R*R*H

=3.14*6.5*6.5*17.5

= 2321 cm^3

Site to Solve Math Equations

Introduction to site to solve math equations:

Tutor vista website is one of the online tutoring services providers; Tutorvista website provides helps in various subjects like English, math, and science. Tutorvista website tutors help regardless of place where they are located.  Student can learn and get homework from their home at any time. Tutors explain step by step so that the students can easily understand. In this article we shall discuss to solve the math equations with example problems and practice problem. Please express your views of this topic Equation of Parabola by commenting on blog.


Site to solve the math equations example problem


Example:

Total number of students in a class is 70. if the number of boys is 37, frame the equations and find the number of girls.

Solution:

Consider the number of girls be x.

The number of boys is 37.

The total number of student is 70.

Therefore simple equation is x+37=70

x =70-37

x = 33 girls in a class.

Example:

Solve the equations 5x-6=3x+2

Solution:

5x-6=3x+2

5x=3x+2+6

5x-3x=8

2x=8

x=`8/2`

Therefore x=4

Example:

Solve the equations for x.

3(4x - 2) + 3x = 3(5x + 1)

Solution:

Multiply the factor value 3 with (4x-2) and 3 with (5x + 1)

12x - 6 + 3x = 15x + 3

Both side subtract 3x on the equation

12x - 6 +3x-3x = 15x -3x + 3

12x - 6 = 15x + 3

Both side subtract 15x on the equation

12x-15x-6 = 15x-15x+3

-3x-6 = 3

-3x = 3+6

-3x = 9

Solve the x value

x =`9/-3`

x = -3

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Site to solve the math equations practice problem

Problem:

Total number of students in a class is 60. if the number of boys is 35, frame the equation and find the number of girls.

Answer:

The number of girls 25

Problem:

Solve the equation 2x-3=15

Answer:

x=9

Problem:

Solve the equation for x.

3(3x - 1) + 2x = 2(6x + 2)

Answer:

Therefore x = -7

What is Probability for Math

Introduction to what is probability for math:

Probability math is the way of expressing an event that will occur. The probability for math is the event, the experiments that are repeatedly done under some conditions. The results of the experiments are not the same for all the events. These experiments are called as the random experiments or simply experiments. The probability contains trial, sample space, event.


Terms used in the probability for math:


Sample space stands for the number of possibilities in an experiment.
Trial stands for the experiment is performed.
Event stands for the outcome of the experiments.
Exhaustive events are an event which contains all the possible outcomes of the experiment.
Mutually exclusive events are the two events that cannot occur simultaneously.

Formula used in probability for math:


If s be the total number of cases and n be the number of favorable cases means the required probability for a event A is  P(A) =`n/s` .
The probability for the impossible event is zero.
For any event A the probability of the event is between 0 and 1.
P(AUB)=P(A)+P(B)-P(An B)
P(B/A)= P(An B)/ P(A)    where P(A)? 0
P(A/B)= P(An B)/ P(B)   where P(B)? 0

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Example problems for probability for math:


Example 1 for probability for math:

An urn has 4 white and 2 red balls. Find the probability of the number of red balls when three draws one by one from the urn without replacement.

Solution:

The total number of balls= 4 w+ 2r =6 balls

1) P( no red ball) = 8 C3 / 6 C3= `14/5`

2)  P( 1 red ball ) =8C2 x 2C1/6 C3 =`28/ 5`

3) P( 2 red balls) = 2C2  x 8C1 / 6C3=`2/ 5`

Example 2 for probability for math:

In tossing a fair die, what is the probability of the numbers greater than 2?

Solution:

The sample space for the die is S= {1, 2, 3, 4, 5, 6}

The total number of sample space =6.

A is the event for getting the number greater than 2.

A= {3, 4, 5, 6}

The number of events greater than 2 n (A) =4

The required probability is P (A) =n (A)/ n(S)

The required probability is P (A) = `4/6`

The required probability is P (A) =` 2/3`

The probability for getting the numbers greater than 2 is `2/3` .

Associative Property of Math

Introduction of associative Property of Math:

Associative is a property of some binary operations. It means that, within an expression containing two or more occurrences in a row of the same associative operator, That is, rearranging the parentheses in such an expression will not change its value. Consider for instance the equation.

(Source: Wikipedia)

Addition associative Property:

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

Multiplication associative Property:

(a x b) x c = a x (b x c)


Example problems for Associative Property of Mathematics:


Associative Property in math Example 1:

Find the values of given expression using associative property. 16 + (5 + 8)

Solution:

Step 1:

16 + (5 + 8)

Formula :

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

Step 2:

(16+5)+ 8 = 16 +(5+8)

21+8 = 16+13

29 = 29

Associative Property in math Example 2:

Find the values of given expression using associative property. 6 x (5 x 3)

Solution:

Step1:

The property in which altering the alignment of factors does not change the product is called associative property of multiplication.

Formula:

(a x b) x c = a x (b x c)

Step 2:

6 × (5 × 3) can be written as (6 × 5) × 3.

Step 3:

6 × (5 × 3) = (6 × 5) × 3 show the property of associative multiply

6 x 15 = 30 x 3

90     =   90

Associative Property in math Example 3:

Find the values of given expression 6 x (6 x 7) are associative or not.

Step 1:

Explanation:

Formula:

a x (b x c)
Step 2:

Using the multiplication property formula

6 x (6 x 7) = (6 x 6) x 7

6 x 42 = 36 x 7

252 =252

Associative Property in math Example 4:

Find the values of given expression using associative property. 6 x (3 x 15)

Solution:

Step1:

The property in which altering the alignment of factors does not change the product is called associative property of multiplication.

Formula:

(a x b) x c = a x (b x c)

Step 2:

6 × (3 × 15) can be written as (6 × 3) × 15.

Step 3:

6 × (3 × 15) = (6 × 3) × 15 show the property of associative multiply

6 x 45 = 18 x 15

270  =  270

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Practice Problems for associative Property of mathematics :-


1. Find the values of given expression using associative property 18 x (35 x 52)

Answer:

32760

2. Find the values of given expression using associative property. 61 + (56 + 64)

Answer:

181

Home Work Help Thats Math

Introduction to home work help thats math:

Home work help thats math is the homework given in mathematics to work out in home as a practice. Homework problem on mathematics helps to sharpen the brain by solving more steps and more problems. Home work help thats math relating the life. Home work must be in all chapters of math so that it can help the students to know more about the help of math. Below are some of the home work help thats math.

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Home work help thats math problems


1. The cost of a sweet pizza is $15.20.Find the cost of 7 sweet pizza?

Solution:

The cost of 1 sweet pizza= $15.20

The cost of 7 sweet pizza = 15.20 * 7

= 1 5.2 0

7*

10 6 .4 0

The cost of 7 sweet pizza $106.40

2. The monthly salary of Reena is $420. She spends 70% of her salary every month. How

much does Reena save every month?

Reena’s monthly salary = $ 420

Expenditure = 70% of 420

=70 /100 × 420 = $ 294

∴ Savings = 420 – 294 = $126.

Another method of solving this problem is

Expenditure = 70% of 420

∴ Savings = 30% of 420

= 30/100×420 = $126.

3. A car with marked price $1200 was sold to a customer for

$1140. Find the rate of discount allowed on the car.

Solution:

Marked price of the car = $1200

Selling price of the car = $1140

Discount = $1200 – $1140 = $60

Rate of discount = discount/markedprice * 100

= 60/1200 *100

= 5%

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Home work help thats math practice problems


1. The monthly salary of Tony is $800. He spends 80% of his salary every month. How

much does Tony save every month?

Answer: $160

2. A house with marked price $6000 was sold to a customer for

$5400. Find the rate of discount allowed on the house.

Answer:10%

What is Identity in Math

Introduction to identity in math:

Tautologically true is used in an identity of a relation. Usually to identity the tautologically definition is true, each definition is directly, or as a consequence of it. For case, algebraically, it create the expression is satisfied for every values of the occupied variables. Let us see about articles of identity in math.

I like to share this Inverse of Identity Matrix with you all through my article.

Definition of identity in math


Triple bar symbol is denoting the definitions. Such as x2 ≡ x·x. The symbol ≡ is used in other method for different meanings, but definition is used to interpret in many ways. In other ways tautologically definition is true.

In algebra, binary operation with a set of S is a identity or identity element to e element, when connecting with every element x of S, that same as produces x. Therefore, e.x = x.e = x for all in S. This is a correct illustration of identity matrix.

A set of element of S itself to the identity function, it denoting by id or ids, in identity function every maps element together. In other texts, id(x) = x for all x in S. Identity function  give out process of identity element in the set of each functions from set of S to  itself with correct value to function composition.

Understanding Exponential Growth and Decay is always challenging for me but thanks to all math help websites to help me out.

Examples for identity in math


Identity relation in math:

A general illustration of the initial meaning is the trigonometric identity

Sin2θ + cos2 θ = 1

This identity of the complex values of θ is true (here the complex digit of C are the element of sin and cos), as different to

Cos θ = 1,

True value for only for several θ, not for all values. For case, when the last equation of the value θ = 0, then false when θ = 2.

Identity element in math:

Additive identity and multiplicative identity is the concepts of the middle to the Peanoaxioms. The integers, real numbers and complex digits of the number 0 are additive identity. For all the real integers, for all a Є R,

0 + a = a,

a + 0 = a, and

0 + 0 = 0.

Alike, the multiplicative identity is the number of 1 for integers, real numbers and complex numbers. For the real numbers, for all a Є R,

1 * a = a,

a * 1 = a, and

1 * 1 = 1.

What are Edges in Math

Introduction to edges in math:

In math, what are edges?. The edges are created when two surfaces of objects are intersected. The two-dimensional and three-dimensional objects have one or more edges. We can also refer the edges as boundary of objects or sides of shape. For example the cube shape contains 12 edges by surface intersection.


Explanation for edges in math


Edges in math:

Edges are considered as connector that is connect the one-dimensional line segment and two zero dimensional objects in math. The edges form the closed figure as polygon.

What are lateral edges?

The solid’s lateral faces are created by edges is called as lateral edges. For example consider the pentagonal prism. It has five lateral faces and these faces are connected by five lateral edges.

What are vertices?

The vertices are created by intersection of two edges and it is also called as corner of the shape. For example if the object has six edges means the number of vertices are six. The edges of shape are used for identify the name of shape.

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

More about edges in math

Examples for edges in math:

What are edges in square and rectangle?

The square and rectangle are considered as quadrilateral. The square has equal length for each sides. The number of sides in square and rectangle is four and these sides are intersect and creates a four edges.

Edges in triangle:

The equilateral triangle has three sides. These three sides are intersected and create a the three edges.

Edges in pentagon:

The five sided polygon is called as pentagon and these sides are connected as edges. So the pentagon has five edges.

Edges in hexagon:

The hexagon is regular polygon and it has six edges and six vertices.

We can find the area and volume of shape by using edges with respect to formula and also find the angles of each vertex is estimated.

Help in Math Now

Introduction to help in math now:

Online Tutoring is one of the best way for getting help in various subjects. Tutor Vista is the best choice for getting help not only in math but also in English and Science.

In this article of help in math now, several problems related to various branches of mathematics are given with their respective answer. In addition, several practice problems are given with answer key which helps for better understanding.


Get help in math now through examples:


Example 1:

Find the Mean of the given data set: { 8, 9, 21, 12 }

Solution:

Mean   =  ( 8 + 9 + 21 + 12 ) / 4

=  50 / 4

= 12.5

Answer: Mean  = 12.5

Example 2:

Find the volume of cylinder given the radius is 23 cm and 42 cm.

Solution:

Volume of cylinder = `pi` r2 h cubic units.

= (3.14) * 232 * 42

=  3.14 * 529 * 42

=  69764.52 cm3

Answer: Volume of cylinder = 69764.52 cm3

Example 3:

Find the area of the square with the side length of 12 cm.

Solution:

Area of square  =  ( a ) 2

= ( 9 )2

= 12 * 12

= 144 cm^2

Answer: Area of square =  144 cm^2

Example 4:

Find the area of a triangle through base of 4 m and a height of 2 m.

Solution:

Area of a triangle = ½ b h

= ½ ( 4 ) ( 2 )

= 0.5 * 4 * 2

= 4 m2

Answer: Area of triangle = 4 m2

Example 5:

Solve :  3 ( x + 3 ) = 30

Solution:

3( x + 3 )  =  30

x + ( 3 x 3 )  =  30

3x + 9  =  30

3x  =  21

x  =  7

Answer:  x =  7

Example 6:

Find lateral surface area of cone with radius 10 cm and slant height 20 cm.

Solution:

Given:  Radius r =10 cm

Slant height l = 20 cm

Lateral surface area  = `pi` r l   square units.

= 3.14 x 10 x 20

= 628 cm^2

Answer: Lateral surface area = 628 cm^2



Example 7:

Find the range of the data set { 5, 12, 43, 25, 41 }

Solution:

Here, The maximum value is 43

The minimum value is 5

Range  =  Maximum value – Minimum value

=  43 – 5

= 38

Answer: Range  = 38

Having problem with is the square root of 5 a rational number keep reading my upcoming posts, i will try to help you.

Get help in math now through practice problems:


1) Find the range of the data set { 25, 55, 29, 32, 19 }

Answer: 36

2) Find the area of the square with the side length of 17 cm.

Answer: 289 cm^2

3) Find the Mean of the given data set: { 2, 7, 8, 11 }

Answer: 7

4) Find lateral surface area of cone with radius 4 cm and slant height 12 cm.

Answer: 150.72 cm^2

How 2 Do Math Work

INTRODUCTION TO HOW 2 DO MATH WORK

How 2 do math work is nothing but doing math problems. The main importance of how 2 do math work is the sequence of steps we follow to solve the math problem. Solve math problems relates important role in our daily life. Everyone should know the importance of math and how 2 do math work. How 2 do math work depends on the topics of the math work we do. Every topic has different steps to do the problem. Some topics follow formula method. Problems of different topics have many logic's. Many chapters undergoes math. All the problems of math cannot be solved by same way.  Every problem has to be solved by using different methods, different steps, etc.

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PROBLEMS ON HOW 2 DO MATH WORK


1. Find the area and perimeter of a square of the side a = 9cm

Solution

This problem is based on formula method.

The side of the square = 9 cm

Formula to calculate the area of the square = a^2 or (side * side)

Area of the square = 9 * 9

= 81 square centimeter.

Formula to calculate the perimeter of the square is 4* side

Perimeter of the given square = 4 * 9

= 36 cm

2. How 2 do math work of (5*7) + 9 – 8 / 2 *2 + 2

Solution

Here we work out this problem by using PEMDAS rule

35 + 9 – 8 / 2 * 2 + 2 ------------(Parenthesis first)

35 + 9 – 8 / 4 + 2------------------(No exponents so net multiplication)

35 + 9 – 2 +2 ---------------------(Division)

44-4---------------------------------(Addition)

40

3. How 2 do math work of Multiplication of 7.8 x 3.2

Solution

7.8

3.2 x

----------

156

234   +

-------------

2 4.96

--------------

The process is first multiply the once digit and then multiply the tens digit. After the multiplication add at last and count the number of digits after decimal point in the question and place the decimal digit counting from last digit. This is the process of how 2 do math work of this multiplication.

Understanding 7th grade math problems with answers is always challenging for me but thanks to all math help websites to help me out.

Practice problems on how 2 do math work

Multiply 78 * 51
Add 84569 + 45213
Divide 235 / 5
Answer

3978
129782
47

Math Term Relation

Introduction for math term relation:

When comparing (relate) the objects (human beings) the concept of relation becomes very important. In a similar fashion we connect two sets (set of objects) by means of relation.

Let A = {2, 5, 7} and B = {4, 6, 8}. Consider a subset of the Cartesian product. A × B = {(2,4), (2,6, (2,8), (5,6), (5,8, (7,8)} If R denotes the relation “is less than”, then 2R4 (since 2 < 4), 2R6, 2R8, 5R6, 5R8, 7R8. This gives R = {(2,4), (2,6, (2,8), (5,6), (5,8, (7,8)}. The relation is R from A to B. The math term relation example problems and practice problems are given below.

I like to share this Graphing Ordered Pairs with you all through my article.

Example problems for math term relation:


Example problem 1:

Give examples of relations of the following type

(i) Reflexive and transitive but not symmetric

(ii) Neither reflexive nor symmetric but transitive

(iii) Nither reflexive nor transitive but symmetric.

Solution:

(i) The given relation “a divisor of ” is reflexive and transitive but not symmetric on the set of M natural numbers.

(ii) Consider the given relation “is greater than” on N. Since a > a is not true, the relation is not reflexive. If a > b, then b R a is not true. The above example relation is transitive.

(iii) Consider the relation R = {(2,3), (3,2),(3,4),(4,3)} on the set A = {2,3,4}. Evidently R is not reflexive as (2,2), (3,3), (4,4) are not in R. Since (2,3) and (3,2) are in R, it is symmetric. It is not transitive as (2,3), (3,2) ? R, but (2,2) ? R.

Example problem 2:

Let M represents the set of integers. S on I is defined as a S b if a – b is an even integer. Prove that S is an equivalence relation.

Solution:

By definition a S b if a – b is an even integer. Since a – a = 0 is even, we have a S a. Hence S is reflexive. Let a S b so that a – b is an even integer.

But then b – a = – (a – b) is also even and so b R a. Hence S is symmetric. Let a S b, and b S c so that a – b and b – c are even integers. Then (a – c) = (a – b) + (b – c) is also an even integer. Hence S is transitive so that S is an equivalence relation.

These example problems are very helpful to study of math term relation.

Having problem with college level math help keep reading my upcoming posts, i will try to help you.

Practice problems for math term relation:


Practice problem 1:

Given that A = {6, 7, 8, 9, 10} and B = {2, 3, 4, 5}. Write down all ordered pairs (a, b) such that a is divisible by b and hence write down the set of ordered pairs given the relation ‘is a multiple of’ from A to B.

Answer: (6,2), (6,3), (8,2), (8,4), (9,3), (10,2), (10,5)

Practice problem 2:

In the set N of natural numbers, examine the kinds of relation given below

(i) If a^2 + b^2 is a perfect square, a R b

(ii) if a^2 = b, a R b.

Answer: (i) symmetric (ii) not a relation

Studying For Math

Introduction to studying math problems:

Mathematics is the studying 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. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. In this article we shall studying math problem with detailed solution. (Source: wikipedia)


Studying for math example problems


Example:

The diameter of a cylinder base is 18 cm and the height of the cylinder is 13 cm. Find the solid cylinder surface area.

Solution:

Radius of cylinder = 9 cm

Surface area of cylinder = 2πr (r + h)

=2x`22/7` x9x (9+13)

= 2x`22/7` x9x (22)

=2x3.142x198

=1244cm^2

Example:

Isolate the variable x in the equation

8x + 2y = 16.

Solution:

The following steps are used to isolate variable x in the given equation

Subtracting the value  2y from both sides of the equation

8x + 2y - 2y = 16 - 2y

Simplify the above equation it gives the equation as:

8x = 16 - 2y

Now to divide the equation both side by 8both sides of the equation
8x / 8 = (16 - 4y) / 8

x = (16 - 4y) / 8

Now we get the isolated x.

Example:

Find the volume of a cylinder the area of the base of the cylinder is 18 cm^2 and the height of the cylinder is 12 cm.

Solution:

Volume of cylinder = Area of base of cylinder x height of cylinder

= 18 cm^2 x 12 cm

= 216 cm^3

Problem:

Find the triangle perimeters, whose length of a triangle sides are 22 cm, 35 cm and 50 cm,

Solution:

Perimeter of triangle formula = a+ b+ c

a=22

b=35

c=50

Perimeter of triangle = 22 + 35 + 50 = 107

Therefore perimeter of triangle = 107

Is this topic Perimeter and Area of Similar Figures hard for you? Watch out for my coming posts.

Studying for math practice problems


Problem:

Find the volume of a cylinder the area of the base of the cylinder is 20 cm^2 and the height of the cylinder is 11 cm.

Answer:

220 cm^3

Problem:

Isolate the variable x in equation

6x + 4y = 12.

Answer:

x = (12 - 4y) / 8

Math Radicals Solver

Introduction to math radicals solver:

Radicals is a form of symbol which is used in the mathematics. It is shown that the radical  symbol as  root "v". The number inside the radical symbol which is called as the radicand of the radical value, for example if the given value is square root of `sqrtx` . The x is called as the radicand which is the number inside the radical symbol root "v". There are more number of rooting methods available depending upon the value we have. The roots are square root `sqrtx` , cube root `root(3)(x)` , Fourth root `root(4)(x)` this up to nth root `root(n)(x)` . Here we are going to see about the math radicals solver in different methods and the solved example problems on it.

I like to share this Rules of Radicals with you all through my article.

Math radicals solver - Some properties:


Radicals form - Representations:

Function `a^(1/n)` :

The radical exponent  `a^(1/n) = root(n)(a)`

If n has odd value then,

If a is positive value then the function  `a^(1/n)` is positive.

If a is negative value then the function `a^(1/n)` is negative.

If a is zero value then the function `a^(1/n)` is also zero

If n has even value then,

If a is positive value then the function `a^(1/n)` is positive.

If a is negative value then the function `a^(1/n)` is not a real number.

If a is zero value then the function`a^(1/n)` is also zero

Radical Expression:

`x^(1/n) = root(n)(x)`    it is n root of x value.

Relation between expression and Radical:

`(x^(1/n))^n`   is the relation between the expression and radical .

Radical Exponent of Product:

`root(n)(axxb) = (axxb)^(1/n) = root(n)(a)xxroot(n)(b) =a^(1/n) xx b^(1/n)`

Radical for a quotient:

`root(n)(a/b) = (a/b)^(1/n) = (root(n)(a))/(root(n)(b)) = a^(1/n)/b^(1/n)`

Radical of a fraction:

`msqrta^n = a^(n/m) `

I have recently faced lot of problem while learning Properties of Radicals, But thank to online resources of math which helped me to learn myself easily on net.

Math radicals Solver Example Problems:


Math radicals Solver - Problem 1:

Solve `root(4)(81)`

Solution:

solve the 4th root for the given function.

`root(4)(81)` = `(9^2)^(1/4)`

= `9^(2/4)`

=` 9^(1/2)`

= 3

Math radicals Solver - Problem 2:

Solve radical form for `sqrt645`

Solution:

The root value 645 is nearly equal to the square values between 25 and 26, because 252 = 625 and 262 = 676

Step 1: Divide 645 by 15.

`645 / 25` = 25.8

Step 2: Take average for 25.8 and 25.

` (25.8 +25)/2` =  25.4

Step 3: Divide 645 by 25.4

`645/25.4` = 25.3937008

Step 4: Take average for the 25.3937008 and 25.4

`( 25.3937008 + 25.4)/2 `  =  25.3968504

Step 5: Now check the above result by taking square

25.39685042 = 645.00001

This value is more or less equal to 645

If the value is not equal repeat the step 3 and step 4

Math Rules of Integers

Introduction to math rules of integers:

In mathematics, rules of integer is one interesting topics in number representation. Integer contains a set of numbers in which are positive integer, negative integer and zero. It contains complete entity or unit. In integer, there are no fractional parts. Integer performs different arithmetic operations such as addition, subtraction, multiplication and division. Let us solve some example problems using math rules of integers.

Example for integers:

287, -547, 0, 31, etc,

I like to share this Positive and Negative Integers with you all through my article.

Different math rules of integers:


Different math rules of integers are,

Rules of Integer Addition:

In addition, we use the same sign. If we add the same sign integer values then we get the same sign.

Positive integer + Positive integer    =   Positive integer

Negative integer + Negative integer  =    Negative integer

Otherwise, we use different signs. We subtract the different sign integer values then we get the largest absolute value.

Positive integer + Negative integer

Negative integer + Positive integer

Rules of Integer Subtraction:

In subtraction, we keep the first integer as same, change the subtraction sign to addition and change the second integers sign into its opposite then we follow the rule for integer addition.

Rules of Integer multiplication:

Like addition rule,

Positive integer  ×  Positive integer     =   Positive integer

Negative integer  ×  Negative integer   =  Positive integer

Positive integer   × Negative integer    =  Negative integer

Negative integer  ×  Positive integer    =  Negative integer

Rules of Integer Division:

Positive integer  ÷  Positive integer  =  Positive integer

Negative integer  ÷  Negative integer  =  Positive integer

Positive integer   ÷ Negative integer  =  Negative integer

Negative integer  ÷  Positive integer  =  Negative integer

Having problem with Adding Integers keep reading my upcoming posts, i will try to help you.

Example problems using math rules of integers:


Some example problems using math rules of integers are,

Example 1:

Using integer addition rule in math, solve the given integers

450 + 257

Solution:

Given two integer numbers are

450 + 257

Both are two positive integers so, the result is also a positive numbers

Here we add 450 into 257, and then we get the result

450 + 257

707

Solution to the given two integers is 707.

Example 2:

Using integer subtraction rule in math, solve the given integers

897 – 456

Solution:

Given two integer numbers are

897 – 456

Both are two positive integers so, the result is also a positive numbers

Here we subtract 897 into 456, and then we get the result

897 – 456

441

Solution to the given two integers is 441.

Example 3:

Using integer multiplication rule in math, solve the given integers

754 × 12

Solution:

Given two integer numbers are

754 × 12

Both are two positive integers so, the result is also a positive numbers

Here we multiply 754 into 12, and then we get the result

754 × 12

9048

Solution to the given two integers is 9048.

Example 4:

Using integer division rule in math, solve the given integers

45870 ÷ 30

Solution:

Given two integer numbers are

45870 ÷ 30

Both are two positive integers so, the result is also a positive numbers

Here we divide 45870 by 30, and then we get the result

45870 ÷ 30

1529

Solution to the given two integers is 1529.

Example 5:

Using integer multiplication rule in math, solve the given integers

- 720 × 18

Solution:

Given two integer numbers are

- 720 × 18

Given integer number has both positive integer and negative integer so, the result is a negative numbers

Here we multiply - 720 into 18, and then we get the result

- 720 × 18

- 40

Solution to the given two integers is -40.

Example 6:

Using integer addition rule in math, solve the given integers

- 42 + (- 85)

Solution:

Given two integer numbers are

- 42 + (- 85)

Both are two negative integers so, the result is also a negative numbers

Here we add -42 into -85, and then we get the result

-42 - 85

-127

Solution to the given two integers is -127

Help This Math Problem For Me

Introduction to help with math problem:

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. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences.(Source: From Wikipedia).

In mathematics, step by step explanation is very helpful to understand the problems easily. Now, we are going to get help with some math problems.

Please express your views of this topic How do you Find the Degree of a Polynomial by commenting on blog.

Help some algebra math problems:


Math help-problem 1:

Add Fractions: 1/4 + 1/3

Solution:

The denominators of the given fractions are different. So, the common denominator of 4 and 3 is 12.

To find the corresponding value of numerator, we need to multiply 1/4 by 3 and multiply 1/3 by 4. So, Equivalent fractions of 1/4 and 1/3 are 3/12 and 4/12. Now the denominators are same.

So, (3/12) + (4/12)

Now add the numerators

(3+4)/12 =7/12

So the answer is 7/12.

Math help-problem 2:

Solve for the variable x: (x / 3) + 1 = 16

Solution:

(x / 3) + 1 = 16

Subtract 1 on both sides of the equation

(x / 3) + 1 - 1 = 16 – 1

(x / 3) = 15

Multiply 3 on both sides of the equation

3*(x / 3) = 15*3

x = 45

So, the variable x is 45.

Math help-problem 3:

Find the value of the expression: xy + xz + yz If  x=0, y=1, z=2

Solution:

Substitute the value of x, y and z in the given expression

xy + xz + yz = 0(1) + 0(2) + 1(2)

=0 + 0 +2

=2

So, the answer is 2.

Is this topic percentage change calculation formula hard for you? Watch out for my coming posts.

Help some geometry math problems:


Math help-problem 4:

Find the area of a circle of diameter is 60 cm (use pie = 3.14).

Solution:

The diameter of the circle is 60cm.

Radius = diameter / 2

So, the radius of the circle is 30cm

Area of the circle = pie*r2 = 3.14 × 302 = 2,826 cm2

Math help-problem 5:

Find the area of parallelogram whose base is 7cm and the height is 4cm.

Solution:

Area of the parallelogram = b × h

= 7 cm × 4 cm = 28 cm2

Math help-problem 6:

A triangle has a perimeter of 8cm. If one of the side is 1cm, another one side is 2cm then find the length of the third side?

Solution:

Perimeter of the triangle = addition of all the outer sides.

8cm = 1cm + 2cm + third side

Third side=8cm – 3cm =5cm

So, the third side is 5cm.

Math Calculater

Introduction to math calculator:

In general, calculators are used to perform various operations. Mathematical calculators perform both simple and complex operations. Simple mathematical calculators are used to perform various simple mathematical operations such as addition, subtraction, multiplication, division etc.,
In this article, we are going to discuss about various simple mathematical operations using calculators.

Please express your views of this topic Distributive Property of Multiplication over Addition by commenting on blog.

Addition and Subtraction Calculator:


Examples for addition calculator:

1) 24 + 44 = ?

Step 1: Enter the numbers 24

Step 2: Press the + sign

Step 3: Enter the numbers 44

Step 4: If we press = sign, the result can be obtained as 68.

2) 456 + 214 = ?

Step 1: Enter the numbers 456

Step 2: Press the + sign

Step 3: Enter the numbers 214

Step 4: If we press = sign, the result can be obtained as 670.

Examples for subtraction calculator:

1) 180 - 80 = ?

Step 1: Enter the numbers 180

Step 2: Press the - sign

Step 3: Enter the numbers 80

Step 4: If we press = sign, the result can be obtained as 100.

2) 250 - 149 = ?

Step 1: Enter the numbers 250

Step 2: Press the - sign

Step 3: Enter the numbers 149

Step 4: If we press = sign, the result can be obtained as 101.

Is this topic Simple Interest Calculator hard for you? Watch out for my coming posts.

Multiplication and Division Calculator:


Examples for multiplication:

1) 15  * 20 = ?

Step 1: Enter the numbers 15

Step 2: Press the  *  sign

Step 3: Enter the numbers 20

Step 4: If we press = sign, the result can be obtained as 300.

2) 27  * 29 = ?

Step 1: Enter the numbers 27

Step 2: Press the  *  sign

Step 3: Enter the numbers 29

Step 4: If we press = sign, the result can be obtained as 783.

Examples for Division:

1) 60/ 5 = ?

Step 1: Enter the numbers 60

Step 2: Press the  /   sign

Step 3: Enter the number 5

Step 4: If we press = sign, the result can be obtained as 12.

2) 260 / 8 = ?

Step 1: Enter the numbers 260

Step 2: Press the  /  sign

Step 3: Enter the number 8

Step 4: If we press = sign, the result can be obtained as 32.5.

3) 4298 / 146 = ?

Step 1: Enter the numbers 4298

Step 2: Press the  /  sign

Step 3: Enter the numbers 146

Step 4: If we press = sign, the result can be obtained as 29.4383.