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.

Having problem with Definition of Alternate Interior Angles keep reading my upcoming posts, i will try to help you.

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.

I like to share this Converting Mixed Numbers to Improper Fractions with you all through my article.

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.

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

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.

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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.

Looking out for more help on meaning of variable in algebra by visiting listed websites.

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

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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.

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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.