BODMAS

BODMAS is one of the most important concepts in mathematics. Taught in the middle school, BODMAS plays a major role throughout every mathematical calculation. BODMAS is an abbreviation of rules of operations in mathematics. It is used to make the rules easy to remember and perform. BODMAS is referred by various other names. BODMAS is also known as BEDMAS where E means Exponents. It is also known as PEMDAS where P means Parenthesis. Let’s have an in depth look at the full-forms of BODMAS and its meaning in this post.

B – Brackets First
O – Orders such as powers, square roots etc.
DM – Division and Multiplication
AS – Addition and Subtraction
• BODMAS defines the rules to be followed in orders of operations. According to the rule, the operation within brackets should always be calculated first.
Example: (2 toys for infants x 3 kids) + (2 crib toys for baby girls x 2 girls) + 5 toy action figure for kids
6 toys for infants + 4 crib toys for baby girls + 5 toy action figure for kids
15 toys for kids
• According to the BODMAS rule, exponents such as power and roots should be calculated prior to multiplication, division, addition and subtraction.
Example: 5 infant toys x 22
= 5 infant toys x 4
= 20
• According to the BODMAS rule, multiplication and division should be performed prior to addition and subtraction.
Example 1: 2 + 5 x 3
= 2 + 15
= 17
Example 2: 45 – 16 / 4
= 45 – 4
= 41
• According to the BODMAS rule, addition and subtraction comes at last when there are other operations to be performed.
Example 1: 2 + 3 x 6
= 2 + 18
= 20
Example 2: 7 – 2 x 3
= 7 – 6
= 1
These are the basics about BODMAS.

How can you be the best tutor for your kid's?

Get the best tutor and reduce your kid’s anxiety in all subjects. Enroll for a smart learning session using an online tutoring site where qualified tutors work on your child's academic skills. Online tutoring offers several simple methods to learn the subject at your child's pace and time.

The child's responsibility is the primary concern of every parent. Right from keeping an eye on their health, their food habits and behavior to monitoring their academic performance, every activity is challenging as well as important for the parents. Each child is unique. For instance some are academically strong and some take a little more time to understand a subject. For a child, the parents are the best tutors as they are well acquainted with their learning and mental abilities. Now days, getting a child’s assignment done are the first and foremost priority for a parent. It is their job to give them a better education and make them understand about the importance of education in the real world. However, it is not possible for every parent to teach their kid each subject across grades. This is because learning has undergone a sea change in the last decade or so. Concepts are no longer taught the way they used to be. The books, curriculum and learning methodologies have also completely changed.  Parents can motivate their child but teaching is something that requires ample time, attention and a thorough knowledge in a specific subject.

Finding a good tutor for kids is quite a difficult task for parents these days. A well-qualified tutor who meets the educational needs and the learning style of a child is what a parent should look for. Every parent wants their child to prosper and do well in the academic field but it is not that easy as some students struggle a lot academically and require an extra learning resource. Online tutoring or a good learning center is the ideal resources to improve a child’s academic skills. Before putting a child into a learning center or enrolling him/her to an online tutoring website, parents should clear certain doubts like what is the tutoring plan they would choose for their kids, what subjects free tutoring online offers and what would be the teaching style of a particular tutor. These questions will surely give a clear idea to parents about how online learning sessions work in real-time and their benefits.

Hiring a tutor is easy but it is extremely important to monitor your child's grade. Online tutoring not only provides unlimited interactive learning sessions with the best tutors but also helps to evaluate a student’s performance from time to time. Several online tutoring sites also conduct regular assessments and provide progress reports to parents so as update them on their child's performance. These one-on-one learning sessions will help your child do better in exams. Being a parent, it is important to look after a child’s academic development. Online learning sessions are a great option that give your child enormous time and offer them several ways of learning at a convenient pace.

Factoring polynomials

When factoring out polynomials,  we find   the  polynomial  that divide out evenly from the original polynomial  .   How to factor  Polynomials:  For this we have to find all the terms that if multiplied together we get the  original polynomial.  This is continued to all the terms until this cannot be simplified any more.  If the polynomial cannot be factored any more then the polynomial is said to be completely factored.


A factor of a polynomial is any polynomial which divides evenly into   the given polynomial   For example, x + 2 is a factor of the polynomial x^2 – 4.
The factorization of a polynomial is its representation as a product its factors. For example, the factorization of x^2 – 4 is (x – 2)(x + 2).

In mathematics, factorization or factoring is the breaking apart of a polynomial into a product of other smaller polynomials. If you choose, you could then multiply these factors together, and you should get the original polynomial.
This example shows how to factoring polynomials.    Take 3x^2 – 12x + 9.   The common term in these is 3.  So take 3 out and divide each term by 3.  We get   3 (x 2-4x + 3).

Step by step explanation as how to Factor out Polynomials is given below
Factor 4a^2 + 20a – 3a - 15


The first two terms have a common factor in 4a.  The last two terms have a   common factor in 3.
We need to factor those terms out.

4a ( a + 5)  -3(a+5)

Now you have a binomial.  Each term     has a factor of (a + 5).

(4a -3) (a+5) is the factored terms.


Another example is given below on factoring of polynomials
X2 -8x + 15

start by looking at the factor pairs of 15.  We are looking for a pair of factors which add up to equal -8.  Look for the factor pairs of  +15 so that they add up to -8    The negative factor pairs of 15 are:
-15  and  -1
 -5 and  -3
Since -5 + -3 = -8 this is the pair we are looking for and we can factor the
original expression into:  (x-5)(x-3)

Matrix types: Diagonal matrix

The term diagonal matrx refers to the topic of linear algebra which is a branch of mathematics. In general a matrx would look like as follows:
[a11 a12 a13 … … a1m]
[a21 a22 a23 … … a2m]
[a31 a32 a33 … … a3m]
[… … … … … …    ]
[… … … … … …    ]
[an1 an2 an3 … … anm]

The above matrx has n rows and m columns. The diagonal of such a matrx consists of all the entries where in the row number = column number. Therefore if r = row number and j = column number. Then the entries of the type a(ij) where i=j are the diagonal entries. Therefore in the above matrx the diagonal would be the highlighted entries as shown below:

[a11 a12 a13 … … a1m]
[a21 a22 a23 … … a2m]
[a31 a32 a33 … … a3m]
[… … … … … …    ]
[… … … … … …    ]
[an1 an2 an3 … … anm]

Now if we have a matrx where in all the entries except the diagonal entries are zero, then such a matrx would be called a diagonal matrix. In general a diagonal-matrx would look like this:

[a11 0 0 … … 0]
[0 a22 0 … … 0]
[0 0 a33 … … 0]
[0 0 0 … … 0]
[… … … … .. 0]
[0 0 0 … … ann]

Note that a diagonal-matrx has to essentially be a square matrx. An example of a 3x3 diagonal-matrx is shown below:

[2 0 0]
[0 -1 0]
[0 0 5]

Scalar matrix:

A diagonal-matrx in which all the entries of the diagonal are equal is called a scalar-matrx. The general form of a scalar matrx would be like this:
[a 0 0 … … 0]
[0 a 0 … … 0]
[0 0 a … … 0]
[0 0 0 … … 0]
[… … … … .. 0]
[0 0 0 … … a]

Determinant of diagonal matrix:
Let us try to understand how to calculate the determinant of a diagonal matrix using an example.

Example: Calculate the determinant of the following diagonal-matrx:
[2 0 0]
[0 -1 0]
[0 0 5]
Solution:
D = 2*(-1*5 – 0*0) – 0*(5*0-0*0) + 0*(0*0-(-1)*0))
= 2*(-1)*(5) – 0 + 0
= 2*(-1)*5 = -10
So we see that the value of determinant of a diagonal-matrx is the product of the terms on the diagonal (also called the principal diagonal)