Solve Number Theory Test

Introduction to solve number theory test:

Solve number theory test includes convert between standard and scientific notation, prime or composite, prime or composite, identify factors, prime factorization, greatest common factor, least common multiple. Number theory helps students to learn about the number system with some basic knowledge. In below we have test questions with answer key in number theory. Let us see about solve number theory test.

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Test questions for solve number theory test:


Test question 1: Convert the following number from standard form in to scientific notation: 556.

Test question 2: Write the following scientific notation in to standard form 3.65 × 10^1

Test question 3: Identify the prime number from the following series: 100, 102, 103, 105, 200, and 250.

Test question 4: Calculate the prime factorization of 58.

Test question 5: Do the calculation to find the greatest common factor of 4 and 64.

Test question 6: Do the calculation to find the least common multiples 7 and 8.

Test question 7: Xavier is making stationery sets from 12 sheets of paper and 15 envelopes. If he wants all the sets to be identical without any paper or envelopes left over, find the greatest number of sets Xavier can make.

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Answer keys for solve number theory test:


Answer key 1: The scientific notation of the following standard form 556 is 5.56 × 10^2

Answer key 2: The standard form of the following scientific notation 3.65 × 101 is 36.5

Answer key 3: The prime number from the following series: 100, 102, 103, 105, 200, and 250 is 103.

Answer key 4: The prime factorization of 58 is 2 and 29.

Answer key 5: The greatest common factor of 4 and 64 is 8.

Answer key 6: The least common multiples 7 and 8 are 56.

Answer key 7: The greatest number of sets Xavier can make is 3.

Solve Help Percentages

Introduction – Solve help percentages:

In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred" in French). It is often denoted using the percent sign, "%", or the abbreviation "pct". For example, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. Let us see solve help percentages.

- Source from Wikipedia

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Example problems – Solve help percentages:


Problem 1:

How much is 9% of 1400 dollars?

Solution:

Since 1% is `1 / 100` * 1400 = 14 dollars, then 9% is 9 × 14 dollars = 126 dollars.

Problem 2:

A ice burg losses its weight from 140  to 125. What was its percentage weight loss?

Solution:

First, we have to find the absolute weight loss.

140 – 125 = 15 pounds

15 = (x) (140)

15 ÷ 140 = x

15 ÷ 140 = 0.10

Now we have to convert the decimal value as percent form.

To convert the decimal to percent form multiplies it by 100. That is 0.10*100 = 10.

Hence the ice burg losses its weight by 10%.

Problem 3:

Sham borrowed 950 dollars at 9% simple interest, for 3 years. How much did he have to pay back (principal + interest) after the 2 year period?

Solution:

The interest to pay is given by

Multiply the original amount by 9% and interest periods

Interest = 950 * `9 / 100` * 3 = 256.5 dollars

Total to pay back

950 + 256.5 = 1206.5 dollars.

After two years Sham has to pay 1206.5 dollars.

Problem 4:

A sales man sold his vehicle at 24% profit. Its original cost is 300 dollars. Find out the selling price.

Solution:

The gain is 24% of the 300 dollars cost, so the gain is:

`24 / 100 ` = (0.24) (300) = 72

Add the selling price percentage with original price

300 + 72 = 372

The vehicle sold at 372 dollars

Problem 5:

A person buys a laptop in a shop and paid 450 dollars for laptop and 15% for sales tax and 8% for accessories. How much did he pay for his laptop?

Solution:

He paid for laptop, sales tax and accessories, hence

Sales tax   = 15% = `15 / 100` * 450 = 67.5

Accessories           = 8% = `8 / 100` * 450 = 36

Total paid = 450 + 67.5 + 36 = 553.5 dollars.

Totally he paid 553.5 dollars for his laptop.

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Practice problems – Solve help percentages:


Solve help percentage practice Problem 1:

What is 68% of 840?

Answer:

= 571.2

Solve help percentage practice Problem 2:

The original price of a pen was 20 dollars. Now the price was decreased to 15 dollars. What is the percent decrease of the price of this pen?

Answer:

= 25%

Learn Types of Matrices

Introduction to learn types of matrices:

In mathematical matrix has a list of data. In math matrix elements are arranged in rectangular form. Elements are placed in row and column structure. In math matrix elements are put in the parenthesis or square brackets. Generally matrix is symbolized by capital letters. Many types of matrices are available in math. Let us see learn types of matrices in this article.


Learn types of Matrices:


Matrix:

Common representation of the word matrix is m`xx` n.

Where

Number of rows is represented by the variable ‘m’

Number of columns is represented by the variable ‘n’.

Example:

A = `[[a,b,c],[d,e,f],[g,h,i]]`

The above is 3`xx` 3 matrices.

Learn some other information about matrix:

We can perform addition, subtraction and multiplication process between matrices. But we cannot divide matrices.

Types of matrices

Column matrix
Row matrix
Square matrix
Diagonal matrix
Triangular matrix
Scalar matrix
Identity matrix
Zero matrixes
Equality of matrix


Learn definition for types of matrices:


Definition of column matrix:

Only one column is there in the column matrix.

Example:

A = `[[,a],[,b],[,c]]`

Definition of row matrix:

Only one row is there in the row matrix.

Example:

A = `[[a,b,c]]`

Definition of square matrix:

Square matrix has equal number of row and column.

Example:

A = `[[a,b],[c,d]]`

Definition of diagonal matrix:

Diagonal matrix has zero value (other than diagonal elements)

Example:

A= `[[a,0],[0,b]]`

Definition of triangle matrix:

Triangle matrix necessity is a square matrix. Every element in above the diagonal are zero means called as lower triangle matrix. Every element in below the diagonal is zero means called as upper triangle matrix.

Example for upper triangle matrix:

A = `[[a,b,c],[0,d,e],[0,0,f]]`

Example for lower triangle matrix:

A = `[[a,0,0],[b,c,0],[d,e,f]]`


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Definition of unit matrix:

Unit matrix necessity is a square and diagonal matrix. The diagonal elements are one and the other elements in the array is zero means called as unit matrix.

Example:

A = `[[1,0,0],[0,1,0],[0,0,1]]`

Hardest Math Problem to Solve

Introduction to hardest math problem to solve:

Learn and to solve the  hardest math problems involves the operations like addition, subtraction, multiplication and division and it be viewed as ( +,-,`xx` ,÷ ) .By solving the hardest math problems means  it helps in our daily life also without math there is no calculation involved and so every one is learning the math problems.The math problems helps  to increase our mental ability and to think and execute in some pressure situations with out any mistake. Here we are going to see about the article called hardest math problem to solve .


Solved hardest math problem


Math problem 1:

A ice cream manufacturing organization  produces an amount of 4357 ice cream product flavor  in a year. And that company produces three types of ice cream flavors of products like strawberry, Butterscotch, and chocolates. The amount of chocolates was 199 more than the flavors of Butterscotch. Then the strawberries flavor were made four times of the number of chocolates made in this year. Find the number of strawberry was produced by the company in this year?
Solution:

Let we denote as,

A = strawberry, B = Butterscotch, and C = chocolates.

Step 1:

From the given problem we can write as,

A + B+ C = 4357 (1) 

C = A + 199         (2)

B = 4A                   (3).

Step 2:

In step 2 denote the equations 2nd and 3rd in equation 1,

A+ 4A + A +199  = 4357

6A = 4158.

A = 693

So we get there are  693 strawberry  flavor were produced by the ice cream  company in this year.

Step 3:

Apply the value of A in equation 3 we get,

B = 4(693)

B =2772

So we get there are 2772 Butterscotch flavor were produced by the ice cream company in this year.

Step 4:

Apply the value of A and B equation 1 we get,

A + B + C = 4357

693+ 2772 + C =4357

3465+ C= 4357.

C = 892

So we get there are 892 chocolates flavor were produced by the ice cream company in this year.


One more solved hardest math problem


Math problem 1:

Solve the given problem 20(s – 99) – 87s - 18 = 191(s + 15)

The Solutions follows below:

Given expression is,

20(s – 99) – 87s `-` 18 = 191(s + 15)

Multiplying the integer terms

20s – 1980 – 87s – 18 = 191s + 2865.

Grouping the above terms

–67s –-1998= 191s + 2865

Add 1998 on both sides

–67s –1998+ 1998 = 191s + 2865  + 1998

Grouping the above terms

–67s = 191s +4863

Subtract 191s by on both sides

–67s – 191s = 191s – 191s + 4863

Grouping the above terms

–258s = 4863

S = `- 4863/258`

The required answers is 

S = `- 4863/258`

Nine Grade Math Slope

Introduction to nine-grade math slope:

Nine- grade math slope article deals with how to find the slope from the slope intercept from of the equation and from the two given points of the line. It includes the slope of the parallel and perpendicular line. We have the different formula to find the slope of the given line

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Formula related to nine grade math slope.

When two coordinate points on the line is given

Formula to find slope, m = `((y2-y1)/(x2-x1))`

When slope intercept form is given

The slope intercept form is y = mx+b

m = `((y-b)/x)`

Where m is the slope of the line

b is the y intercept.

When two lines are parallel to each other, the slope of the both lines is equal.

When two lines are perpendicular to each other, the product of slope is -1[ (m1*m2)= -1]

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Model problems for nine grade math slope


Example problems for nine grade math

Find the slope of the line whose coordinate points are (2, 3) and (4, 5).


Solution:

(x1,y1) = (2, 3)

(x2,y2) = (4, 5)

Formula:

Formula to find slope, m = `((y2-y1)/(x2-x1))`

= `((5-3)/ (4-2))`

= `(2/2)`

= 1

The slope of the line is 1

2.find the slope of the line whose slope intercept form is 3y = 6x +9

Solution:

The slope intercept form is y= mx+b

The given equation is 3y= 6x +9
rewrite the equation of the line

y= `(6/3)x+(9/3)`

y= 2x+3

Now it is in the standard form.

Therefore, the slope of the line is 2

3. Line AB and CD are perpendicular to each other, find the slope of the line CD when the two points on the lineAB is (2, 7) and (6, 4)

Solution:

(x1,y1) = (2, 7)

(x2,y2) = (6, 4)

Formula:

Formula to find slope, m = `((y2-y1)/(x2-x1))`

= `((4-7)/(6-2))`

= `((-3)/4)`

= `(-3/4)`

The slope of the line is `(-3/4)`

Since AB and CD are perpendicular to each other.

so, the slope of the CD =` (- 1/"slope of AB")`

= `(-1/ ((-3/4)))`

= `(4/3)`

Slope of the line CD is `(4/3)`

4th Grade Learning Math

INTRODUCTION TO FOURTH GRADE LEARNING MATH

Fourth grade learning math is the learning basic of some more brief of mathematics that was learned in third grade. Fourth grade learning math is the learning based on topic such as addition, subtraction, multiplication, division, equations and variables. Fourth grade learning math consists of chapters like algebra, charts, graph, fractions, decimals and geometry. Fourth grade learning math work consists of more subtopic under each chapter. Here we can learn some of the fourth grade math on some chapters. Fourth grade learning math is advance of third grade learning math.

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FOURTH GRADE LEARNING MATH


1.    Add 7 2 1 0 + 2 4 2 5

Solution

7 2 1 0

2 4 2 5 +

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

9 6 3 5

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

2.  Subtract 9 7 5 3 – 2 6 3 0

Solution

9 7 5 3

2 6 3 0 –

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

7 1 2 3

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

3.  Tony had 15 biscuit packets. Each packet consists of 7 biscuits. How many biscuits totally he had?

Solution

Number of biscuits in one packet = 7 biscuits

So 15 biscuit packets consists = 15 x 7= 105 biscuits.

4. Add the decimal value 75. 36 + 23.21

Solution

75. 3 6

23. 2 1 +

-----------

98. 5 7

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

5. Subtract decimal value given 54.34 – 24.51

Solution

5 4.3 4

2 4.5 1   -

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

2 9.8 3

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

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MORE PROBLEM OF FOURTH GRADE LEARNING MATH


6.   Solve the equation 5x + x = 24

Solution

5x + x = 24

6x = 24

Divide 6 on both sides

x = 4



7. Add `3/11` +`6/11`

Solution

Here the denominators are same. So just add the numerator alone

` (3+6)/11`

`9/11` is the answer.

8. Subtract `8/9` – `4/9`

Solution

Here the denominators are same. So just subtract the numerator alone.

`(8 - 4)/9`

`4/9`

9. Multiply` 3/5` * `3/ 4 `

Solution

`3 / 5 ` * `3 / 4`

3* 3 / 5* 4

= `9 / 20 `

10. Convert 100 centimeter =? Meter

Solution

100 centimeter = 1 meter.

Commission Math Problems

Introduction to commission math problems:

Commission math problems article deals with the definition of the commission and the math problems related to the commission.

Definition of commission math problems:

This math problems deals with the rate of money, which we can earn by selling some product or doing the work behind the target fixed.This is very important things in selling and buying the products and it is used to find the commission amount.

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Formula to commission math problem


In these problems the commission rate r % is fixed, by multiply the commission rate with the original cost of the product, we can get the commission amount on that particular product,

Commission amount = r% *(original cost of the product).

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Model problems to the commission math problems:


Find the monthly income of the john if his monthly salary is $2000 and he gets 4% of commission if he sells a car of cost about $4500.
Solution:

The monthly salary of the john is $2000

The commission rate is r= 4%

Commission amount = r% *(original cost of the product).

= 4 %*( 4500)

= (4/100)*(4500)

=(0.04)*(4500)

= $180

Commission amount is 180 $

The monthly income of the john = monthly income +commission amount

= $ 2000 +$180

= $2180

The monthly income of the john is $2180.

2.Find the income of the sam if his daily salary is $200 and he gets 3% of commission if he sells the product amount morethan $500.

Solution:

The daily salary of the john is $200

The commission rate is r= 3%

Commission amount = r% *(500).

= 3 %*( 500)

= (3/100)*(500)

=(0.03)*(500)

= $15

Commission amount is $15

The daily income of the john = daily income +commission amount

= $ 200 +$15

= $215

The monthly income of the john is $215.

3.Find the commission price of the product of cost $700 and the tax commission is 6%.

Solution:

The tax commission is 6%

The cost of the product is $700

Commission amount = r% *(original cost of the product).

= (6/100)*700

= (0.06)*700

= 42

commission amount is $42.

Learn Gaussian Elimination

Introduction to learn Gaussian elimination:

In linear algebra, Learning Gaussian elimination is an algorithm for solving systems of linear equations, finding the rank of a matrix, and calculating the inverse of an invertible square matrix. Gaussian elimination is named after German mathematician and scientist Carl Friedrich Gauss.

Elementary row operations are used to reduce a matrix to row echelon form. Gauss–Jordan elimination, an extension of this algorithm, reduces the matrix further to reduced row echelon form. Gaussian elimination alone is sufficient for many applications.

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Solving by Learning Gaussian Elimination:


A technique of solve a method of n linear equations in a n unknowns, in which there are first n - 1 steps, the math step of which consists of subtracting a lots of the math equation from both of the pursue ones so as to remove one variable, ensuing in a triangular set of equations which can be solved by turn around substitution, compute the nth variable from the nth equation, the (n-1)st variable from the (n-1)st equation.

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Example problems for learning Gaussian Elimination:


Example problems for learning Gaussian Elimination are as follows:

1) Solve the following system equation using Gaussian Elimination method.

3x + y = 9

3x – y = 15

Solution:

If add down, the y determination cancel out. So sketch an "equals" bar below the system, and add down:

3x + y = 9

3x – y = 15

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

6x = 24

x = 24 / 6

x = 4

At the present divide from side to side to solve for x = 4, and then back-solve, using either of the original equations, to find the value of y. The first equation have lesser facts, so back - explain in that one:

2(4) + y = 10

8 + y = 10

y = 2

Then the solution is (x, y) = (4, 2)

2) Solve the following system using Elimination method.

2x + 2y = 4 --- (1)

4x – 3y = 8 ---- (2)

Solution:

Multiply equation 1 with (3) and multiply equation, 2 with (2)

6x + 6y = 12

8x – 6y = 16

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

14x = 28

x = 28/14

x = 2

Apply x=2 in equation (1)

2(2) +2 y = 4

4 + 2y = 4

2y = 4 -4

y=0

Then the solution is (x, y) = (2, 0).

The World of Math

Introduction to world math :

In this article we are going to discuss about world math  Now a days math is one of the widely used part in the world. Sometimes math will challenge to solve the problems but every math has a solution to prove it. Let we see some math challenge problems to world math.

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Example Problems for math problems:


world math problem 1

Find the value for x in the expression `x/8` +x-`4/8` =0

Solution:

The given expression is `x/8` +x-`4/8` =0

We need to find the value of x

`x/8` +`(8x-4)/8` =0

The above expression can be written has

`x/8` +`(8x)/8` -`4/8` =0

Now add `4/8` on both sides of above equation

`x/8` +`(8x)/8` - `4/8` +`4/8` =`(0+ 4)/8`

`x/8` +`(8x)/8` =`4/8`

`(9x)/8` =`4/8`

Multiply by 8 on both sides of above equation

`(9x)/(8)xx(8)=` `4/8 xx8`

9x=4

Now divide by 9 on both side of the above

x=`4/9`

world math problem 2

Multiply the fraction `120/65` and `148/96`

Solution:-

Given we need to multiply fractions`120/65` and `148/96`

Fractions must multiplied using the formula `(axxc)/(bxxd).`

Here a = 120, b =65, c= 148, d=96

= `(axxc)/(bxxd).` =`(120xx148)/(65xx96) ` by solving it we get

A =`17760/6240`

= `37/13`

world math problem 3

Find the area of the circle with radius 54 feet. Important use symbol pie value approximately as 3.14

Solution:

We know that area of circle is equal to `pi` r2

Here the given radius is 54

Substitute the r value in the formula

=3.14x 542

=3.14x 54x 54

=9156.24

Therefore the area of circle is 9156.24 feet square

world math problem 4

Fine the surface area of cube in kilometers for the side is 30 m

Solution:

Area of cube A=6 * 302

A=6 *900

A=5400sq meters

1 square meter = 0.000001 square kilometer

5400 square meter = 5400 * 0.000001  = 0.0054

now surface area in kilometer is 0.005400 sq kilometers


Few More Example Problems for math problems


world math problems 5

Subtract the two fractions `32/15` and `94/15`

Solution:

The two given fractions are`32/15` and `94/15`

Step1: The given two fractions

`32/15` - `94/15`

Step2: Now we need to find the differences of `32/15` and `94/15`

`(32-94)/15`

Step3: The difference of 32 and 94 is -62

=-`62/15`

world math problem 6

Find equivalent fraction `7333/336`

Solution:

Equivalent fraction has to multiply numerator and denominator by same number

Denominator is 336 and the numerator is 7333

Multiply the denominator and numerator by 160

= `(7333xx160)/(336xx160)`

= `1173280/53760`

So the equivalent fraction is `7333/336` is` 1173280/53760`

Learn to Read a Ruler

Introduction of learn to read a ruler:

Math can understand through various equipment. The ruler is one of the main basic equipment for math. In every math problems the ruler plays a role to compute the answers. The ruler is measurable equipment for math. Ruler learns has two measures with cm in one side and mm in another end. Using the two measures we can have the two types of measuring terms.

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Learn to read a ruler:


The ruler is a measuring tool. The origin of the measuring tool is made from the man’s foot. To find the area’s measurement the man is asked to cross through the area for measuring the area’s measurement. The measure read in the yard can be done through the average man’s normal foot steps. Make the both measures to view, they won’t be exact. Till now the horses are made to measures in hands. This idea shows the origin of the ruler. We can have measuring idea with the ruler through the project on measuring the classroom. The classroom can be measured with the ruler that makes a measure which can be noted through the read that given over the scale. The measures about the book can be made along the measures with the scale.


More Learning to read a ruler:


Hence the learn of ruler can made to have the measures in the two ways. The first way is in the centimeters and the second way is in millimeters. The ruler is the simple measuring tool which is meant for measuring. Ruler is made to have in the way which gives the various changes that makes measures. The measure in the yard can be done through the average man’s normal foot steps. Make the both measures to view, they won’t be exact. Till now the horses are made to measures in hands. This idea shows the origin of the ruler.

Learning Support Math

Introduction for math learning support:

Math support learning  is a most interesting subject comparing to other subjects.It is the lesson for learning support math patterns, numbers, and shapes. Basic concepts of math are  Addition (a + b), subtraction (a-b), multiplication (a*b) and division (a/b) a and b are the numbers or integers. In this article, we are going to see some solved math support learning. I like to share this list of the prime numbers with you all through my article.


Example Problems for math problems:


Learning for support math problem 1:

Perform the Plus operation for 300 and 584

Solution:

Given we need to find the sum of 300 and 584

300

584  (+)

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

884

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

So the answer for 300 and 584 is 884

Learning for support math problem 2:

Multiplying two numbers 168 and 43

Solution:

The given two numbers 168 and 43

We need to find the product of two numbers

By Multiplying  168 and 43

168 × 43

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

5    0  4

6  7   2

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

7  2   2  4

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

We get  7  2   2  4

Learning for support math problem 3:

Find equivalent fraction `166/65`

Solution:

Equivalent fraction has to multiply numerator and denominator by same number

Denominator is 65 and the numerator is 166

Multiply the denominator and numerator by 24

= ` (166xx24)/(65xx24)`

=`3984/1560`

So the equivalent fraction is `166/65` is  `3984/1560`

Learning for support math problem 4.

Subtract the two fractions `174/112` and `224/112`

Solution:

The two given fractions are `174/112` and `224/112`

Step1: The given two fractions

`174/112` - `224/112`

Step2: Now we need to find the differences of   `174/112` and `224/112`

`(174-224)/112`

Step3: The difference of 174 and 224 is 50

= - `50/112`

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Few More Example Problems for math problems


Learning for support math problem 5:

Round the number 136 to the nearest 10

Solution:

The given number is 136

The number in 10 places is 3 and the number 1s places is 6

Since the number ten places is 6 so we make the number 6 as zero and we add 1 to 3

So the number 136 grounded to nearest 10 becomes  140

Learning for support math problem 6:

Identify 135 is a prime number or not

Solution:

The given number is 135

We need to identify prime number or not

To identify 135  is a prime number we need to determine in factors

Factors of 135  are 1  3  5  9  15  27  45  135

The number to be a prime number it must have only two factors 1 and itself

So here 135  has eight factors so it is not a prime number

Math 1010 Answers

Introduction to Math 1010 Answers:

In mathematics, numeration is one of the main sources describing about numerals such as number system. The number is also used for abstract object and symbolic representations of numbers. There is addition, multiplication, division, subtraction operation in math. The common usage of math is to solve the problem and finding the solution. The given problem can be performed by any one of the above operation. Let us see about math 1010 answers in this article.

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Example Problems for Math 1010 Answers


Using Addition Operation in Math

Example 1:

Add 1000 and 10?

Solution:

Let us add the given problem.

Write the given whole number 1000 first and then write the given whole number 10 second one by one.

1000 (addend)

(+)   10 (addend)

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

1010

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

The sum for adding 1000 and 10 is 1010.

Using Subtraction Operation in Math

Example 2:

Subtract 2220 and 1210?

Solution:

Let us subtract the given problem.

Write the given whole number 2220 first and then write the given whole number 1210 second one by one.

2220 (minuend)

(-) 1210 (subtrahend)

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

1010 (difference)

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

The difference for subtracting 2220 and 1210 is 1010.

Using Multiplication Operation in Math

Example 3:

Multiply 101 and 10?

Solution:

Let us write the given problem as in the below form. Here, 101 is multiplicand and 10 is multiplier.

101 ×

10

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

1010

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

The product for multiplying 101 × 10 is 1010.

Using Division Operation in Math

Example 4:

Divide 9090 by 9?

Solution:

Let us write the given problem is in form of 9090 ÷ 9 and put the divisor on the left side of the division bracket and dividend on the right side of the division bracket.

Check whether the 9 goes into 9. The number 9 should go into 9 for 1 time. Continue with the division method.

9)9090(1010

9

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

009

009

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

00

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

The quotient for dividing 9090 by 9 is 1010.


Practice Problems for Math 1010 Answers


1. Add 990 and 20.

Answer: 1010

2. Subtract 4880 and 3870.

Answer: 1010

3. Multiply 220 and 5.

Answer: 1010

4. Divide 7070 by 7.

Answer: 1010

How to do Sets in Math

Introduction to do sets in math:

A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. Let us see about the concept of how to do sets in math. (Source: Wikipedia)

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Sets in math:


By using two methods we can do the sets in math. They are,

Roster or tabular form
Set-builder form
How to do sets in math by using Roster form:

The elements are separated by using the commas, and the elements are placed inside of braces { }. For example, the set of all odd positive integers less than 8 is expressed in roster form as {1, 3, 5, 7}.

How to do sets in math by using Set-builder form:

For example, in the set {1, 3, 5, 7, 11}, all the elements possess a common property, namely, all are prime number, which are not possessed in any other set. Representing this set by P, we write P = {x: x is a prime numbers in real numbers}


Example problem in set:


Problem1: Find the solution set of the following equation by using roster form x 2 + x – 2 = 0.

Solution:

x 2 + x – 2 = 0 can be expressed as (x – 1) (x + 2) = 0, that is x = 1, – 2.

Therefore, the solution is {1, – 2}.

Problem 2: Find the set {x: x is a positive integer and x2 < 30} in the roster form.

Solution:

By the given we need the following numbers to represent the set -1, 2, 3, 4, 5.

So, the given set in the roster form is {1, 2, 3, 4, 5}.

Problem 3: Find the set A = {1, 4, 9, 16, 25 . . .} by using set-builder form.

Solution:

We may write the set A as A = {x: x is the square of a natural number}

Alternatively, we can write A = {x: x = n2, where n ∈ N}

In this section we have seen about the concept of how to do sets in math.

Mixed Numbers in Math

Introduction to mixed numbers in math:

In math, Mixed number is very important study.  We will study mixed numbers under algebra in math. This is very helpful when using fractions in math

Mixed number is a one form of fraction.  Mixed number is also known as mixed fraction. Mixed number will get by converting improper fraction into mixed fraction.

Mixed number includes an integer then a proper fraction.  The example of mixed numbers are 1 `2/3` , 5 `7/8` , - 1 `6/5` .

For example, convert an improper fraction into mixed number.

`4/3` = 1 `1/3` .

Let us see sample problems involving mixed numbers in math.

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Example Problems on Mixed numbers in Math:


Problem 1:

Subtract  `1/2` from 4 `1/2` .

Solution:

First, we need to convert mixed number into improper fraction.  The steps are following,

4 `1/2`

Multiply the denominator by an integer.

4 x 2 = 8

Add that number with numerator.

8 + 1 = 9

Now write the result in the numerator and keep the denominator same.

4 `1/2`  = `9/2`

Now rewrite the operation.

`9/2` – `1/2`

Here the denominator is same in both fractions. So we just subtract numerators and keep the denominator same.

`(9-1)/2` = `8/2` = 4 .

The answer is 4.

Problem 2:

Subtract  - 2 `3/5` from - 1 `3/5` .

Solution:

First, we need to convert mixed number into improper fraction.  The steps are following,

-2  `3/5`

Multiply the denominator by an integer.

2  x 5 = 10

Add that number with numerator.

10 + 3 = 13

Now write the result in the numerator and keep the denominator same.

-2 ` 3/5`  = - `13/5`

Now we need to do same process for another mixed number.

-1 `3/5`

Multiply the denominator by an integer.

1  x 5 = 5

Add that number with numerator.

5 + 3 = 8

Now write the result in the numerator and keep the denominator same.

-1 ` 3/5`  = - `8/5`

Now rewrite the operation.

-1 `3/5` – (- 2 `3/5` ) = -` 8/5` – (-`13/5` )

= - `8/5` + `13/5`

= `13/5` – `8/5`

Here the denominator is same in both fractions. So we just subtract numerators and keep the denominator same.

`(13-8)/5` = `5/5` = 1 .

The answer is 1.

Problem 3:

Multiply the mixed numbers:  -2 `2/3` and  4 `1/10`

Solution:

First, we need to convert mixed number into improper fraction.  The steps are following,

-2 ` 2/3 `

Multiply the denominator by an integer.

2  x 3 = 6

Add that number with numerator.

6 + 2 = 8

Now write the result in the numerator and keep the denominator same.

-2  `2/3`  = - `8/3`

Now we need to do same process for another mixed number.

4 `1/10`

Multiply the denominator by an integer.

4  x 10 = 40

Add that number with numerator.

40 + 1 = 41

Now write the result in the numerator and keep the denominator same.

4 `1/10`  = `41/10`

Now rewrite the operation.

-2` 2/3` x 4` 1/10` = - `8/3` x `41/10`

= - `328/30`

=` -164/15`

= - 10 `14/15`

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

Practice Problems on Mixed numbers in math:


Problem 1:

Find the solution of  -2 `1/5` and -1 `3/4`

Answer:

3 `17/20`

Problem 2:

Find the solution of – 2 `7/8` + 4 `3/8`

Answer:

1 `1/2` .

Problem 3:

Find the solution of `1/6` – 1 `5/6`

Answer:

-1 `2/3`

Learn Online Perpendicular

Introduction to learn online perpendicular lines:

Perpendicular means nothing but when two lines are cross in either direction and form right or 90 degree angles, so a horizontal line  and a vertical line  that cross are perpendicular because they form right angles.
Perpendicular lines are two lines which meet at a right angle. Right angle is 90degrees. Please express your views of this topic Slope of a Perpendicular Line by commenting on blog.


Learn perpendicular lines online through examples


1)Find the equation of the perpendicular line  to y = `(1)/(2)` x-5, passing through the point (4, 10).

Learn perpendicular lines online by using slope-intercept form:

Since the original line has a slope of `(1)/(2)`  , a perpendicular line must have a slope of -2.

Therefore, the equation must look like y = -2x + b.

Substituting the given point in place of x and y we have: 10 = -2(4) + b. Solving, we find that b = 18.

The equation is y = -2x + 18.

Learn perpendicualr lines online by using point-slope form:

Again, the perpendicular slope is m = -2. The equation must look like y - y1= -2(x - x1).

Substituting the given point in place of x1 and y1 we have y - 10 = -2(x - 4).

Rearranging yields y - 10 = -2x + 8 or y = -2x + 18.

2) Show that the lines 6x +3y +9 = 0 and 3x-5y+7 = 0 are perpendicular.

Solution: Given equation of lines as 6x + 3y + 9 = 0 and 3x + 5y+7 = 0

First line:   6x + 3y + 9 = 0                                                Second line:  3x - 5y + 7 = 0

6x + 3y + 9 - 9 = 0 -9                                                              3x - 5y + 7 -7 = 0 -7

6x + 3y = -9                                                                              3x - 5y = -7

6x -6x + 3y = -9 - 5x                                                                3x - 3x - 5y = -7 -3x

3y = -6x - 9                                                                               -5y = -3x-7

3y/3 =  (-6x-9)/3                                                                       5y/5 = (3x+7)/5

y = -5/3x -3                                                                              y =  3/5x +7/5

compare with y = mx + b                                                     compare with y = mx +b

m =`(-5)/(3)` and b = -3                                                              m = `(3)/(5)`  and b = `(7)/(5)`

Condition for lines to be perpendicular is m 1 * m2 = -1

Here, m 1 = `(-5)/(3)`  and  m 2 = `(3)/(5)` ,

m1 * m 2 = `(-5)/(3)` *`(3)/(5)`  =  -1

Therefore the  5x +3y +9 = 0 and 3x-5y+7 = 0 are perpendicular lines.

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learn perpendicular online -formula


Two lines are perpendicular to each other when the product of their slopes is -1

Let slope of first line is m1

Slope of second line is m2

m1 * m2 = -1

Slope of a line between points (x1,y1) and (x2,y2) is     m =`(y_(2)- y_(1))/(x_(2)- x_(1))`

Equation of line in slope intercept form is y = mx +b , where m is the slope of line and b is the y intercept of line

The equation of all lines perpendicular to the line ax +by +c = 0 can be written as bx –ay +k = 0 for different values of k

Learn Online Slope Intercept

Introduction to learn slope intercept:

Slope:

The Slope can be defined as the ratio of the

rising value to the run value between two points on a line.
change in altitude to the horizontal distance between any two points on the line.
Slope of a line is explained with examples in online.

Intercept:

Intercept of a line is a  point at which a line, curve, or surface intersects an axis.
Intercept is an intercepted segment of a line.
Intercept of a line can be learning easily through online.

I like to share this Slope Intercept Form Equation with you all through my article.

Learn online slope:


In the given two points (x1,y1) and (x2,y2) on a line, the slope m of the line is given by

m = (y2 - y1) / ( x2 - x1 )

Example 1: Find the slope of the line segment joining the points (1, 2) and (13, 8).

Solution:

Let  (x1,y1) = (1, 2)

(x2,y2) =(13,8)

m = ( 8 - 2 ) / ( 13 - 1 )

m = 6 / 12

m = 1 / 2

m = 0.5

Therefore, the slope of a line is 0.5

Example 2: Find the slope of the line segment joining the points (6, 10) and (4, 20).

Solution:

Let (x1,y1) = (6,10)

(x2,y2) = (4,20)

m = ( 20 - 10 ) / ( 4 - 6 )

m = 10 / (-2)

m = -5

Therefore, the slope of a line is  -5

This is how we can learn slope of a line through online.


Learn online intercept:


X - intercept

The x-intercept of a line is defined as the point at which the line cuts the X-axis.

Y - intercept

The y-intercept of a line is defined as the point at which the line cuts the Y-axis.

The following example problem helps you to learn intercept through online.

Example: Find X and Y intercept of the equation 6x + 8y =24

To find X intercept, plug y =0

6x + 8(0) =24

6x =24

x = 24 / 6

x = 4

Therefore, X-intercept is ( 4,0 ).

To find y intercept , plug X=0

6x + 8y =24

6(0) + 8y =24

8y =24

y = 24 /8

y =3

Therefore, Y-intercept is ( 0,3 ).

Learn Numeric System

A Numeric system contains real numeric/numbers. In this document we will say numeric s system as numbers.

The real numeric/numbers is further divided into two parts:

• Rational Numeric system
• Irrational Numeric system

I like to share this Lowest Common Multiple with you all through my article.

The rational numeric system is sub divided into further 4 parts namely:

• Natural numeric system
• Whole numeric system
• Integer’s numeric system

Irrational Numeric system:

Irrational Numeric system is not in the form of a/b i.e., if a number is there say 2.5 it can be written in fraction as 5/2 so it is not a irrational number as it is in the form of a/b. And with this we can say that this type of numeric system is not a perfect square, for e.g. `sqrt(15)` or `sqrt(17)` or any number which is not a perfect square comes in irrational numeric system.

Rational Numeric System:

Natural Numeric System: In natural numeric system we have all the natural numbers say 1,2,3....`oo` , these numbers are say increased by 1 and these does not include 0. These numbers are generally represented by 'N'.
Whole Numeric System:  In these type of numeric system we have numbers from 0,1,2,3....`oo`
Integer Numeric System: In these type of Numeric system we have numbers from -`oo`  to +`oo` , say ....-2,-1,0,1,2,... . These numbers inclue both positive and negative numbers. These are generally represented by 'Z'.
Fration Numeric System: In these type of numeric system we have a number in form of a/b, where a and b represents numerator and denominator resp. , e.g., 2/3 is fraction. These are generally represented by  'F'.

Best Way to Learn Probability

Introduction best way to learn probability:

The theory of best way of probability begins to develop for study of games of chance such as roulette and cards. The best way of probability used for not only games, probability also prevails in other walks of life such as commerce, financial system, and even in day-to-day daily activities. Systematic method for probability theory was introduced by French mathematicians Blaise Pascal and Pierre. In this article we shall discuss best way to learn probability with example problems.


Learn probability formula with example problems


Learn probability formula:

Probability P(E) =        Number of way the event happen
The total number of possible outcome of an event

Example 1: A spinner has 5 equal sectors colored blue, white, green, orange and red. Spinning the spinner, Find the probability of leading green color?

Solution:

The possible outcomes of these events are blue, white, green, orange and red.

P(green) = Number of way land green
Total number of colors

= `1/5.`

Example 2: A six sided unbiased die is rolled. Find the probability getting one? Find the probability of an even number rolling?

Solution:

P(E)  = Number of way to get a one
Total number of sides

P(getting number 1)    = 1.

Total number of sides = 6

Therefore probability   = `1/6.`

Example 3: A six sided unbiased die is rolled. Find the probability of an even number rolling?

Solution:

P(E)= Number of way to get even number
Total number of sides

P (getting even number) = 3.

Total number of sides    = 6

Therefore probability      = 3/6 = 1/2

Example 4: If a1 and a2 are two events related with a random experiment such that P(a2)=0.45, P(a1 or a2)= 0.75 and P(a1 and a2)=0.25, Calculate P(a1).

Solution:

Let P (a1) = x then,

P (a1 or a2) =P (a) + P (a2) – P (a1 and a2)

= 0.75 = x + 0.45 – 0.25

Sum the experiment value

x = (0.75-0.45 + 0.25) = 0.65

Hence P(a1) = 0.55.

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Learn probability with practice problem


Problem 1: A six sided unbiased die is rolled. Find the probability of an odd number rolling?

Answer: `1/2`

Problem 2: A spinner has 4 equal sectors colored blue, white, green, and orange. Spinning the spinner, find the probability of leading white color?

Answer: `1/4.`

LCD and LCM in Math

Introduction to math lcd and lcm:

In math, the lcd and lcm are terms used to perform the arithmetic operations in fraction. Expansion of lcd is least common denominator and expansion of lcm is least common multiple. Both are same in basic idea. The least common denominator is least denominator value in fraction addition. The least common multiple is a small number and it is divisible by all factors of number. The lcm s used in least common denominator calculation. The lcm is determined by the factorization method that is list out the multiples of number and find out the least value. Both lcd and lcm are defined in algebra math. We can get the detail description for least common denominator and least common multiple with example from online articles and tutorials.

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Math lcd and lcm


Least common multiples in math:

We can use the two methods for least common multiples determination.

Method 1:

List out the multiples of each numbers.
Find out the least value in that multiples.
Method 2:

List out the prime factors of each numbers. (For example, 6 – 2 x 3 and 12 – 2 x 2 x 3).
Count how many number of prime factors in each factorization. (Prime number 2 counts are three and prime number 3 count is 3).
Select the large count prime number. (2 x 3 x 2)
Multiply the selected prime numbers.(12)
Least common denominator in math:

The steps for least common denominator are same as above. Only difference is the value in fraction denominator.

Multiples of each number is listed.
Find the smallest number in multiples.

Example problems for lcd and lcm


Example 1: Find out the least common denominator of `2/6` and `1/18`

Solution:

Step 1:

Given fraction values are `2/6` and `1/18`

Step 2:

Find the multiples of numbers 6 and 18.

Multiples of number 6 is 12, 18, 24, 30….

Multiples of number 18 is 36, 54, 72…

Step 3:

Smallest number in list of multiples is 18.

Step 4:

The least common denominator of `2/6` and `1/18` are 18.

Example 2: Find out the least common multiple of 4 and 8.

Solution:

Step 1:

Given values are 4 and 8.

Step 2:

Find the multiples of 4 and 8.

Multiples of number 4 is 8, 12, 16….

Multiples of number 8 is 16, 24, 32…

Step 3:

Smallest multiple in list is 16.

Step 4:

The least common multiple of 4 and 8 is 16.

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Practice math problems for lcd and lcm:
1. Find out the least common denominator of `1/2` and `1/10` .

Solution: The least common denominator is 10.

2. Find out the least common multiple of 3 and 9.

Solution: The least common multiple is 9.

Study Learn Division

Introduction of study learn Division:
Study learns Division is the inverse of multiplication in the mathematics operation. It determines the how many times 1 value is consist of other. It can be expressed as x/0.where x is the dividend. Depends upon the arithmetic setting a well defined value can be assigned to the expression. Having problem with Examples of Rational Numbers keep reading my upcoming posts, i will try to help you.

We write division of 2 numbers as a/b, where a is the dividend and b is the divisor.

The division of 2 rational numbers, where the divisor is not equal to zero, results in another rational number.


Basic properties of study learn division:

A number which is divided by it is equal to 1.

A number which is divided by one is equal to the number itself.

Zero divided by anything is equal to zero. It is known as zero property.

Any number divided by 0 is undefined.


Example of study learns division:


1.To solve for dividing 8/4

Sol:

8/4=2

8 divided by 4 equal to 2

The answer is 2

2. To solve for dividing 12/6

Sol:

12/6=2

12 divided by 6 equal to 2

The answer is 2

3. To solve for dividing 5/2

Sol:

5/2 = 2.5

5 divided by 2 equal to 2.5

The answer is 2.5

4. To solve for 100/50

Sol:

100/50=2

100 divided by 50 equal to 2

The answer is 2

5. To solve for 50/2

Sol:

50/2= 25

50 divided by 2 equal to 25

The answer is 25

6. To solve for 100/25

Sol:

100 divided by 25 equal to 4

The answer is 4

7. To solve for 500/100

Sol:

500/100=5

500 divided by 100 equal to 5

The answer is 5

8. To solve for 1000/100

Sol:

1000/100=10

1000 dividing 10 equal to 10

The answer is 10

9. To solve for 500/50

Sol:

500/50=10

500 divided by 50 equal to 10

The answer is 10

10. To solve 1000/500

Sol:

1000/500=2

1000 divided by 500 equal to 2

The answer is 2

11. To solve for 15/5

sol:

15/5 =3

15 divided by 5 equal to 3

The answer is 3

12. To solve for 45/5

Sol:

45/5 =9

45 divided by 5 equal to 9

The answer is 9

Vriable of Math

Introduction to variable of math:

A variable is a symbol that stands for a value that may vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, i.e. completely fixed or fixed in the context of use. The concepts of constants and variables are fundamental to all modern mathematics, science, engineering, and computer programming. Please express your views of this topic Functions Math by commenting on blog.


Example problems of variable in math:


Variable of math problem 1:

James, Mickel and John are friends. James’s age is one-third of Mickel and John is five years elder than Mickel. If the sum of the age of the friends is 40, find the ages of each one.

Sol:

From the statement,

Age of Mickel= x

Age of James   `=x/3 `

Age of John = x+5

Sum of the ages=40.

`x/3 + x+x+5= 40`

`(7x+15)/3 =40`

Multiplying by 3 on both sides,

7x +15=120

Subtracting 15 on both sides,

7x=105

Dividing by 7 on both sides,

x=15

Therefore, age of James=15/3=5

Age of Mickel                 =15

Age of John                  =15+5=20

Variable of math problem 2:

Solve the following system:

x + y = 20

2x - y = 10

Sol:

We cay solve x aid y by using substitution method.

Given         x + y = 20……………. (1)

2x - y = 10……………... (2)

Solve the equation (1) for y,

x+ y= 20

Subtract to the value x on both sides,

y= 20-x ………. (3)

Substitute the value y into the second equation. They we get,

2x-(20-x) =10

2x-20+x=10

3x-20= 10

Add to the value 20 on both sides.

3x-20+20= 10+20

3x= 30

Divide by the value 3 on both sides.

x=10

Substitute the value of x into the equation (1).

10+y=20

Add the value -10 on both sides.

y= 20-10

y=10

Answer: x=10 and y=10

Variable of math problem 3:

Solve the equation 7(-5b - 3) - (5b - 4) = -6(4b + 6) + 3

Sol:

Given the equation 7(-5b - 3) - (5b - 4) = -6(4b + 6) + 3

First we can multiple the factor variables for both left and right hand side.

-35b - 21 - 5b + 4 = -24b - 36 +3

Here we can group the like terms on both sides.

-40b - 17 = -24b – 33

Add 20b+15 on both sides.

-40b-17+24b+33=0

-16b+16=0

Subtract 16 on both sides.

-16b= -16

Divide -16 on both sides.

`b= (-16)/-16`

` = 1`

Answer: b=1

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Practice problems of variable in math:


Find x: 5x+3x-6=74
Solve: 3(y -3) + 5z - 4(y -2z -3) + 8
Answer:

x= 10
13z-y+11

Math Division 10

Introduction math division 10:

In mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that is the inverse of multiplication.

Specifically, if c time’s b equals a, written:

`c * b=a`

Where b is not zero, then a divided by b equals c, written:

`a/b=c`

For instance,

`6/3=2`

Since

`2*3=6` .

In the above expression, a is called the dividend, b the divisor and c the quotient.

Source Wikipedia

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Math division 10 explanations:


Here we will see math division based on divisor 10

Example1:

The division process in based on divisor 10 is very simple to divide any number

50 apples to give 10 apples for each member how many members got this apple to find the answer for this problem?

Solution:

Step 1: the total number of apple is 50

Step 2: to give 10 apples for each member

Step 3: divide `50/10` we got the answer for this problem

10 ) 50 ( 5                              `5 *10=50`

50

----------

0

----------

Quotient is `5 ` the remainder is `zero`

We give `50 ` apples to `5 ` people

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Math division 10 practice problems:


Here we will learn about how to do the math division problem based divisor 10

Example1:

The ramu in hand 230 balls to fill in the bag. The each bag to cover only ten balls .to finds how many bag to need for fill the all balls?

Solution:

Step 1: the total number of balls `230`

Step 2; one bag contain ten balls

Step 3: to find how many bags to fill all balls

10 ) 230 ( 23

20

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

30

30

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

0

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

Example2:

In the each boat cover 10 peoples .the 12495 number of people in near the river   to cross the river in this side to another side. Find how many boats need for they are cross the river?

Solution:

Step 1; the total number of people in near the river `12495`

Step 2: the each boats cover 10 number of people

Step 3: to solve this problem to find the needed boats

3) 12495 (1249

10

-----------

24

20

-----------

49

40

-----------

95

90

-----------

5

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

Quotient is `1249 ` and Remainder is `5 ` so, we arrange one boat for `5 ` member

Needed boats for they are cross the river = 1250

Dividing Radicals

Radicals in algebra are defined as the roots of a number or a variable. It is denoted with a symbol like v. The number which is mentioned in the ‘v’ portion of the symbol is called as the index of the symbol and the number or the variable or an expression entered inside the symbol is called radicand.
The meaning is that if the radicand is multiplied by itself index number of times, the product is the number that represents the radicand. If the index is 2, then the radical is called a square root and if the same is 3, then it is referred as cube root.

Usually for square roots, the index 2 is not mentioned. Thus radicals a type of expressions and like any other expression they can also undergo basic operations.
A radical can also be expressed in equivalent exponential form, with a rational exponent.. In general, nth root of am is equivalent to am/n. This concept is used in dividing radicals with variables. For example, (x^2)/v(x) can be simplified as (x^2)/(x1/2), which is, as per exponential rules is equal to (x3/2). This can be switched back to the radical form and can be expressed as v(x^3).

Let us discuss how do you divide radicals in general. Consider a radical in rational form. The division is possible if the indices of both the numerator and the denominator are same. In such a case, we can express the division of the radicands inside one symbol of the same index.

For example, v(a)/v(b) = v(a/b), b ? 0. In many cases it is possible to simplify the fraction (a/b) and at times it may turn out to a perfect power and hence the answer may be an integer free from radical sign.
Let us explain the concept of dividing radical with some examples.
v(3)/v(7) = v(3/7). In this case, the fraction cannot be simplified and this is the final answer.
v(14)/v(7) = v(14/7) . In this case, the fraction can be simplified as 2 and the final answer is v(2).
Now let us consider this one. v(28)/v(7) = v(28/7). The fraction 28/7 can be simplified as 4, which is a perfect square of 2. Therefore, in this case the answer turns out to be an integer.

There is one more concept in radical divisions. Suppose you arrive at an answer with a radical in the denominator. Never leave it in that form.
Multiply both the numerator and the denominator by the a radical which will make the denominator in integer form. This is called rationalizing the denominator.

Math Terminalogy

Introduction to math terminology:

Mathematics use a lot of terms. Mathematics term contains some symbol representation. Symbolic representation is easy to remain. Mathematics can be divided into many branches. Every branch contains many terminals to represent the mathematical word. Now we see some terms only.

Example for mathematics operation:

• Addition
• Subtraction
• Multiplication
• Division

Math Terminology in Various Branches of Maths:


Now we see mathematical terms in various branches. They are

• Math terminology in number system
• Math terminology in arithmetic
• Math terminology in measurements
• Math terminology in complex numbers
• Math terminology in geometry
• Math terminology in algebraic geometry
• Math terminology in trigonometry
• Math terminology in sets and functions
• Math terminology in analytical geometry
• Math terminology in probability

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Math Terminology:


Math terminology in number system:

The following terms are involved or used in number system. Now we see the math term with symbolic representation.

Real numbers =R
Whole number =W
Natural numbers =N
Greatest common divisor =GCD
Least common multiple=LCM
Arithmetic Progression =A.P
Geometric progression=G.P
Math terminology in arithmetic:

• Ratio
• Proportion
• Percentage
• Profit
• Loss
• Square root
• Cube root
• Time and work
• Simple interest

Ratio: Ratio means contrast of two related quantities by division.

Proportion: Proportion is a sameness of two ratios.

Percentage: A percentage is a portion whose denominator is 100.

Profit: Profit= selling price- cost price

Loss: Loss=cost price-selling price

Math terminology in measurements:

• Length
• Density
• Mass
• Breath
• Area
• Volume
• Surface area
• Curved surface area
• Perimeter

Math terminology in complex numbers:

• Real numbers
• Imaginary numbers

Math terminology in geometry:

• Circle
• Cone
• Square
• Rectangle
• Triangle
• Angle
• Line
• Trapezium
• Rhombus
• Cylinder
• Slope
• Perpendicular
• Circumcenter

Math Terminology in Probability:

• Mean
• Median
• Mode
• Standard deviation
• variance

Math Terminology in Analytical Geometry:

• Conic
• Parabola
• Ellipse
• Hyperbola
• Locus
• Circle
• Line
• Center point

Math Terminology in Sets and Functions:

• Union
• Intersection
• Associative law
• Distributive law
• Demorgor’s law
• Symmetric relation
• Transitive relation
• Equivalence relation
• Into function
• Onto function
• One to one function:
• Many to one function
• Constant function
• Identity function

Math Terminology in Trigonometry:

• Sin
• Cos
• Tan
• Cosec
• Sec
• Cot

Math Terminology in Algebraic Geometry:

• Cartesian coordinate system
• Slope of line
• Equation of straight line
• Distance between two points

Learn How to Pass Algebra

Introduction to Learn Algebra:-

Algebra is the division of arithmetic that uses letters in place of some unknown numbers. Algebra is a cluster of mathematics, which is used to create mathematical problems of valid-globe actions and control problems that we cannot explain using arithmetic. Algebra uses the cipher as calculation for addition, subtraction, multiplication and division and it includes constants, operating signs and variables. Algebraic equations represent a collection, what is finished on one side of the range with a number to the other side of the range.This kind of algebra easy to learn and easy to pass also. I like to share this Equation with no Solution with you all through my article.


Learn topics to Pass algebraWe need to study the above topics to pass:-


algebra Exponential and Logarithms

algebra Absolute Value Equations and Inequalities

algebra Sequences and Series Combinatorial

algebra Advanced Graphing

Graphing Polynomials for algebra

Graphing Rational Functions

Exponents for algebra

Radicals for algebra

Polynomials for algebra

Factoring for algebra

Division of Polynomials for algebra

Solving Equations for algebra

Solving Inequalities for algebra

We need to learn the above topics to pass algebra.


Learn tips to pass algebra:-

Distributive Law of algebra

a (b + c) = ab + ac

a (b - c) = ab – ac

Combine like variables of algebra

2a + 3a = 5a

3x + 5 + 7x = 10x + 5

9y – 4y = 5y

6c – 2 – 2c = 4c – 2

Combine like variables and exponents of algebra

4x^2+ 3x^2= 7x^2

2x^2+ 3x + 2 + 4x^2+ 3x + 4 = 6x^2+ 6x+ 6

5x^2- 3x^2= 2x^2

7x^2+ 8x + 3 - 2x^2- 4x - 2

= 5x^2+ 4x + 1

Problem:

Solve for x : X/4=-2

Solution:

X*4/4=-2*4

x = -8

Solve for x

2 x + 2 = -18

Solution:-

2x + 2 - 2 = -18 – 2

2x = -20

2x/2=-20/2

x = -10

By go through the above problems and workout the following problems, you can pass algebra.

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Practice problems for algebra:-


1. Find factors and root of the equation x^2 - 10x + 24

Answer: -6, -4

2.Find factors and root of the equation x^2 -11x + 28

Answer: -4, -7

3. Find factors and root of the equation x^2 + 2x + 8

Answer: 4, -2

To pass algebra above practice problem we are going help through exam perpetration it mainly help to pass the algebra exams.

Free Algebra Answers

Introduction for learning free algebra answers:

Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. The Algebra executes the four basic operations such as addition, subtraction, multiplication and division. The most important terms for learning free algebra answers are variables, constant, coefficients, exponents, terms and expressions. In Algebra, besides numerals we use symbols and alphabets in place of unknown numbers to make a statement. Hence, Learning free algebra answers may be regarded as an extension of Arithmetic.

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Order of the operation for learning free algebra answers:


1. First, we have to evaluate the expressions within the parenthesis.

2. Next,  we have to evaluate the exponents.

3. Next, we have to evaluate the multiplication or division operations.

4. Finally, we have to evaluate the addition or subtraction operations.


Examples for learning free algebra answers:


Example 1:

3(a-2) + 10 = 0

Solution:

3(a-2) + 10 = 0

3a – 6 + 10 = 0

3a + 4 = 0

3a + 4 - 4= 0 – 4 (Add -4 on both sides)

3a = -4

3a / 3 = -4 / 3 (both sides divided by3)

A = -4 /3

Example 2:

5x - 10 = 15x - 20

Solution:

5x - 10 = 15x - 20

5x - 10 + 10= 15x – 20 + 10    (Add 10 on both sides)

5x =15x -10

5x – 15x =15x -15x  - 10 (Add  -15x on both sides)

-10x = -10

-10x / 10 = -10 / 10 (both sides divided by 10)

-x = - 1 which is equal to x=1

Example 3:

10x + 20 = 30

Solution

10x + 20 = 30

10x + 20 - 20 = 30 - 20 (Add -20 on both sides)

10x = 10

10x / 10 = 10 / 10 (both sides divided by 10)

x = 1

Example 4:

Solve the equation   |-25x + 50| -75 = -100

Solution:

|-25x + 50| -75 = -100

|-25x + 50| -75 + 75= -100 + 75(Add 75 on both sides)

|-25x + 50| = -25

|-25x + 50| is same as -25x + 50, now solve for x

-25x + 50= -25

-25x + 50= -25 - 50 (add -50 on both sides)

-25x=-75

-25x /- 25 = -75 / -25 (both sides divided by -25)

x = 1

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Practice problem for learning free algebra answers:


1. 4(x-6) + 15 = 1

Answer: x=2.5

2. 3x - 7 = 15x – 8

Answer: x=0.1

3. 2x + 8 = 3

Answer: x=-2.5

Learn Different Quadrilaterals

Introduction of quadrilateral:  We know that on combining three non-collinear points in pairs, the figure so obtained is a triangle. Now, let us mark four points and see what we obtain on combining them in pairs in some order. Such a figure formed by combining four points in an order is called a quadrilateral. In a quadrilateral, a pair of opposite sides is parallel. I like to share this Slope Intercept Formula with you all through my article.




Definition of Quadrilateral and its types:


Definition of Quadrilateral:   Quadrilateral is a geometrical figure that consists of f our end points called verticals joined to each other by straight-line segments or sides called edges. The quadrilateral are classified depends on the length of side, angle and diagonals of object.

Methods of Quadrilateral:

Parallelogram

Square

Rectangle

Rhombus

Trapezium

Kite

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Types of Description of quadrilateral:


Parallelogram:     Parallel lines are lines are the exactly same distance between two lines that has never cross. A couple of lines of quadrilateral that are parallelograms that you may already know about are squares and rectangles.

Formula:

Area = b × h sq. units (b – Base, h - Height)

Square:    The square is a parallelogram having an angle, equal to right angle and adjacent sides equal. Parallel lines are lines are exactly the same length and height that has never cross.

Formula:

Area = a2    (a - area)

Rectangle:     Parallel lines are the same distance between their two lines and that has never cross. Probably those angles know about a couple of lines quadrilateral that also called as parallel sides and four right angles.

Formula:

Area = l × b sq. units

Where

l – Length

and b – breadth)

Trapezoid:    A quadrilateral should have at least one pair of parallel sides. The quadrilateral one side of opposite sides are parallel if non parallel of opposite sides of a trapezoid are congruent it is called as isosceles triangle.

Formula:

Area = 1 / 2 (a + b) × h sq. units.

Rhombus:     All the four sides of this quadrilateral are equal. Rhombus is a parallelogram having its adjacent sides equal but more of whose angles is a right angles.

Formula:

Area = 1 / 2( d1 × d2) sq. units

Where

d1, d2 are diagonals.

Kite:    A quadrilateral with two pairs of equal sides and hence only one pair of equal angles. The longer one bisects its diagonal. The area of the kite is equal to the product of its diagonals.

Formula:

Area = 1 / 2 * d1 * d2

Where

d1, d2 are diagonals.

Learn Divisor

Introduction to learn divisor:

In learning divisor many students undergo difficulties in it. They find difficulty in multi-digit divisor. To overcome that we should be careful in selecting the numerals, so it may help the students a lot  with the divisor learning–and also from the arithmetic operations used from the divisor. They have to group the numbers when they multiply the numerals with the quotient of the divisor. Please express your views of this topic What is a Divisor by commenting on blog.


Definition of Integers in learn divisor:


The divisor is the digit that the dividend is divided by (in long division). The dividend divided through divisor is known as the quotient (plus a remainder).

One of two or more integers that can be exactly divided into another integer, the number by which a dividend is divided. What does n|m mean? It explains n divides m. For an example 5|10, or 5 divides 10. Do you know when n divides m or when n is a correct divisor of m? I think you do. Understanding List of Composite Numbers is always challenging for me but thanks to all math help websites to help me out.


Let’s see an example on learn divisor:


1)10 divides 20 or 10|20, we know..

The value twenty is divided by ten is written as two x two x five.

The value ten can be written as two x five

20 = 2 X 2 X 5 = 2^2 X 5 and

10 = 2 X 5

2) But 15 does not divides 20,

The value twenty cannot be divide by 15

20 = 2^2 X 5 and

15 = 3 X 5

3) Then why does 10 divide 20 but not 15 ?

We already know, 20 = 2^2 X 5

15 does not divide 20 for the reason that, 15 contains a prime factor ( 3) which is not exist in 20.

Likewise, 14 does not divides 20 as it contains a prime factor (7) which is not exist in 20.

Note that, 14 = 2 X 7

4) Again, 8 does not divides 20. Why?

20 = 2^2 X 5

8 = 2^3

Do you get it? 8 do not include any prime factors which do not exist in 20, then why does 8 not divide 20?

Answer is very easy; just have a close look at the power of 2.

Learn About Algebraic Expressions

Introduction to learn about algebraic expressions:

The Expressions are a central concept in algebra. A variable can take various types of values. Its values are not fixed. Otherwise, a constant has a fixed value. We combine variables and constants with operations this forms the algebraic expressions. For this, we can use the operations of addition, subtraction, multiplication and division. We have already known some simple algebraic expressions like y + 3, p – 5, 4a + 5, 10y – 5a and so on. The above expressions were formed by combining variables with constants.


Learn about Terms of an Expression


When terms have the same algebraic factors, they are like terms. When terms have different algebraic factors, they are unlike terms. For example, in the expression 5xy – 8x + 7xy – 17.

Learn about Like terms:

5xy and 7xy because the factors of 5xy are 5 and x and y. and factors of 7xy are 7 and x and y both factors are same. So these are like terms.

Learn about Unlike terms:

The terms 5xy and –8x, have different algebraic factors. They are unlike terms. Similarly, the terms, 5xy and -17 are unlike terms. Also, the terms –8x and -17 are unlike terms.

Learn about Coefficient of the Term:

The numerical factor is said to be the numerical coefficient or simply the coefficient of the term. The above example the coefficient of x is -8.

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Learn about Kinds of Expressions


Monomial Expression:

An expression with one term is called a monomial. For example, 5pq, 10z,

Binomial Expression:

An expression, it contains two unlike terms is called a binomial. For example,

a + b, b – 5

Trinomial Expression:

An expression, it contains three terms is called a trinomial. For example, the expressions p + q + 17, a b + a +b

Polynomial Expression:

An expression with one or more terms is known as a polynomial. Thus, a monomial, a binomial and a trinomial are all the type of polynomials. For Example: 4x^3+x^2+7x+2

Factoring Quadratic Polynomials

Introduction:

In algebra, the sum of a countable number of monomials is referred as  a polynomial. The way of writing a polynomial as a product of two or more simpler polynomials is referred as factorization.
The process of factorization is also known as the resolution of factors. Factoring quadratic polynomials is one of the basic operations of polynomials. The process of factoring the quadratic expression ax^2 + bx +c is explained below: Looking out for more help on Factor a Polynomial in algebra by visiting listed websites.

Method of factoring quadratic polynomials:


Let us consider the coefficients a, b and c as integers and a is not equal to 0. When the coefficients a, b and c satisfy certain conditions, the quadratic expression ax^2 + bx +c can be factorized.

First, we consider a simpler case with a = 1 and b and c as integers.Now, we have to factorize  x^2 + bx + c. We try to write the integer constant term c as a product of two integers p and q such that p + q = b. If we find solution in our attempt, then

x^2 + bx + c  =  x^2 + (p + q)x + pq

=  (x^2 + px) + (qx + pq)

=  x(x + p) + q(x + p)

=  (x + p) (x + q)

General Rule for factoring quadratic polynomials : If the constant term c of quadratic expression x^2 + bx + c can be expressed as a product of two integers p and q such that the sum p + q is the coefficient b of x, then x^2 + bx + c = (x + p)(x + q).

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Example for factoring quadratic polynomials


An example for factoring quadratic polynomials is given below:

1) Factorize x^2 + 5x + 6.

Step 1 : Possible factorization of 6 is    6 = 1 x 6

6 = 2 x 3

Step 2 : Sum of factors are                      1 + 6 = 7

2 + 3 = 5

Step 3 : Factorization:

Now we need to compare the coefficient of x and the sum of the factors. We find that the sum of the factors 2 and 3 is the coefficient of x. The factorization of quadratic expression is explained below:

x^2 + 5x + 6   =   x^2 + (2 + 3)x + 6

=   (x^2 + 2x) + (3x + 6)

=  x(x + 2) + 3(x + 2)

x^2 + 5x + 6  =  (x + 2) (x + 3)

Continuous Probability Learning

Introduction to continuous probability learning :

Definition: Learning to define continuous probability of an event occurs when the one or more events occurred. Consider any two probabilities A and B. when the event A occur and it depends on the other event which is already occurred then we can say the conditional probability of above two events are P(A | B). Learning  conditional probability of events using the following formula :

`P((A)/(B))=(P(A U B))/(P(A))`

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Learning to solve conditional probability problems 1:


Learning some problems to find the conditional probability.

Pro 1:Consider a population, the probability a men life at least 70 years is 0.70 and is 0.65.if he won’t live more than 80 years. If a man is 70 years old, find the conditional probability that he will survive on 80 years. If A subset of B then P (A U B) = P (A)

Solution:Let us take A is the event that he lives to 70 years and B is the event that he will live at least 80 years.

So given that P (B) = 0.55 and P (A) = 0.70

So Conditional probability P (`(B)/(A)) = ( P (A U B)) / ( P (A))`

The given condition is P (A and B) = P (B) = 0.65

Conditional probability P (`(A)/(B)` ) = `(0.65)/(0.70)`

P (`(A)/(B)` ) = 0.9286

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Learning to solve conditional probability problems 2:

A box contains red and blue marbles. We are choosing two marbles without replacement. Probability of choosing red and blue marbles is 0.45 and choosing the red marbles on the first draw is 0.57. Find the probability if the second marble is blue if the first one is red?

Solution:Probability of choosing red and blue marbles is 0.45

Probability of choosing red in the first draw is 0.57

So probability of choosing second marble ids blue then the probability is

P (`(Blue)/(Red) = ( P ( Red and Blue))/ (P(Red))`

P (`(B)/(R)` ) = `(0.45)/(0.57)`

P (`(B)/(R)` ) = 0.79 = 79 %

How to Learn Geometry

Definition:

Geometry is the defined as the study of the size, shape and position of 2 dimensional shapes and 3 dimensional figures. However, geometry is used daily by almost everyone. Geometry begins with undefined items, definitions, and assumptions; these lead to theorems and constructions. It is an abstract subject, but easy to visualize, and it has many concrete practical applications. Please express your views of this topic What is a Acute Angle by commenting on blog.


Geometrical objects:

Point

A point is the most fundamental object in geometry. It is represented by a dot and named by a capital letter. A point represents position only; it has zero size

Line

A line can be thought of as connected set of infinitely many points. It extends infinitely far in two opposite directions. A line has infinite length, zero width, and zero height. Any two points on the line name it. The symbol ↔written on top of two letters is used to denote that line. A line may also be named by one small letter

Collinear points

Points that are lie on the same line are called collinear points. If there is no line on which all of the points lie, then they are non-collinear points.

Plane

A plane has an infinite set of points forming a connected flat surface extending infinitely far in all directions. A plane has infinite length, width, and zero height (or thickness). It is usually represented in drawings by a four-sided. A single capital letter is used to denote a plane. The word plane is written with the letter so as not to be confused with a point . Is this topic How to find Area of a Circle hard for you? Watch out for my coming posts.


Postulates:

Postulate 1: A line contains at least two points.

Postulate 2: A plane has at least three non-collinear points with it.

Postulate 3: If we cross through any two points, there is exactly one line.

Postulate 4: If we cross through any three non-collinear points, there is exactly one plane.

Postulate 5: If two points lie in a plane, then the line joining them lies in that plane.

Postulate 6: If two planes intersect with each other, then their intersection is a line.