What is Stratified Random

Introduction:

Stratified random is the process of set of members of the population which having  uniform subgroups  of sampling. In the stratum there is equally exclusive, all elements are considered in  one stratum in the process of population. In the stratum there is jointly exhaustive, population element is not presented. Stratified random can create a strong mean better  than the arithmetic mean for random sample. This process is simple sample statistics.


Strategies of Stratified Sample Statistics:


What is Stratified random?

Stratified sample statistics is the method to know what probability sampling in statistics .
The stratified sample statistics having proportional sample statistics.
In this separating the population into uniform subgroups and taking a sample random sample from each sample groups.
This process is simple sample statistics.
What are Choosing Stratified Sample Statistics?

The population having number of N elements.
The population is separated into H group which is known as strata.
All part of the population should be assigned to one of the stratum.
The number of annotations within every stratum Nh noted as total of all notations.
The researcher contains a probability sample from every stratum.

Examples:


Let us consider an examples,

Example1:

Let us see what is meant by Stratified random,

If the total population consists of 60% of gents and 40% ladies then the relative size of the above population  is 3 ladies and 2 gents .It will reflect the proportion.

Example2:

Let us see what is meant by Stratified random,

Let us consider worker’s of one company we are separate them into number of subgroups. There are three categories, which includes Managers, Team leaders and Staffs (Employees).Here Team leaders and Employees are relatively small percentage. If we did simple random fractions where total population n =200 in the sampling fraction of 20%. We can imagine 20 and 15 persons from the strata.

Growth Factor Math

Introduction to growth factor math:

Growth factor in math article deals with the definition of growth factor math and the model problems related to growth factor.

Definition of growth factor math:

Growth factor is defined, as the constant value that is multiplied by it self over a certain period.the growth factor is always a positive number. Growth factor cannot be represented in percentage.

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Formula to growth factor math:


When the growth rate is given

Increase in value = P* G*N

P is the principle or original value.

G is the growth rate.

N is the period.
Growth factor is calculating by dividing the increased value by original value

Growth factor = `(("increased value")/("original value" ))`


Model problems to growth factor math:


Problem: 1

What is growth factor of the original value $600 over a period of 7 years with the growth rate of 6%.

Solution:

The original value is $600

Period of time = 7 years

Growth rate is 6%

The increase value is `(600*7*(6/100))`

(6*7*6)

= 252

The increased value is $852

Now we have to calculate the growth factor:

Growth factor =` (("increased value")/("original value"))`

= `(852/600)`

= 1.42

The growth factor is 1.42

Problem: 2

What is growth factor of the original value $400 over a period of 9 years with the growth rate of 8%.

Solution:

The original value is $400

Period of time = 9 years

Growth rate is 8%

The increase value is `(400*9*(7/100))`

(4*9*7)

= 252

The increased value is $652

Now we have to calculate the growth factor:

Growth factor = `(("increased value")/("original value"))`

= `(652/400)`

= 1.63

The growth factor is 1.63


Problem: 3 what is growth factor of the numbers behind the numbers 30, 60, 120, 240,480

Solution:

To find the growth, we have to divide the previous value by present value

(60/30) = 2
(120/60) =2
(240/ 120)= 2
(480/240)=2


Here the growth factors between the numbers are 2

The growth factor of the number is 2

Math Grade 4 Fraction

Introduction for math grade 4 fraction:
A fraction is a part of a whole. Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator.

Numerator
denominator

In a fraction, if the numerator is smaller than the denominator, it is called as proper fraction. Proper fractions are in completely reduced form. If the numerator is bigger than the denominator, this type of fractions is called as improper fractions. If a fraction is constructed by a whole number and a proper fraction is called as mixed fraction.

For example, `4/5` is a proper fraction (4 < 5)

`6/2 ` is an improper fraction (6 > 2)

2 `1/3 ` is a mixed fraction (2 is a whole number, `1/3 ` is a proper fraction)


Math 4 grade fraction – Methods and example problems:


Math 4 grade fraction - Adding fraction and adding unlike denominator:

Math 4 grade fraction- Addition fraction - Steps and problem:

To add algebraic fraction, follow these steps:

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

` 2 / 5` + `8 / 5`

Solution:

`2 / 5` + `8 / 5`

= `(2 + 8) / 5`

= `10 / 5`

= 2

Math 4 grade fraction - Adding fraction involving unlike denominator – Steps and problem:

1. Express the fraction as equivalent fraction by finding the lowest common denominator (LCD) (the least numbers into which the denominator of two or more fractions will go evenly).

2. Add the numerator and place the sum over the lowest common denominator.

Example:

`5 / 6` + `4 / 3` =?

Solution:

These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two fractions, before adding them together.

For the denominators here, the 6 and 3, a common denominator for both is 6. LCD = 6

`5 / 6` = `5 / 6`

` 4 / 3 ` = `8 / 6`

`5 / 6` + `8 / 6 ` = `(5 + 8) / 6`

Answer = `13 / 6`

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Math 4 grade fraction - Subtracting fraction and subtracting unlike denominator:


Math 4 grade fraction - Subtraction fraction - Steps and problem:

To subtraction algebraic fraction, follow these steps:

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

`8 / 3 ` – `4 / 3`

Solution:

` 8 / 3` – `4 / 3`

= `(8-4)/3`

= `4 / 3`

Math 4 grade fraction - Subtracting fraction unlike denominator - Steps and problem:

1. Express the fraction as equivalent fraction by finding the lowest common denominator (LCD).

2. Subtract the numerator and place your answer over the lowest common denominator.

Example:

`15 / 4` – `6 / 2 ` =?

Solution:

These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two fractions, before subtracting them together.

For the denominators here, the 4 and 2, a common denominator for both is 4. LCD = 4

` 15 / 4 ` = `15 / 4`

`6 / 2` = `12 / 4`

` (15 / 4) ` – `(12 / 4) ` =  ` (15-12) / 4`

Answer = `3 / 4`

Matrice De Math

Introduction to matrice de math:
In mathematics, Matrix (plural: Matrices) is defined as the rectangular arrangements of elements in a rows and columns arranged with in the square brackets. The entries may be any type of elements such as numbers, polynomials and expressions. In math matrices can be expressed in terms of capital alphabetical letters.  Examples of matrices de math are:

A = `[[1,2,3, 1st row R1],[4,5,6, 2nd row R2],[7,8,9, 3rd row R3],[1st col,2nd col,3rd col,.],[C1,C2,C3,.]]`

Note:

Horizontal arrangements are called rows of the matrix.
Vertical arrangements are called column of the matrix.

Order of the matrix:


By using the number of rows and columns the order of the matrix is calculated. For example in the above mentioned matrix number of row is three and number of column is three. Hence the order of the above said matrix is 3 x 3.


Operations of matrix:

The operations of matrices are

Addition
Subtraction
Matrix multiplication
Transpose

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Examples of matrices:


Example 1:

If A =`[[1,2,1],[2,1,2],[2,2,1]]`and B =`[[3,2,1],[2,1,4],[3,5,1]]` .Then find A + B, A - B, A x B and AT.

Solution:

A + B = `[[1,2,1],[2,1,2],[2,2,1]]`+`[[3,2,1],[2,1,4],[3,5,1]]`

= `[[4,4,2],[4,2,6],[5,7,2]]`

Note:

Same order of the matrix can be added. The resultant matrix should also be the same order of matrix. Similarly, for subtraction.

A – B = `[[1,2,1],[2,1,2],[2,2,1]]` - `[[3,2,1],[2,1,4],[3,5,1]]`

=  `[[-2,0,0],[0,0,-2],[-1,-3,0]]`

Matrix multiplication:

A x B = `[[1,2,1],[2,1,2],[2,2,1]]` x `[[3,2,1],[2,1,4],[3,5,1]]`

=  `[[3+4+3,2+2+5,1+8+1],[6+2+6,4+1+10,2+4+2],[6+4+3,4+2+5,2+8+1]]`

=  `[[10,9,10],[14,15,8],[13,11,11]]`

Note:

Different order of matrices can be multiplied. If matrix A of order p x q is multiplied with the matrix B of order q x r, then the resultant matrix is p x r.

Matrix Transpose:

A   = `[[1,2,1],[2,1,2],[2,2,1]]`

AT = `[[1,2,2],[2,1,2],[1,2,1]]`

Note:

Interchanging rows into columns and columns into rows is known as transpose of the matrices de math.

These are the concepts on matrices de math.

World Math Word Problems

Introduction to world math word problems:

In mathematics education, the term word problem is often used to refer to any mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. As word problems often involve a narrative of some sort, they are occasionally also referred to as story problems and may vary in the amount of language used.(Source - Wikipedia )

In this article of world math word problems, we are going to discuss some word problems on world math.

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Examples for World math word problems:


Example 1:

At a car park there are 70 vehicles, 40 of which are trucks, 25 are buss and the remainder are vans. Find the probability of

a) Bus leaving first.

b) Van leaving first.

Solution:

a) Let S be the sample space and A be the event of a bus leaving first.

n(S) = 70

n(A) = 25

Probability of a bus leaving first:

P(A) = 25/70 = 5/14

b) Let B be the event of a van leaving first.

n(B) = 70 – 40 – 25 = 5

Probability of a van leaving first:

P(B) = 5/70 = 1/14

Example 2:

Three times the larger of two numbers is three more than the three times the smaller, and the sum of three times the larger and four times the smaller is 73. Find out the numbers.

Solution:

Let x be the larger number and y be the smaller number.

Three times the larger = 3x

Three more than the three times the smaller = 3y + 3

Relationship:  3x = 3y + 3

Three times the larger = 3x

Three times the smaller = 4y

Relationship: 3x + 4y = 73

Now, we have two equations

3x = 3y + 3

3x + 4y = 72

From the first eqn,substitute the value of 3x in the second eqn

The equation will be,

3y+3+4y = 73

7y + 3 = 73

7y = 70

y = 10

Plug in y = 10 in the equation

3x = 3y + 3

3x = 3(10) + 3

3x = 30 + 3

x = 11

Larger number x  = 11

Smaller number y = 10.

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Additional World math word problem:


Example 1:

A side of a large tent is in the shape of an isosceles triangle whose area given is 22.5 m2 and whose base is four feet shorter than its height. Find the height of the tent.

Solution:

Height of the side   =  x

Base of the side      =  x – 4

Area of the triangle  = `<< 1/2>>` b * h

22.5  = `<< 1/2>>` ( x - 4 ) * x

22.5  = `<< 1/2>>`   x^2 - 4 x

45  =  x^2 - 4 x

x^2 - 4 x - 45 = 0

x^2 - 9x + 5x - 45 = 0

x ( x -9 ) + 5( x - 9 ) = 0

( x - 9 ) ( x + 5 )  = 0

( x - 9 ) = 0  and ( x + 5 ) = 0

x  = 9  and  x = - 5

Height of the tent x = 9 feet.

Square Root in Math

Introduction to square root in math:

In math, we use a radical symbol which is known as square root. Square root is also said to be as radical and the radical symbol is (sqrt). Rubicund is referred to a number which is present inside the root (i.e. sqrt (x), here x is referred as rubicund). Square root math is deals with the different properties of expressing square root by using various calculations. Let us see what properties of square root in math briefly.

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Different properties of square root in math:


Different properties of square root in math are described below,

General expression with exponent and radical:

`^nsqrt (a) ^m`   =`(^nsqrt (a)) ^m`   = (`a1/n) ^m ` = `am/n`

Multiplication property for radical expression: `^nsqrt (ab)` = `(^nsqrt (a))` ` (^nsqrt (b))`

Division property for radical expression: `(^nsqrt (a/b))` = `(^nsqrt (a))` / `(^nsqrt (b))`

Example for square root in math:


Example for square root in math: Add: `(8 * sqrt (2))` `-` `(6 * sqrt (2)) ` `+ ` `(9 * sqrt (2))`

Solution: Unite like terms by adding together the numerical coefficients.

`(8 - 6 + 9) * sqrt (2)`

` (17 - 6) * sqrt (2)`

After adding together, we get the answer like,

` 11 * sqrt (2)`

Answer: `(8 * sqrt (2))-(6 * sqrt (2)) + (9 * sqrt (2)) = 11 * sqrt (2)`

Example for square root in math:   Simplify, `sqrt (64)` `+ ` `sqrt (8)`

Solution: Take the given question and split the terms like,

`Sqrt (4 * 16)` `+ ` `sqrt (2 * 2 * 2)`

Rewrite the square root by using product of square root theorem.

`sqrt (4) * sqrt (16)` `+ ` `sqrt (2) * sqrt (2) * sqrt (2)`

`sqrt (2)* sqrt (2)* sqrt (4)* sqrt (4) ` `+` `sqrt (2) * sqrt (2) * sqrt (2)`

To simplify even further we use the definition of square root,

`(2 * 4) + 2(sqrt (2))`

Simplify by adding like terms to get the answer.

`(8 + 2(sqrt (2)))`

Simplify: `sqrt (64) + sqrt (8) = (8 + 2(sqrt (2)))`

Practice problem for square root in math:

Example for square root in math:` (^3sqrt (729))`

Answer: cubic root of (729) = `9^3`

Example for square root in math: `(^4sqrt (1296))`

Answer: fourth root of (1296) = `6^4`

Example for square root in math: `(sqrt (1225))`

Answer: (sqrt (1225))= 35

Point Math Term

Introduction to point math term:

The zero-dimensional object is called as point and it is defined the objects in space in math term. It is also referred as simple geometric concepts. The term point is represented in n-dimensional space and it is specified by dot. It give the exact position of object on surface. The diameter of point is 0.2 mm.

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Explanation for point in math


Math Euclidean geometry:

Euclidean geometry has a framework for point representation and in Euclidean space ordered pairs are called as point. The ordered pairs are represented as (x, y).  Here x is represent the horizontal axis number and y represent the vertical axis number.

In three-dimensional space, the ordered pairs are represented as (x, y, z) and z is represent the depth. The straight lines are created by connect the points in math. The key for point construction is postulates by Euclid.

Other branches of math:

The point-set topology is explain the topological space by point. The noncommutative geometry and pointless topology is fundamental of notion term.

The points arranged in some order and create a higher dimensional geometry like line, plane and space. These are considered as basic structures in geometry.

Coordinates of a point:

In two-dimensional plane, the position of point is defined by ordered pairs in math. The term coordianates is express the location of objects in two dimensional plane.These coordinate points are plotted in xy axis.

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More about point term


Decimal point term:

The decimal point is one type of number representation. This is define the place value of numbers like tens, hundreds and so on. For example the multiplication of 0.2 x 2 = 0.4 here 0.2 and 0.4 are decimal value.This is used in decimal expansion.

Fixed point:

The function’s fixed point is mapped to itself.If the real number is proceed with function and get the same number as output means that real number is called as fixed point. Here the number is considered as point.

Prime Numbers Math

Introduction to Math prime numbers:

In mathematics, a prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. The first twenty-five prime numbers are:

Prime Numbers:- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Condition: - If x is the prime number then the next factors of the number x is 1 and X.(Source:Wikipidea)


Prime numbers in math:


To finding a prime number up to hundred is very easy. Suppose we need to find above 100 means it is just difficult. So let us follow the short cut method.

For example:
Authenticate if 149 is prime number.

Step 1:

Now we have to take Square root for 149 = 12.20
Now rounding the value 12.20 to the nearest big whole number. We can write 12.20 as 13.

Step 2:

Then find the Prime Numbers below 13. The factors up to 13 are 2, 3, 5, 7, 11 and 13.

Step 3:
The given number 149 is not divisible by 2, 3, 5, 7, 11 and 13.
So the number 149 is considered as prime number.

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Example problems for math prime number:


Problem 1:

Find the number 71 is prime number or not?

Solution:

The given number 71 is a prime number. Why means it includes two factors 1 and 71 only. So the given number 71 is a prime number.

Problem 2:

Find the number 101 is prime number or not?

Solution;

The given number 101 is divisible by one and itself only. So it is called as prime number.

Problem 3:

Work out the number 39 is prime number or not?

Solution:

The given number 39 includes more than 2 factors. This is 1, 6, 13 and then 39. Thus the given number 39 is not a prime number.

Problem 4:

Work out the number 434 is prime number or not?

Solution;

The given number 434 includes more than 2 factors. This is 1, 2, 7, 31, 217, and then 434. Thus the given number 434 is not a prime number.

Problem: - 5

Work out the number 638 is prime or not?

Solution:

The given number is 638 divided by 2. So the factors for 638 are 1, 2, 11, 29,    319 and 638. Thus the number is not a prime number.

Practice problem for math prime numbers:

Problem 1:

Find the number 97 is prime or not?

Solution:

The given number 97 is a prime number.

Problem 2:

Find the number 178 is prime or not?

Solution:

The given number 178 is not a prime number.

Math 24 Solutions

Introduction to Math 24 Solutions:

The four basic operations in math are subtraction, addition, division and multiplication. The simplifications can be performed using the above operations. Simplifying can be expressed in the form of algebraic expression. The solution can be obtained with decomposing numbers or else written as one’s, ten’s, hundred’s, and thousands, etc. Let us see about how to solve a math 24 solution.


Example Problems using Place Values in Math


Decomposing numbers is one of the methods used to determine the solutions for given problem.

Example 1:

Decompose the number 24.

Solution:

Step 1:

Let us write the given problem as 24.

Step 2:

Split up into (2) and (4).

Step 3:

24 = 2 ten’s + 4 one’s.

Step 4:

Write the digits in the same place values in the given problem.

Write 2 in the ten’s place and 4 in the one’s place.

Example 2:

Add the given numbers.   24

Solution:

Let us write the numbers one by one.

2
4
----------
6
---------

Solution for adding 24 is 6.

Example 3:

Subtract the given numbers 24.

Solution:

The highest number should be subtracted by the lowest number in the subtraction.

The number 4 should be subtracted by 2.

4
2
-----------
2
-----------

Solution for subtracting 24 is 2.



Worked Examples to Practice for 24 in Math

Example 4:

Multiply 24

Solution:

Multiply 2 × 4

2 ×

4

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

8

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

The solution for multiplying 2 × 4 is 8.

Example 5:

What solution will you obtain by adding 11 + 13?

Solution:

11

13

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

24

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

The solution for adding 11 + 13 is 24.

Example 6:

What solution will you obtain by subtracting 87 – 63?

Solution:

87

63

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

24

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

The solution for subtracting 87 – 63 is 24.


More Problems to Practice for Math 24 Solution


1. Add 9 and 15.

Key: 24

2. Subtract 98 and 74.

Key: 24

3. Add 7 and 17

Key: 24

4. Subtract 83 and 59

Key: 24

Search How To Do Math

Introduction  for  math:

In this article we are going to discuss search how to do math. Actualy math rolls a major part in our life  we should know how to search the math techniques when we need.  We can search our needed math topics in internet. There are many web sites are available in internet and we can search our required topics ,if we know how to do the math concepts then seacrching is very simple to get solutions.

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Example Problems for math problems:


search math  problem 1

Add the two fractions `5874/547` and `8745/547`

Solution:

The given two fractions `5874/547` and `8745/547`

Step1: The given two fractions

= `5874/547` + `8745/547`

Step2: Now we need to find the sum of  `5874/547` and `8745/547`

=`(5874+8745)/547`

step3:The sum of 5874 and 8745 is 14619

=`14619/547`

search math  problem 2

Add the two numbers 1346 and 1557

Solution:

The given two numbers 1346 and 1557

We need to find the two numbers

By adding 1346 and 1557

We get 2903

So the answer is 2903

search math  problem 3

Multiply the fraction `1360/168` and `1450/190`

Solution:-

Given we need to multiply fractions `1360/168` and `1450/190`

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

Here a = 1360, b = 168, c= 1450, d=190.

= `(axxc)/(bxxd)` . =`(1360xx1450)/(168xx190)` by solving it we get

A =`1972000/31920`

=`493/798`

search math  problem 4

Multiplying two numbers 2614 and 215

Solution:

The given two numbers 2614 and 215

We need to find the product of two numbers

By Multiplying 2614 and 215

We get 562010

So the answer is 562010

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Few More Example Problems for math problems


search math  problem 5.

Subtract the two fractions `3285/350` and `4494/350`

Solution:

The two given fractions are`3285/350` and `4494/350`

Step1: The given two fractions

`3285/350` - `4494/350`

Step2: Now we need to find the differences of `3285/350` and `4494/350`

`(3285-4494)/350`

Step3: The difference of 3285 and 4494 is -1209

=-`1209/350`

search math  problem 6

Subtract the two numbers 4654 and 5387

Solution:

The given two numbers 4654 and 5387

We need to find the differences of two numbers

By differences 4654 and 5387

We get -1333

So the answer is -1333

Math Study Guide Notes

Introduction to math stude guide notes:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.(SOURCE : WIKI)

Math study guide notes:

Algebra learners with low arithmetic knowledge require special instruction.

Do again learners need something new to hold their attention

Learners need Math Study Knowledge.

Learner with disabilities benefit from multi-modality instruction.

Math Study Guide Notes - Homework:

Ten Steps to Doing Math study guide notes Homework

Analysis related textbook material.
Analysis appropriate lecture notes.
Entire homework carefully complete.
Mark all problem steps.
Value reasons for problem steps.
For hard problems repeat 1 -5 and analysis like problems, call another student, use other references, and see a tutor or teacher.
Conclude by working a problem successfully.
Remember main concepts.
Formulate note cards for difficult concepts.
Do not get behind.
Ten Steps to Doing Online math study guide notes Homework

Analysis related textbook material.
Analysis appropriate lecture notes.
Perform homework efficiently.
Mark all problem steps.
Realize basis for problem steps in its place of using the click and go method.
For difficult problems use the resources provided by the software (videos /tutor line).
Finish by working a problem successfully.
Remember important concepts.
Develop virtual note cards by using www.tutorvista.com
Don’t get behind you could get block out.

Math Study Guide Notes - Taking the Test


Ten Steps for taking a Math Study Guide Notes Test:

Memory Data Dump
Analysis Test
2Nd Memory Data Dump
Test Progress Schedule
Answer Easy Questions
Skip Difficult Questions
Analysis Skipped Questions
Guess at Remaining Questions
Analysis All of the Test
Use all the Test Time
Six Types of Test-taking math study guide notes Errors:

Misread Directions
Sloppy Errors
Concept Errors
Function Errors
Test Procedure Errors
Learning Errors
Math study guide notes – Example Problem:

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Example for expanding number:

Expanded form to understand expanded form better, one needs to be good at place value

Consider the number 543 arrange the digits in a place value chart as shown below

Hundreds Tens Ones

5             4        3

Solution:

From the chart above, we see that:

The value of 5 is 5 x 100      = 500

The value of 4 is 4 x 10       = 40

The value of 3 is 3 x 1         = 3

Therefore, the expanded form of the number 543 is 500 + 40 + 3.

10th Grade Math Level

Introduction to 10th grade math level:
In the 10th grade math level, the students will learn various topics. Some of the topics related to 10th grade math level includes algebra, pre-calculus, trigonometry, geometry etc. Various problems available under these branches. Here we are going to discuss about some of the problems in 10th grade math level. The example problems for 10th  grade math level with detailed solutions are given below.


Example problems for 10th grade math level:


Example 1:

Solve the following equation using quadratic formula:

x^2 - 7x + 12 = 0

Solution:

Identify a, b and c

a = 1, b = -7 and c = +12

Quadratic formula is` X = (-b +- sqrt (b^2 - 4ac))/ (2a)`

substitute the a, b and c values in quadratic formula

`x` = ` (-(-7)+ sqrt((-7)^2 -4(1)(12)))/(2 xx 1) `

`x` = `(-(-7)- sqrt((-7)^2 -4(1)(12)))/(2 xx 1)`

` x` = `(7 + sqrt (1))/2` = `8/2`

`x` = `(7 - sqrt (1))/2`  = `6/2`

x = 4  or  x = 3

Example 2:

Solve  the equation ( 7x−1)2 − 49 = 0.

Solution:

Applying square root method: (7x − 1) 2 = 49

7x − 1 = `sqrt49` or 7x - 1 = − `sqrt49`

7x − 1 = 7     or  7x − 1 = −7

Solve equations:

7x −1+1= 7+1 or 7x -1+1= -7 +1

7x = 8 or  7x = −6

x = `8/7` or x = − `6/7`

Additional problem for 10th grade math level:


Example:

Solve the linear equation y = x + 10 and  4x + y = 60

Solution:

Given first order linear equation is y = x + 10 and  4x + y = 60

Here,

y = x + 10 -------- (1)

4x + y = 60 ------------ (2)

Substituting equation 1 in equation 2, we get

4x + x + 10 = 60

After simplification, we get

5x + 10 = 60

Subtracting 10 on both the sides, we get

5x = 50

Dividing by 5 on both the sides, we get

x = 10

Substituting the value of x = 10 in equation 1, we get

y = x + 10

y = 20

The answer is x = 10 and y = 20

Math 20 What Is It

Introduction to Math 20 what is it:

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 20 what it is in this article.


Example Problems for Math 20 what is it


Using Addition Operation in Math

Example 1:

Add 20 and 60?

Solution:

Let us add the given problem.

Write the given whole number 20 first and then write the given whole number 60 second one by one.

20 (addend)

(+)   60 (addend)

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

80

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

The sum for adding 20 and 60 is 80.

Using Subtraction Operation in Math

Example 2:

Subtract 20 and 10?

Solution:

Let us subtract the given problem.

Write the given whole number 20 first and then write the given whole number 10 second one by one.

20 (minuend)

(-)   10 (subtrahend)

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

10 (difference)

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

The difference for subtracting 20 and 10 is 10.

Using Multiplication Operation in Math

Example 3:

Multiply 20 and 8?

Solution:

Let us write the given problem as in the below form. Here, 20 is multiplicand and 8 is multiplier.

20 ×

8

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

160

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

The product for multiplying 20 × 8 is 160.

Using Division Operation in Math

Example 4:

Divide 20 by 10?

Solution:

Let us write the given problem is in form of 20 ÷ 10 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 10 goes into 2 or not. The number 10 cannot go into 2. So that takes the dividend as two digit number. Now the divisor 10 goes into 20 for 2 times.

10)20(2

0

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

20

20

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

0

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

The quotient for dividing 20 by 10 is 2.

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Practice Problems for Math 20 what is it


1. Add 20 and 140.

Key: 160

2. Subtract 20 and 5.

Key: 15

3. Multiply 20 and 5.

Key: 100

4. Divide 20 by 5.

Key: 4

Third Grade First Math

Introduction about third grade first math:

In this article we are going to discuss the third grade first math solving problems. Third grade first math solving problems is easy to understand and solve. Third grade first math solving problems involves basic addition, subtraction, multiplication and division problems. Third grade first math solving problems are given below.

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Third grade first math Example problems:


Example 1:

Add (1) + (2) =?

Solution:

The sum of positive number is a positive number obtained by adding the two numbers.

1 + 2 = 3

The addition solution is 3.

Example 2:

Subtract (5) – (2) =?

Solution:

To subtract a digit from another digit, add the additive number of the second number to the first number.

5 – 2 = 3

The subtract solution is 3.

Example 3:

Multiply (17) * (5) =?

Solution:

The product of two positive numbers is a positive number.

17 * 5 = 85

The multiple solutions are 85.

Example 4:

Divide `60/20`

Solution:

Positive number/ positive number = positive value

`60/20` = 3

The division solutions are 3

Example 5:

Which is bigger? `5/7` and `6/7`

In fraction, Bigger the numerator, bigger the fraction:

So `6/7` is the bigger fraction.

Example 6:

Determine the factor for 50

Solution:

Given number 50

50 contain the prime factor of 2, 5 and 5. It has a multiplicity of 1.

50 = 2 * 5 * 5

Solution: Factor for 50 = 2 * 5 * 5

Example 7:

Simplify 37.62 – 14.05 + 15.467 – 27.108

Solution:

To simplify the following steps

a)      First add the positive numbers

b)      Add the negative numbers

c)      Find the difference

d)     Put the sign of the greater number

Add the positive number of 37.62 + 15.467 = 53.087

Add the negative number of (-) 14.05 + (-) 27.108 = (-) 41.158

The difference between 53.087 – 41.058 = 11.929

The sign of greater number is positive, so, solution is positive 11.929

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Third grade first math practice problems:


Problem 1: Add (5) (7) =?

Choice:

a)      12

b)      13

c)      11

d)     2

Problem 2: Sub (5) (2) =?

Choice:

a)      7

b)      10

c)      3

d)     2

Problem 3: Multiply (5) (3) =?

Choice:

a)      15

b)      8

c)      2

d)     10

Problem 4:

Divide (10) (5) =?

Choice:

a)      15

b)      5

c)      2

d)     8

Answer key:

Problem 1: a

Problem 2: c

Problem 3: a

Problem 4: c

What R The Math Properties

Introduction of math:

Math is defined as the learning of quantity, structure, space and transform. Math is evaluated from counting, computation, measurement, and systematic learning of the forms and movements of physical entities by the use of abstraction and logical idea. Math is used in the world as an main tool in various areas, such as natural science, engineering, medicine and the social sciences. Today all the functions is based on problematic mathematics.

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Important math properties:


The properties of math are already defined by the mathematician who is very knowledge about the mathematics. Let we learn about properties of math. These properties are very useful for all the levels of people.

Let us consider p, q, r are real numbers.

Commutative Property:

It defines the altering the order of the values but without altering the result.

It is given by,

Addition: p+q =q+p

Multiplication: p*q = q*p

Example:

Find the value of 32*5 and prove the commutative property value is equal.

Solution:

Given 32*5

=32*5= 160

Commutative property: 5*32=160

Hence, two results are similar by the commutative property.

Associative Property:

Associative property defines that combining of element within the parenthesis. It is defined for addition and multiplication and more than three elements present in it.

It is given by,

Addition: p+(q+r) = (p+q)+r

Multiplication: p*(q*r) = (p*q)*r

Example:

Find the value of 32+(12+4) and 32(12*4) using associative property.

Solution:

Given 32+(12+4)
Associative property: (32+12)+4

=44+4

=48

Given 32(12*4)
Associative property: (32*12)4

= 384*4

= 1536

Distributive property:

It defines distributing something. It is given by,

Addition: p*(q+r) = pq+pr

Subtraction: p*(q-r) = pq – pr

Example:

Find the value of 15*(12+3) using distributive property.

Solution:

Given 15*(12+3)

Distributive property: (15*12) + (15*3)

= 180 + 45

= 225

Additive Identity Property:

Zero is known as identity. If the value that is added with 0 the final result is same as given value. It is given by,

p + 0 = p and 0 +  p = p

Multiplicative Identity Property:

If the value that is multiplied with 0 the final result is zero. It is given by,

p * 0 = 0 and 0 *  p = 0

Additive Inverse Property:

It is defined as if the value that is added with inverse of the same value the result is 0. It is given by,

p + (-p) = 0

Multiplicative Inverse Property:

If the value is multiplied with inverse of the same value the result is 1.

p * (1/p) = 1

Now all are understand the properties of math. Now learn some other properties.

Is this topic Graphing Linear Equations hard for you? Watch out for my coming posts.

Some more math properties:


Reflexive Property of Equality:

It is defined as reflection, that is p=p.

Symmetrical Property of Equal:

It is given by p=q then q=p

Transitive Property of Equal:

It is given by, if p = q and q = r, then r = p

Substitution Property:

If p = q, then q can replace p in any equation.

Subtraction:

p - q = p + (-q)

Division:

0 / p = 0, p / p = 1, p / 0 = infinity

Now all are clear about the math properties.

Math 222 Solution

Introduction to Math 222 Solution:
The four basic operations in math are subtraction, addition, division and multiplication. The simplifications can be performed using the above operations. Simplifying can be expressed in the form of algebraic expression. The solution can be obtained with decomposing numbers or else written as one’s, ten’s, hundred’s, and thousands, etc. Let us see about how to solve a math 222 solution.


Example Problems using Place Values in Math

Example 1:

Decompose the numbers 222.

Solution:

Step 1:

Let us write the given number 222.

Step 2:

Split up into (2) (2) and (2).

Step 3:

2 hundred’s + 2 ten’s + 2 one’s

Step 4:

Place the digit as it is in the above step.

Put 2 in the hundred’s place, 2 in the ten’s place and 2 in the one’s place.

Example 2:

Add the given numbers.

222

Solution:

Let us write the numbers one by one.

2

2

2

----------

8

----------

The solution for adding the given numbers is 8.

Example 3:

Subtract the given numbers 222.

Solution:

Subtraction can be performed from the highest number to the least number.

Step 1:

The number 2 can be subtracted from 2.

2

2

-----------

0

-----------

Step 2:

The number 2 can be subtracted from the number 0.

2

0

----------

2

-----------

The solution for subtracting 222 is 2.


More Examples to Practice for 222 in Math


Example 4:

Multiplying

1 × 111 × 2

Solution:

Step 1:

Multiplying first 1 × 111

1 ×

111

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

111

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

Step 2:

Multiplying the third term with the above result you obtained from the step (1).

111 ×

2

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

222

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

The solution for multiplying 1 × 111 × 2 is 222.

Example 5:

What solution will you obtain by adding 121 + 101?

Solution:

121

101

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

222

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

The solution for adding 121 + 101 is 222.

Example 6:

What solution will you obtain by subtracting 1085 – 863?

Solution:

1085

863

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

222

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

The solution for adding 1085 – 863 is 222.

Grade 6 Math Fractions

Introduction for grade 6 math fractions:

A fraction is a part of a whole. Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator. The numerator of a fraction is the number that shows how many equal parts of the, whose are taken.

Numerator
denominator

A mixed number is the sum of a whole number and a proper fraction. This sum is implied without the use of any visible operator such as "+"; for example:

2 + `3 / 4` = 2 `3/4`

An improper fraction as a way to write a mixed number, consider the 2 `3/4` . A complex fraction is a fraction in which one or both of the terms are fraction or mixed number, as in example `3/4` / 6

(Source: Wikipedia)


Grade 6 math fractions – Mixed number as improper fraction and examples:


Grade 6 math fractions - Express mixed number as improper fractions:

Procedure: To express a mixed number as an improper fraction

Multiply the whole number by the denominator.
Add the numerator to obtain the numerator of the improper fraction.
The denominator is the same as that of the original fraction.
Example problems:

Express 5 `2/3 ` as an improper fraction

Solution:

Multiply the whole number by the denominator.

Add the numerator to obtain the numerator for the improper fraction.

= `(5*3+2)/3` = `(15 + 2) / 3`

The denominator is the same as that of the original fraction.

Answer = `17 / 3`

Grade 6 math fractions - Expressing improper fraction as mixed numbers:

Procedure: To express an improper fraction as a mixed number

Divide the numerator by the denominator
Example problems:

Express the following improper fractions as mixed numbers

`13 / 4` = 3 `1/4`
`46 / 3` = 14 `4/3`
`522 / 8` = 65 `2/8`

Grade 6 math fractions - Adding, subtracting fractions and unlike denominator:


Grade 6 math fractions - Adding and subtracting fractions steps:

Steps for adding and subtracting fractions:

To add and subtract algebraic fraction, follow these steps:

Write the given fraction make sure the fraction have common denominator.
Add or  subtract the numerators values.
The result give Solution for the problem
Adding fraction -Example:

(`3 / 2` ) + (`7 / 2` )

= `(3 + 7) / 2`

= `10 / 2`

= 5

Subtracting fraction - Example:

(`9 / 4` ) – (`3 / 4` )

= `(9 - 3) / 4`

=  ` 6 / 4`

=  `3 / 2 `

Grade 6 math fractions – Adding and subtracting unlike denominator fraction steps:

To adding and subtracting fraction that have unlike denominator, follow these steps:

1. Express the fraction as equivalent fraction by finding the lowest common denominator (LCD) (the least numbers into which the denominator of two or more fractions will go evenly).

2. Add and subtract the numerator and place the sum over the lowest common denominator.

Adding unlike denominator fraction -Example:

`7 / 4 ` + `8 / 2 ` =?

Solution:

For the denominators here, the 4 and 2, a common denominator for both is 4. LCD = 4

` 7 / 4` = `1 / 4`

` 8 / 2 ` = `16 / 4`

` 7 / 4 ` + `16 / 4 ` = `(7 + 16) / 4`

Answer = `23 / 4`

Subtracting unlike denominator fraction - Example:

`11 / 4` – `3 / 2` =?

Solution:

For the denominators here, the 4 and 2, a common denominator for both is 4. LCD = 4

`11 / 4` = `11 / 4`

`3 / 2 ` = `6 / 4`

(`11 / 4` ) – (`6 / 4` ) =  ` (11-6)/4 `

Answer = `5 / 4` .

Define a Function in Math

Introduction to the Functions

The functions are defined as mathematical thoughts that get one or more variable and make a variable. In math, a function connects a few domains onto a few varieties. For everything in the area, there is a corresponding item in the range of the function. The domains are inputs and all ranges are feasible to the all outputs.


Types of Functions


In math,every item in the field corresponds to a particular item in the collection of the define function. Thus the domain is all of the possible inputs to the function and the variety is all of the possible outputs. Every item in the domain corresponds to a particular item in the range.However, an item in the range may communicate to several items in the domain.The type of  functions are defines as follows.

Composite function
Monotonic functions
Even and Odd functions
Periodic functions
Inverse functions
Linear, Quadratic, and Cubic functions

Explanation


In math, some of the function explanation defines as follows.

Composite function

Composite function in math, the output of a one function is an input of another function. So here the composition of functions is R1→R1. That is a real number as an input and a real number as an output. The notation for this is (fοg) (x) =f (g(x)), the output of g(x) turn into the input of f(x) and is defines as (fοg)(x). The actual example, let’s use f(z)=z2+2*z-2 and g(z)=3*z+2.

The same sort of limitations is also made for the monotonic no-decreasing and monotonic non-increasing functions, only the rules leading the derivative’s domain are not strict inequalities.
Inverse function

General Procedure for finding the inverse of a function is interchanging the variables.

Example

Take y=6x+10.First we will swap the variables. We can do this one since we desire to locate the function that goes the further mode, by mapping the old range onto the old domain. So our new equation is x=6y+10.

Solve for y

6y+10=x

6y=x-10

y =(x-10)/6

Intersect in Math Term

Introduction to Intersect in Math Terms

In math,the set X,Y and Z are the set of all elements of X, Y and the elements are also in Z is called the intersection set. That is one element available in all groups. The intersect in math term represented by the symbol of n. We can select the common element form that group. The intersect made in between two or more sets. We can draw the venn diagram in this intersect math term. Here we see the examples.

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Example 1


Find the intersect values from the following sets.

A={1,2,4,5,6} B={3,4,6,7,8}

Solution

The given sets are A={1,2,4,5,6}

B={3,4,6,7,8}

Now we find the intersect. That is the common values in the above sets.

The 4,6 is the common element in the above two sets.

So the AnB = {4,6}


Example 2


X={12,14,16,18,20} Y={10,13, 15,13,18} Z={12,13,18,20,21}

Find out the following intersect in math terms.

i)XnYnZ

ii)XnY

iii)XnZ

Solution

The given set is X={12,13,16,17,20} Y={10,13,15,13,18} Z={12,15,18,20,21}

i) XnYnZ

There is no common element from the above 3 sets.

So XnYnZ = {}

This is known as null set or empty set.

ii)XnY

The common elements from the above X and Y sets are 13

So XnY = {13}

iii)XnZ

The common elements from the above X and Z sets are 12 and 20.

So XnZ={12,20}

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Example 3


A={5,6,7,8} B={6,7,9,10}C={7,9,11,12}.Find the followingiin math term.

i)A-(BnC) ii) B-(AnC)

Solution

i)A-(BnC)

First find the BnC

BnC ={7,9}

Now find the A-(BnC)

We can take the numbers from A which is not in BnC.

The number is 5, 6, and 8

So the A-(BnC)={5,6,8}

ii) B-(AnC)

First we will find the An C

The common elements are in A and C is 7.

An C={7}

Now find the B-(AnC)

We take the element from B which is not in AnC.

So B-(AnC) = {6, 9,10}

Math Times and Division

Introduction for math times and division:

In algebra basic arithmetic operation (addition, subtraction, multiplication, and division) widely used in day to day life. In these articles we are going to see about math times and division.

Multiplication (symbol ‘x’) is the mathematical operation of scaling one number by another; it is one of the four basic operations in elementary arithmetic. Multiplication is a product of number of two numbers. It is another name is times. I like to share this Define Dividend with you all through my article.

Division is an arithmetic function, which is the opposed process of multiplication. From the process of division, the proportion or ratio of two numbers be capable of be calculated. Otherwise, the process of decision how many periods of one number is included in a further one. Symbol of division is ‘/’ or ‘÷’.

If we divide a number by another number, then

Dividend = (Divisor * Quotient) + Remainder


Math times and division – Times example problems:


Problem 1:

Erin can run 603 meters in one minute. How far could she run in 8 minutes?

Solution:

Erin can run 603 meters in one minute

She runs in 8 minutes.

= 613 times 8   (613 * 8)

= 4904

So, the answer is 4904meters

Problem 2:
Jessie wants to mail out 36 copies of her resume on special paper. Her resume is 6 pages long. How many sheets of the special paper does she need?

Solution:

Jessie wants to mail out 38 copies of her resume on special paper

Her resume is 6 pages long.

= 36 times 6

= 216

216 sheets of the special paper does she need.

Problem 3:

Jordan plans to read 174 pages on each day of his vacation. His vacation is 13 days. How many pages will he read during his vacation?

Solution:

Jordan plans to read 184 pages on each day of his vacation.

His vacation is 13 days.

= 174 times 13

= 2262

2262 pages will he read during his vacation.

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Math times and division– Division Example problems:

Problem 1:

Emily has 798 eggs stored in boxes. If they are 57 boxes, how many eggs must go in each box?

Solution:

Emily has 798 eggs stored in boxes.

They are 57 boxes.

= 798 ÷ 57

= 14 eggs

14 eggs must go in each box.

Problem 2:

There are 3328 tickets in Brenda's ticket collection. If the tickets are organized into 52 groups, how big is each group?

Solution:

There are 3328 tickets in Brenda's ticket collection,

If the tickets are organized into 52 groups,

= 3328 ÷ 52

= 64 tickets.

5th Grade Math Probability

Introduction to 5th grade math probability:

The 5th grade math probability is the mathematics. This is used to find the expected value of the combination possibles. The 5th grade math probability is the number of possible outcomes is divided into the total number of outcomes. This is called the 5th grade math probability. I like to share this Math Probability Problems with you all through my article.

Probability = `"(Number of possible outcomes)"/ "(Total number of possibles)"`


5th grade math probability Examples:


Coins Problems:

5th grade math probability - Example 1:

Suppose a word chosen at random from a person X has a character missing with probability 0.1, has a letter inserted with probability 0.2, and contains both kinds of error with probability 0.05. What are the probabilities that a script chosen at random

P (missing or inserted, but not both) = 0.25 - 0.05 = 0.2

5th grade math probability – Example 2:

Toss four coins and find the probability of all tails. The possible outcomes are:

Solution:

Step 1:

n (s) = {TTTT, TTTH, TTHT, TTHH, HTTT, HTTH,THHT, HTHH, THTT, TTHH, THHT, HTHH, HTHT, HTHH,HHHT, HHHH }=16

Step 2:

There are 4 tosses with only two tails:

n (a) = { TTTT}=1

Step 3:

Formula:

P (A) = n(a)/n(s)

Answer:

P (A) = 1/16.

Convert into a decimal 0.0625

The probability of two tails is 0.0625 or Rounded 6%.

5th grade math probability Example 3:

To toss a coin finds to get one head of the possible outcomes

Solution:

Step 1:

n (s) = {T, H}=2

Step 2:

Tossing a coin with only one head:

n (a) = {H}=1

Step 3:

Formula:

P (A) = n(a)/n(s)

Answer:

P (A) = 1/2.

Convert into a decimal 0.5

The probability of one head is 0.5 or Rounded 50%.

Dice Problems:

5th grade math probability Example 4:

Roll a single dice; find the probability of get number 1.

Solution:

Total Number of possible = n (a) = {1, 2, 3, 4, 5, 6}

n (s) = 6

The number of outcomes n (a) = {1}

n (a) = 1

The probability of getting value = 1/6.

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Practice problems for 5th grade math probability:


1.     Roll a single dice; find the probability of get number 1.

Answer:

1/6

2. To toss a coin finds to get one head of the possible outcomes

Answer:

1/2 or 50 %

Linear Equations Math

Introduction to linear equations in math:

A linear equations is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one or more variables. Linear equations occur with great regularity in mathematics. The general form of the liner equation is y =mx +b. Otherwise it can be written as ax + by=c. Here we are going to how to solve the liner equation in math and its example problems. (Source from Wikipedia)


Solving method for linear equations in math:


Elimination method
Substitution method

Example problems for solving linear equations in math:


Example: 1

Solve the following liner equation using elimination method 2x+3y = 5 and x + y = 2

Solution:

2x+3y = 5 -----------------------1

x + y = 2 -------------------------2

Multiply equation(2) by 2, we get

2x + 2y = 4 ----------------------3

Take equation 1 and 3 subtract equation 3 from 1 we get

2x+3y = 5

2x + 2y = 4   (change the sign and add)

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

y = 1

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

Now we have to find the x value

Substitute y value in to the equation 1 we get

2x + 3y = 5

2x + 3 (1) = 5

2x + 3 = 5

Add both sides -3 we get

2x + 3 - 3 = 5 - 3

2x = 2

Divide both sides 2 we get

x = 1

Therefore the solution of the given liner equation is x = 1 and y = 1

Example: 2

Solve the following liner equation using substitution method

x+4y = 10

x+12y = 20

Solution:

x+4y = 10 ----------------------- 1

x+12y = 20 ----------------------2

Form equation 1 we can write

x = 10 - 4y -----------------------3

Substitute the x value into the equation 2

10-4y+12y = 20

10 + 8y = 20

Add both sides -10

8y = 20-10

8y = 10

y = `10 / 8`

y = `5/4`

Substitute y value into equation 3 we get

x = 10 – 4`(5/4)`

x = 10 -`20/4`

x = `(40 - 20) / 4`

x = `20/4`

x = 5

Therefore the solution of the given liner equation is x = 5 and y =` 5/4`

What is a Quotient in Math

Introduction to what is a quotient in math:-

In mathematics, a quotient is the result of a division. For example, when dividing 6 by 3, the quotient is 2, while 6 is called the dividend, and 3 the divisor. The quotient can also be expressed as the number of times the divisor divides into the dividend.Let us see about some example problems about division.(Source : Wikipedia)


Example problems for what is a quotient in math:-


Problem 1:-

Solve 427÷13 by using long division method.

Solution:-

In the following Step by step process of how to divide

Step 1:-

-------
13| 427

In the above equation 13 is divisor and 427 is dividend. In the divisor has two decimal numbers put the value dividend of 42.

Step 2:-

3
-------
13| 427
39
---------
37

In 13 x 3 = 39 the divisor number 13 is multiplied with 3 to get an answer 39. In 37 is less than from 42.So use the value then subtract the value and get 37.

Step 3:-

32
-------
13| 427
39
---------
37
26
----------
11

In 13 x 2 = 26 the divisor number 13 is multiplied with 2 to get an answer 26. In 26 is less than from 37.So use the value then subtract the value and get 11.

Step 4:-

32.8
-------
13| 427
39
---------
37
26
----------
110
104
----------
6

The value 11 has no more value in the right side. So put 0 to get 110 and put decimal point on the quotient. Then normal division 13 x 8 = 104 the divisor number 13 is multiplied with 8 to get an answer 104. In 104 is less than from 110.So use the value then subtract the value again we get 6.

Step 5:-

32.84  --------> (Quotient)
-------
13| 427
39
---------
37
26
----------
110
104
----------
60
52
------------
8 (continued)

Repeat the step again the value 6 have no more value in the right side. So put 0 to get 60 and put decimal point on the quotient. In math normal division 13 x 4 = 52 the divisor number 13 is multiplied with 4 to get an answer 52. In 52 is less than from 60.So use the value then subtract the value again we get 8. Finally we get the quotient 32.84.


Problem 2:-

Solve 325÷15 by using long division method.

Solution:-

In the following Step by step process of how to divide

Step 1:-

______
15| 325

In the above equation 15 is divisor and 325 is dividend. In the divisor has two decimal numbers put the value dividend of 32.

Step 2:-

2
-------
15| 325
30
----------
25

In 15 x 2 = 30 the divisor number 15 is multiplied with 2 to get an answer 30. In 30 is less than from 32.So use the value then subtract the value and get 25.

Step 3:-

21
-------
15| 325
30
---------
25
15
----------
10

In 15 x 1 = 15 the divisor number 15 is multiplied with 1 to get an answer 15. In 15 is less than from 32.So use the value then subtract the value and get 10.

Step 4:-

21.6
---------
15| 325
30
---------
25
15
----------
100
90
----------
100

The value 10 has no more value in the right side. So put 0 to get 100 and put decimal point on the quotient. In math normal division 15 x 6 = 90 the divisor number 15 is multiplied with 6 to get an answer 90. In 90 is less than from 100.So use the value then subtract the value again we get 10.

Step 4:-

21.66  --------> (Quotient)
-------
15| 325
30
---------
25
15
----------
100
90
----------
100
90
-----------
10  (continued)

Repeat the step again the value 10 have no more value in the right side. So put 0 to get 100 and put decimal point on the quotient. Then normal division 15 x 6 = 90 the divisor number 15 is multiplied with 6 to get an answer 90. In 90 is less than from 100.So use the value then subtract the value again we get 10. Finally we get the quotient is 21.66.

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Practice problem for what is a quotient in math:-


Problem 1:-

Solve 524÷12 by using long division method.

Answer: - 43.66

Problem 2:-

Solve 33÷7 by using long division method

Answer: - 4.714

Problem 3:-

Solve 63÷3 by using long division method

Answer: - 21

Problem 4:-

Solve 86÷4 by using long division method

Answer: - 21.5

Problem 5:-

Solve 210÷6 by using long division method

Answer: - 35

Range Math Term

Introduction to Range Math Term:

In math term range is a difference between the maximum and minimum value in the set of numbers or elements. In math term, group of numbers or elements is called set. A set can have finite number of elements. There are two steps to find the range the range of set of numbers.

Step 1: Arrange the numbers in ascending order by size.

Step 2: Subtract minimum value by maximum value.

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Range Math Term - Examples


Example 1: Find the range of set of numbers: {18, 28, 30, 49, 54, 62, 31, 32, 59, 25}

Solution:

Arrange the set of numbers in ascending order

{18, 25, 28, 30, 31, 32, 49, 54, 59, 62}

Range = Maximum value – Minimum value

= 62 – 18 = 44

Therefore range of set of numbers is 44.

Example 2: Find the range of set of numbers: {36, 42, 47, 55, 21, 52, 122, 156, 260, 140}

Solution:

Arrange the set of numbers in ascending order

{21, 36, 42, 47, 52, 55, 122, 140, 156, 260}

Range = Maximum value – Minimum value

= 260 – 21 = 239

Therefore range is 239.

Example 3: Ten student’s weight is as follows {35, 45, 85, 74, 96, 46, 73, 60, 55, 60}. Find the range.

Solution:

Arrange the set of numbers in ascending order

{35, 45, 46, 55, 60, 60, 73, 74, 85, 96}

Range = Maximum value – Minimum value

= 96 – 35 = 61

Therefore range of ten student’s height is 61.

Example 4: Ten student’s heights as follows {133, 120, 160, 170, 170, 140, 165, 142, 135, 158}.  Find the range of set of numbers:

Solution:

Arrange the set of numbers in ascending order

{120, 133, 135, 140, 142, 158, 160, 165, 170, 170}

Range = Maximum value – Minimum value

= 170 – 120 = 50

Therefore range of ten student’s height is 50.

Example 5: Find the range of set of numbers: {7.52, 5.25, 3.65, 9.47, 8.52, 9.60, 6.29, 3.20, 5.68, 2.34}

Solution:

Arrange the set of numbers in ascending order

{2.34, 3.2, 3.65, 5.25, 5.68, 6.29, 7.52, 8.52, 9.47, 9.6}

Range = Maximum value – Minimum value

= 9.6 – 2.34 = 7.26

Therefore range of set of numbers is 7.26.

Example 6: Twelve students’ marks in math as follows {35, 43, 98, 99, 73, 81, 65, 95, 37, 42, 46, 57}. Find the range of set of numbers:

Solution:

Arrange the set of numbers in ascending order

{35, 37, 42, 43, 46, 57, 65, 73, 81, 95, 98, 99}

Range = Maximum value – Minimum value

= 99 – 35 = 64

Therefore range of set of numbers is 64. Having problem with Find the Median keep reading my upcoming posts, i will try to help you.


Range Math Term - Practice


Problem 1: Ten students’ marks in math as follows {31, 53, 75, 49, 77, 46, 59, 74, 99, 25}

Find the range of marks.

Answer: 74

Problem 2: Find the range of set of numbers: {27, 27, 25, 27, 22, 52, 24, 40, 25, 92}

Answer: 70

Problem 3: Find the range of set of numbers: {1.45, 2.27, 6.25, 2.47, 6.52, 21.6, 12.9, 31.3, 25.87, 2.04}

Answer: 29.85

What are Functions in Math

Introduction for functions in math:

A math function is a one of the type of relation. In a function, number 2 ordered pairs can have the same first element and a different second element. That is, for a functions, corresponding to every 1st element of the ordered pairs, there must be a different 2nd element. i.e. In a function we can't have ordered pairs of the form (a1, b1) and (a2, b2) with a1 = a2 and b1 ? b2. It is called as function. Types of functions and example problems are given below.

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Types of functions in math:


Let us see about some important math functions types are given below.

1. Into function:

A function f: A ? B is said to be into function if its range is a proper subset of its co-domain.

Let f: A ? B, where A = {a, b, c}, B = {p, q, r, s} be defined by f(a) = p, f(b) = q, f(c) = r. Then the range of f is {p, q, r}, a proper subset of B `=>` f is an into function.

Let g: C ? D where C = {6, 1, 3, 4} and D = {m, n, p} be defined by g(6) = p, g(1) = p, g(3) = p and g(4) = p. Then g is into as its range {p} is a proper subset of D `=>` g is an into function.

2. Onto function:

A function from A to B is said to be an onto function if its range is equal to its co-domain B. In other words, f is called ‘onto’ if every element of B has a Preimage in A.

For example:

(i) Let A = {1, 3, 4, 5} and B = {3, 6,7}, f(1) = 6, f(3) = 3, f(4) = 7 and f(5) = 6. Evidently the range of f is B and is onto.

(ii) Consider g : C ? D where C = {3, –3, 4, –4} and D = {9, 16} and g(3) = 9, g(–3) = 9, g(4) = 16, g(–4) = 16. Evidently g is onto.

3. One to one function:

A function f from A to B is called an one to one function (one – one function) if for a, b ? A, where a ? b, we must have f(a) ? f(b). Here the domain and the range of f will have the same cardinality.

For example:

(i) Let f : A ? B where A = {a, b, c}, B = {–1, 2, 3, 5} f(a) = 5, f(b) = –1, f(c) = 3. Then f is one to one. Note that the range of f is a subset of B and so f is into. We call such functions as one to one into.

(ii) Let g: C ? D where C = {3, 5, 7} and D = {4, 6, 8} be defined by g(3) = 4, g(5) = 6, g(7) = 8. Then g is one to one and the range of g is equal to the co domain D. So g is onto. We call such functions as one to one onto.

4. Constant function:

A function f from A to B is called a constant function if every element of A has the same image in B.

Let A = {4, 5, 6, 7}, B = {7, 8, 10} and if f : A ? B is defined by f(4) = 10, f(5) = 10, f(6) = 10 and f(7) = 10 then f is constant function. I have recently faced lot of problem while learning algebra 2 math help, But thank to online resources of math which helped me to learn myself easily on net.


Example problem for functions in math:


Example problem:

Given A = {a, b, c, d}, B = {p, q, r, s} and if f : A ? B is defined as below find the type of the function:

(i) f = {(a, p), (b, p), (c, q), (d, r)}

(ii) f = {(a, q), (b, q), (c, q), (d, q)}

(iii) f = {(a, p), (b, q), (c, r), (d, s)}

Solution:

(i) Since a, b are mapped to p ? B and the element s of B has no Preimage in A, it is many to one and into function

(ii) All the elements of A are mapped to the similar element q ? B. Hence it is a constant function. It is also many to one.

(iii) Because all the images are different and no element in B is left out without any Preimage, f represents a one to one and onto function.

Word Math Problems

Introduction to Word sums math problem

The Word sums math problem are can be expressed in algebraic or equation format. The word problems can be specified in simple form. Here also algebra concept is helped to do the word sum math problems. Algebra is an important part in mathematics which is used to find unknown variables by using the known variable. Let we see about the words sum math problems. Having problem with free algebra 2 answers keep reading my upcoming posts, i will try to help you.


Solved Examples in word sums math problem


Example 1 in word sums math problem
A Boy crosses an 800 m long street in 4 minutes. What is his speed in km per hour?

Solution: First we  have convert the algebra word problem to a numerical form to get the solution.

800

Speed = _____ * 60

4

m/sec = 5 m/sec

Now convert the m/sec to km/hr

= ( 5 * 120/4 )

= 150 km/hr

Example 2 in word sum math problem :
Maria has 12 cars and 16 Venus. How many cars does she have?

Solution:

Let P = Total number of cars
The sum of 12 cars and 16 Venus is equal to the total number of cars . It translates the problem into an equation.
P = 12 + 16

Solve this equation.
Let P = Total number of cars

P = 28.

There are 28 total numbers of cars

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Some more Solved Examples in word sums math problem


Example 3 in word sums math problem
There were 88 apples in each enclosure. 44 such enclosure of apples were serviced to a company. 14 apples were decayed and had to be thrown away. The remaining apples were packed into boxes of 4 apples each. How many boxes of apples were there?

Sol:

Find the total number of apples serviced to a company.

44 × 88 = 3872

The total number of apples delivered to company was 3872.

Get the number of remaining apples.

3872 – 14 = 3858

Get the number of boxes of apples.

3858 ÷ 4 = 964.5

There were 964.5 boxes of apples

Example 4 in word sums math problem
The normal of a list of 10 numbers is 30. If we throw out one of the numbers, the normal of the remaining numbers is 15. What is the number that was removed?

Sol:

Step 1: The throw out the number could be obtained by difference between the sum of original 8 numbers and the sum of remaining 15 numbers i.e.

Sum of original 10 numbers – sum of remaining 15 numbers

Step 2: Using the formula

Sum of terms = Average* Number of terms

Sum of original 10 numbers = 30 × 10 = 300

Sum of remaining 15 numbers = 15 × 10 = 150

Step 3: Using the formula from step 1

Number removed = sum of original 10 numbers – sum of remaining 15 numbers

500 – 150 = 350

Answer: The number removed is 350.

General Patterns in Math

Introduction for general patterns in math:

In math, Patterns are generally the group of numbers which are listed in an order under a certain conditions. There are three different types of general patterns in math. Each pattern has some properties. In this article, we shall discuss about different types of general patterns in math. Also we shall solve some sample problems based on general patterns in math. Please express your views of this topic Double Integrals over General Regions by commenting on blog.


Types of General Patterns in math:


Arithmetic Pattern
Geometric Pattern
Alphabetic Pattern
These are the 3 different types of general patterns in math.

Arithmetic patterns:

Mostly the patterns are denoted as sequences. There are two types of sequences that are possibly occurs. They are finite and infinite sequences. On the other hand, we can express a number pattern using some special symbols. We can explain the number patterns in multiple ways. Let us consider a pattern of numbers {1, 2, 4, 8, 16,….}. In this pattern, the first term of this pattern is 1; and the second term can be obtained by multiplying 2 with the first term.

Geometric Patterns:

The pattern that involves geometric shapes are said to be Geometric Patterns. Geometric Patterns cannot create patterns, but it remains part of Space and Geometry. Ellipses are developed from circles. Likewise, polygon shapes do not have an exact dimension.

Alphabetic Patterns:

Patterns based on alphabetical characters are said to be alphabetic pattern. Moreover the alphabets in a sequence are the alphabetical pattern for the particular sequence.

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Example for general patterns in math:


Determine the next two terms in the given pattern

2, 4, 6, 8, 10, 12, ___, ____

Solution:

The first number in the given pattern is 2

The second number in the given pattern = 2 + 2 = 4

The third term is 4 + 2 = 6

The fourth term is 6 + 2 = 8

Likewise, the missing terms can be evaluated as follows.

The seventh term will be 12 + 2 = 14

The eighth term is 14 + 2 = 16

This is an even number sequence.

So the exact pattern is 2, 4, 6, 8, 10, 12, 14 and 16.

Math Subtraction Facts

Introduction to math subtraction facts:

Subtraction is one of the basic arithmetic operations.There are various types of subtraction like taking out a number from given numbers, or in a measurement removing a small part of it in its own units. In math subtraction can be expressed as removing a portion of a given quantity expressed in the same unit as  given. In math subtraction is removing particular quantity from a given. Please express your views of this topic Proportion Solver by commenting on blog.

The basic types include,

1.subtraction without borrowing.

2.subtraction with borrowing.


Facts about Subtraction without borrowing :


This method is commonly applied to mathematical numbers where on digit of a number is smaller than the the corresponding digit of the number from which it is subtracted.

Example: 34-23=11.

one's place: 4-3=1

Ten's place: 3-2=1

The fact here is the digits of minuend are m1=3, m2 =4.Digits of the subtrahend are a1 = 2, a2 = 3. . Starting from the mathematical one's place, 4 is not less than 3 so the difference 1 is written down in the result's one place. In the ten's place, 3 is not less than 2 so the difference 1 is written down in the result's ten's place.


Facts about subtraction with borrowing.

In this method when a particular place digit is larger in a number which is subtracted from other.

Eg: 705 − 511=194

One's place: 5-1=4

Ten's place: 0 becomes 10. so 10-1=9.

Hundred's place: 7 becomes 6 by lending 1to 0. so 6-5=1.

The minuend digits are d3 = 7, d2 = 0 and d1 = 4. The subtrahend digits are a3 = 5, a2 = 1 and a1 = 1. Starting from the mathematical one's place, 5 is not less than 1 so the difference 4 is written down in the result's one place. In the ten's place, 0 is less than the value 1, so the 0 is increased to 10, and the difference with 1, which is 9, is written down in the ten's place. This method corrects for the increase of 10 by reducing the digit in the minuend's hundreds place by one. That is, the 7 is replaced by 6. The subtraction then proceeds in the hundred’s place, where 6 is not less than 5, so the difference is written down in the result's hundred's place. We are now done, the result is 194. Is this topic What are Real Numbers hard for you? Watch out for my coming posts.


Example problems for math subtracting facts:


1.100-40=60  Here  in mathematical the ten's position 4 is greater than 0 so 1 is borrowed an made 10. the difference of 10 and 4, 6 is written in the tenth position of result

2.35-11=24. Here the digits of  minuend are greater than the digits of the subtrahend.

3.67- 21= 46. In this problem  the digits of  minuend are greater than the digits of the subtrahend.


Practice problems on math subtracting facts:

1. 55-22 = 33 (Without  borrowing).

2.45-16 = 29 (Borrowing)

3. 88-59 = 29 (Borrowing)

Math Family Letter

Introduction of Math family letter:

The math family letter is nothing but the math masters which are given at the starting of the year and at the end of the year. This not only end with this, some of the home links are made to select and to establishing a link with the parents and the tutors for briefing the content and activities. I like to share this Vector Calculator with you all through my article.



Math family letter:


The routines are made for the students in the classrooms. These routines help the students with predictability and to create the aspects in classroom. The possibilities to integrate math and other curricular activities are made through the routines in the class room.

Number and numeration: The counting can be made through different ways through different numbers, the first type can be done by 1’s and backward and 5’s and 10’s. Through this method they would have a lot of practice on reading and writing numbers and also to compare the numbers through routines.


Mid-year math family letter:


Operations and computation: The addition and subtraction can be explored through the concrete activities. They are asked to build strategies for finding the solution of the addition and subtraction. The usages of fingers are till used for the process of counting.

Data and chance: The terms like organize, collect and display in classroom are organized by the students through the weather, temperature and survey routines. These processes can be made through the dice rolls and they are also work on graphing activities.

Geometry: The pattern blocks and building blocks are made to explore through the 2 and 3-dimensional shapes and its manipulative. The games like spy play an important role in geometry.

Patterns: Creating, identifying, movement are done by the students. The number line are used for exploring the number patterns. Please express your views of this topic How to Calculate Sample Size by commenting on blog.


End of year- Math family letter:


Summer math ideas:

1) the maps in the zoo, museum, or shopping mall can be followed through reading.

2) Did your children help you in dialing the phone numbers while arranging for the outing?

Math Division Symbol

Introduction:

Math division symbols are represented as (÷), (/) ,These two symbols are Math division symbol. a division is called a division by zero if the divisor is zero. Such a division can be formally expressed as a / 0 where a is the dividend. Whether this expression can be assigned a well-defined value depends upon the mathematical setting. In ordinary real number arithmetic, the expression has no meaning.(Source –Wikipedia)

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Example:

Let us consider, if 10 times 4 equals a, written:

10*4 =a (c/b=a)

Where b (not zero), then a divided by b equals c,  (a/4=10)

Then we written like c=b*a

For example:

12/2=6    =>(2*6=12.)


Rules for division Math symbol:


Rules for division Math symbol:

Basic rules for Math Division symbol:

The basic rules for division are given as below:

Terms of Math division symbol:

(1)Division of two numbers are same sign we get the answer  Positive

(2)Division of two numbers are different sign mean we got the negative answer

Division of two numbers is same sign

Positive number(+4)/ positive number(+2)=  (+2)positive number (+/+=+)
Negative number(-4) / negative number (-2)= (+2)positive number(-/-=+)
Division of two numbers is different sign

Positive number(+4)/ negative number(-2)=(-2) negative number(+/-=-)
Negative number(-4)/ ÷ positive number(+2) =(-2)negative number(-/+=-)
Example problems in Math Division symbol:

Examples for division:

Examples1:

50 ÷ 5 = 610(same signs)

(-36) ÷ (-6) =+6  (same signs)

14 ÷ (-2) = -7 (different signs)

(-12) ÷ 3 = -4 (different signs)

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Example problems in Math Division symbol:


Example 2:

There are 50 books, and 5 student want to distribute same no of books, how do we share the books equally using division ?

Solution:

Given total no of Book are 50

Sharing part is 5

Division= Total number of books / sharing of books

= 25 ÷ 5 = 5

Each should have no of 5 books

Example 3:

Find how many minutes in 240 second?

Solution:

One minute 60 second

Given second  is 240

No of minute in 240 second => x*60=240

X=240/60

X=4minute

Practice problems:

1. Problem 1: Harry has 890 ice creams. If he gave his friends 10 ice creams each, how many friends can he share his ice creams with?

Answer: 89

2. Problem 2: How many meters are there in 720centimeters?

Answer: 7.2 meters

Independent Events

Independents Events is a key word often referred to in probability calculations. Knowingly or unknowingly , we use Independents Events often in the theory and application of probability. Two events are independent events, if the occurrence of one event  does not affect the probability of other. I like to share this Definition of Independent Events with you all through my article.

While calculating probability of COMPOUND EVENTS ( having two are more events in a sample or test ), it is necessary to consider whether the events are  INDEPENDENT EVENTS or not. A simple case study may make things better understandable. If a basket has 4 balls in which 2 are black and 2 are white. If a ball is taken and kept aside and then second ball is taken, the probability for the second ball being black depends on whether we have taken a black or white in the first chance. thus the probability in the second chance is depending on the first case or event, thus they become dependent events.

Same example can be slightly modified to make it INDEPENDENT EVENT. If in the example mentioned above, if the ball is not kept aside but placed in the basket itself. then the probability of getting a black is same always. the event of taking a black ball becomes INDEPENDENT EVENTS.


Independent events - Explained


The types of events that we have discussed so far are all independent events. By independent we mean that the first event does not affect the probability of the second event.

the probability of  independent events is product of each event.

If A and B are not independent, then the probability of A and B is

P(A and B) = P(A) × P(B|A)

where P(B|A) is the conditional probability of B given A.

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Examples of Independent Events


1) The event of getting a 6 the first time a die is rolled and the event of getting a 6 the second time are independent

2) If two cards are drawn with replacement from a deck of cards, the event of drawing a red card on the first trial and that of drawing a red card on the second trial are independent.

3) Landing on heads after tossing a coin and rolling a 5 on a single 6-sided die.

4)Choosing a marble from a jar and landing on heads after tossing a coin.

5)Spinning a number 6 and then spinning a number 5 on the same spinner.

6)Picking a marble from a jar, then picking another marble after replacing the first one.

7)Picking a red marble from one jar and picking a red ball from another jar.