Lcm of a Math Number Examples

Introduction for lcm of a math number examples:

The lowest common multiple (LCM) or least common multiple (LCM) of two rational numbers a and b is the smallest positive rational number that is an integer multiple of both a and b. Since it is a multiple, it can be divided by a and b without a remainder. If either a or b is 0, so that there is no such positive integer, then LCM(a, b) is defined to be zero.

- Source wikipedia

Examples for Lcm of a Math Number Examples:

Example 1:

Find the lcm of a math number examples 3 and 9.

Solution:

Multiples of the given number,

3      : 3, 6, 9, 12, 15, 18,21,24,27,

9      : 9, 18, 27

Now we have to pick out lest common multiple of the both number examples 3 and 9. Therefore, The LCM of math number examples 3 and 9 is 9

Example 2:

Find the lcm of a math number examples 4 and 12.

Solution:

Multiples of the given number,

4     : 4, 8, 12, 16, 20, 24, 28, 32, 36

12   : 12, 24, 26

Now we have to pick out lest common multiple of the both number examples 4 and 12. Therefore, The LCM of math number examples 4 and 12 is 12

Example 3:

Find the LCM of a math number examples 5 and 6.

Solution:

Multiples of the given number,

5      :  5, 10, 15, 20, 25, 30, 35, 40, 45, 50

6      :  6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Now we have to pick out lest common multiple of the both number examples 5 and 6. Therefore, The LCM of math number examples 5 and 6 is 30.Understanding how to find the variance is always challenging for me but thanks to all math help websites to help me out.

Practice Problems for Lcm of a Math Number Examples:

Problem 1:

Find the LCM of a math number examples 6 and 7.

The LCM of math a number examples 6 and 7 is 42

Problem 2:

Find the LCM of a math number examples 7 and 8.

The LCM of a math number examples 7 and 8 is 56

Problem 3:

Find lcm of a math number examples 8 and 9.

The LCM of a math number examples 8 and 9 is 72

Fractions with Regrouping

Introduction of fractions with regrouping:
The fractions with regrouping are nothing but the fractions which has the formation of the understanding and easy recalling of the particular fractions can be done through the fractions. The regrouping fractions are made along the process that had done in the way which has the computation of the process. The computations of the fractions are done through the regrouping of the fractions.I like to share this Compare Fractions with you all through my article.

Fractions with Regrouping:

Let us have the briefing of the quotient or the ratio. The quotient is nothing but the term that has the 2/3 in which the 2 is the numerator and the 3 is the denominator. The method can be mentioned as 2/3. The ratio is made to have the briefing that gives the situation on it. Hence there are two boys or the every three girls in the team hence in this case two-thirds of the teams are boys.

The regrouping of the fractions are made through the way that happen in the way which gives the understandings through the fraction of summing and the changes that works on the principle of the various changes that would be made useful for the regrouping of the fractions. These regrouping fractions can be made through the various methods like numerical and the x, y terms.Having problem with online math tutor keep reading my upcoming posts, i will try to help you.

Examples for Fractions with Regrouping:

Example 1: Compute the fractions with regrouping in the fractions like “1/80 + 4/80 + 9/80 + 6/80” is made to regrouping as “1/80+9/80 +6/80+4/80” the second terms are considered as simpler one these terms leads to the sum of ten [(1+9)/80, (6+4)/80] this made easier to keep the track off.

Example2: Compute the fractions with regrouping like “3x/80 + 2y/80 + 4x/80 + y/80 = 7” hence the regrouping of the x and y terms which can be made simpler.

This can be regrouped as 7x/80 + 3y/80 = 7.

Multiple Regression Equation

Introduction to multiple regression equation:

Multiple regression analysis is a statistical tool in which a mathematical model is developed to predict a dependent variable by two or more independent variables or in which atleast one predictor is non-linear. The principal advantage of multiple regression is that it allows us to utilize more of the information available to us to fit curves as well as lines.

Multiple Regression Model with Two Independent Variables:

The simplest multiple regression model is one constructed with two independent variables, where the highest power if either variable is one.

The model is given by  y = β0 + β1x1 + β2x2 + ε.
The constants and coefficients are estimated from sample information, resulting in the following model.

Y = b0 + b1x1 + b2x2

Multiple Regression Model Equation:

Multiple regression analysis is similar to simple regression analysis. However, it is more complex conceptually and computationally. The general equation for the probabilistic multiple regression model is given by


y = β0 + β1x1 + β2x2 …+ βkxk +  ε.

Where y = the value of the dependent variable

β0 = the regression constant

β1 = the partial regression coefficient for independent variable 1

β2 = the partial regression coefficient for independent variable 2

.....

.....

βk = the partial regression coefficient for independent variable k

k = the number of independent variables

In multiple regression analysis, the dependent variable, y, is some times reffered to as the responsive variable. The partial regression coefficient of an independent variable, βi represents the increase that will occur in the value of y from a one unit increase in that dependent variable if all other variables are held constant. The partial regression coefficient occur because more than one predictor is included in model.

In actuality, the partial regression coefficients and the regression constant of a multiple regression model are population values and are unknow. In virtually all research, these values are estimated y with sample information.Please express your views of this topic how to cross multiply by commenting on blog.

Y= b0 + b1x1 + b2x2 …+ bkxk

Where Y = the predicted value of y

b0  = the estimate of the regression constant

b1 = the estimate of the regression coefficient 1

b2 = the estimate of the regression coefficient 2

bk = the estimate of the regression coefficient k

k = the number of independent variables.

Determining the Multiple Regression Equation:

The procedure for determining formula to solve for multiple regression coefficients is similar to that of solving for simple regression coefficients. The formulas are established to meet an objective of minimizing the sum of squares of error for the model. Hence, the regression analysis shown here is reffered to as least square analysis. Methods of calculs are applied, resulting in K+1 unknowns for regression analysis with k dependent variables.

For multiple regression models with two independent variables, the result is three simultaneous equations with three unknowns( b0, b1 and b2).



The process of solving these equations is tedious and time consuming. Solving for the regression coefficients and regression constant in a multiple regression model with two independent variable requires `sum` x1, ∑ x2, ∑ y, ∑ x12, ∑ x22, ∑ x1x2, ∑ x1y  and ∑ x2y.

Set Theory Subsets

Introduction to set theory subsets:

The set is represented as the collection of the object. There are different kinds of the set. They are set of set, proper test, power set, and universal set. The set inside of the set is called the subset. The one type of the set is called the subset. Now we see the detailed information about the set theory subset.

Subset and Subset Theory:

Subsets:

The P is the subsets of the set Q, if the set P is inside of the set Q, the connection of single set being a subsets of another set is called the inclusion.

Set theory:

The set theory is the division of the mathematics, which are the group of the object. Some kinds of the object can be grouped into the set, the set theory is applied the majority often to object that are applicable to mathematics.

There are the two set, X and Y.  The Y is the subsets of the X. This is represent by `X sube Y`.


Set Theory of the Subsets:

The group of the object is known as the set. They are various types of the set are included. These are the set of the letter and set of number.

Example:

The set of the letters is {A, B, C, D, ....}.

Odd number set is the {1, 2, 3...}.

Even number set is the {2, 4, 6...}.

Upper case of the letter is set is representing as the {A, B, C, D….}.

The lower case of the letter is set represent as the {a, b, c...}.

The element A is belong to a is represented by A`sube` a.

The given number A is not a n set of the X is denotes as A`sube`X. the A is not the number of the set is S.

Looking out for more help on algebraic word problems in algebra by visiting listed websites.

Examples:

They are different kinds of the set. The one set is the mathematics and other set is the algebra. The algebra is the subset set of the mathematics.

The two specific kinds of the set are class A and class B. The class B is the subsets of the class B. These subsets are represented as the class A `sube` class B.



These are the details about the set theory subset.

Partial Fraction Decomposition

Introduction:

If f(x) and g(x) are two polynomials, then $\frac{f(x)} {g(x)}$ defines a rational algebraic function or a rational function of x.

If degree of f(x) < degree of of g (x), then $\frac{f(x)} {g(x)}$ is called a proper rational function.

If degree of f (x) > degree of g(x) then $\frac{f(x)} {g(x)}$ is called an improper rational function.

If $\frac{f(x)} {g(x)}$is an improper rational function, we divide f(x) by g(x) so that the rational function $\frac{f(x)} {g(x)}$ is expressed in the form F (x) + ?$\frac{f(x)} {g(x)}$ where F(x)and ?(x) are polynomials such that the degree of ?(x)is less than that of g(x)is less than that f(x). Thus, $\frac{f(x)} {g(x)}$ is expressible as the sum of a polynomial and a proper rational functions.

Any proper rational function $\frac{f(x)} {g(x)}$ can be expressed as the sum of rational functions, each having a simple factor of g(x). Each such fraction  is called a partial fraction and the process of obtaining then is called the resolution or decomposition or decomposition of $\frac{f(x)} {g(x)}$ into partial fractions.

How to Find Partial Fraction:

The resolution of $\frac{f(x)} {g(x)}$into partial fractions depends mainly upon the nature of the factors of g(x) as discussed below.

Case:- When denominator is expressible as the product of non-repeating linear factors.I like to share this Cdf of Uniform Distribution with you all through my article.

Let g(x) = (x – a1) (x – a2) … (x – an). Then we assume that

$\frac{f(x)} {g(x)}$ =  A1/ x + A2/x x – a2 + … + An/x – an

where A1, A2, … An are constants and can be determined by equating the numerator on RHS to the numerator o LHS and then substituting x = a1, a2, …, an.

My Previous Blog :- http://wanttolearnmath.blogspot.in/2012/11/multiplying-three-factors.html

Independent Dependent Events

Introduction to independent dependent events:

Let we will discuss about the independent and dependent events in probability. If the two events should be said to be dependent when occurrence or outcome of first event affects the occurrence or outcome the second event. Therefore, their probability will changed in independent and dependent events.

If two events should be called independent when the outcome of first event should not affects the outcome of second event.

Independent Dependent Events-dependent Events:

Let us consider more than two events that are dependent.
When p1 should be probability of first event, p2 be the probability that happens after first event and p3 will be the probability that occurs after first and second events.
Then probability of all events will happen will be the product p1 - p2 - p3.

Please express your views of this topic formula for calculating probability by commenting on blog.

Example problem:

A bag has 6 blue balloons, 4 green balloons and 2 black balloons. In every draw, a balloon is drawn from the bag and not replaced. In three draws, find the probability of obtaining blue, green and black in that order.

Solution:

Given, Blue balloons = 6

Green balloons = 4

Black balloons = 2

Total number of balloons = 6 + 4 + 2 = 12

Here, the three events are dependent.

So the probability = ( 6 / 12 ) × ( 4 / 11 ) × ( 2 / 10 )

= ( 1 / 2 ) × ( 4 / 11 ) × ( 1 / 5 )

=  4 / 110

=  2 / 55

Independent Dependent Events-independent Events:

Two events P and Q are called independent when reality that P occurs should not affect the probability of Q happening.

Example problem:

A die should be tossing two times. What will be the probability of getting 2 or 4 on first toss and 1, 3, or 5 in second toss.

Solution:

Let, probability of getting 2 or 4 is P(E1) and probability of getting 1,3 and 5 will be P(E2).

Now, P(E1) = P (2 or 4) = 2 / 6 = 1 / 3

P(E2) = P (1,3 or 5) = 3 / 6 = 1 / 2

Here, they are independent events.

Therefore, P(E1 and E2) = P(E1) × P(E2)

= 1 / 3 × 1 / 2

= 1 / 6

My Previous Blog :- http://wanttolearnmath.blogspot.com/2012/11/multiplying-three-factors.html

Multiplying three Factors

Introduction to multiplying three factors:

This article we will discuss about multiplying three factors and factorization methods. Any numbers that when multiplied together form a product called as factors. Each number should have a factors each factor is unique it must not zero. For example 2 is a factor of 8 because 2 can be multiply by 4 to give 8 this is called factors. Lets us see about prime factors, and multiplying three factors.Understanding Prime Factors of 72 is always challenging for me but thanks to all math help websites to help me out.

Factors:

Prime factorization:

A Prime number is a whole number that can be divisible by itself. This called prime number. For Example 1, 3, 5, 7 are some of the prime numbers.

Factorization is finding which prime number need to multiply together it gets the original number. Factoring is to express a number as the product is called factors. Factors are numbers.

Multiplication: repeated addition of number is called multiplication for example   4* 3=12 it just add  4 times of  3 like 4+4+4=12 or 3 times of 4 (3+3+3+3=12) Let us see example of multiplying three factors.

Example1: multiplying three factors 20 * 6 * 18

Solution:

Multiply three factors:

Step 1:   20  *

6   

120

we multiply 20 *6 factors we can get 120 now we multiply 120 * 18.

Step2: 120 *

18  

1960

120  

2160

Step 3: Therefore multiplying three factors 20 * 6 * 18 is 2160

Example2: multiplying three factors 10 * 40 * 8

Solution: 

Multiply three factors

Step 1: multiply 10 * 40

10   *

40   

00

40  

400

If we multiply 10 *40 factors we can get 400 now we multiply 400 * 8.

Step 2: multiply 400 * 8

400 *

8 

3200

Step 3: Therefore multiplying three factors 10 * 40 * 8 is 3200.

Multiply three Factors Using Associative Property:

Associative property means the factors are same on either side of the equal sign and when we multiply two or grouping of factors does not change the product. (a * b) * c = a* (b * c) following example for multiply three factors.

solve:2* 6 * 3

Solution:

multiply 2 * 6 * 3

Step 1: 2 * 6 * 3 = 36

Step 2: apply associative property

2 * (6 * 3)

= 2 * (18)

= 36 when we multiply two or grouping of factors does not change the product.

Step 3: therefore multiplying three factors 2 * 6 * 3 is 36.

My Previous Blog :- http://learnmathsrightway.blogspot.in/2012/11/define-random-variable.html