Mixture Problems as Words

We are solving the equations in mathematics always having direct problems but when we are solving the problems in the word or description format then it is known to be as mixture problems. Formation of the question or getting the problems in the form of word problems is the approach to check your analytical skills.

It is very useful in the future profits as if you go further in the studies then you have to face the Operational Research type of subject or the optimization techniques used in the process of various functional aspect of the organization.

When the problem comes in the word format then you have a better experience to do that it means that you have to do the lot of problems before attempt the problems given in your papers. As it is must to know the formats in the word problems. Algebra mixture problems are creating a mix of two or more than two things to determine something related to quantity of the mixture problems.

It is the conversion of qualitative analysis into quantitative analysis. Say for example of mixture problems in algebra like if the trains are moving in a same direction and both the speeds of the train is 7km/s then tell us the relative speed of both the trains?

This is an example of the problems which is word problem. Solving this kind of the equation you have to focus on what the question want and then proceed further to reach to the final equation.

The other part of solving the equation is form the tabular form as when the polynomial type of the equation is given and then solves it as per the logical reasoning. Mixture problems in algebra is to mix up the qualitative type of problems in a quantify manner to check the data interpretation of yours while solving this kind of problems.

As if you understand these kinds of problems then you are able to solve all the problems in the mathematics. Operation research is a big scope for good data interpreter and it works in your competitive advantage also. So try to better solve more and more number of problems based on word problems to increase your IQ level.

Few tips we want to share is use go through the problem and in rough do the analysis part what is given in the problem and then to start the solution. Procedure wise solve the question to reach the final goal what you want to achieve and make it as a sequential wise approach.

Concept of Simplification of Radicals

Various concepts are used in mathematics. Radicals are also one among them. They can also be represented with the help of a symbol. Basically they are used to represent the root of a number. The number can from the various number systems in mathematics. There are various number systems in mathematics.

The natural number system, whole number system, integer number system and real number system are some of them. There can also be irrational numbers and also complex numbers. The complex numbers have a real part and an imaginary part attached to them.

Do they are said to be complex numbers. The operations that are performed on real numbers like addition and subtraction can also be performed on the complex numbers as well. But to perform these operations one must be clear with the concept of the complex numbers.

The next question that arises is how do you simplify radicals in mathematics. The radicals have to be simplified in order to arrive at the final answer. The process to simplify radicals is quite simple. The root that has been applied to a number can be a square root, cube root and so on.

Sometimes fourth root can also be used. The number inside the square root symbol must be present two times then it can be taken out of the square root symbol. In case of cube root symbol it should be three times and in the case of the fourth root it should four times and so on.

In simplifying radicals practice is required; otherwise it becomes very tough to solve the problems. In mathematics practice is very important otherwise it will be very difficult to arrive at the final answer. Many mistakes can also be committed en-route to the answer. This can be avoided by proper practice.

There can questions to simplify radicals with variables like the simplification of normal radicals. The process is quite similar to the process of simplification of the radicals of the normal nature. Only proper practice can help one to reach at the right answer. There can be signs that can be used before the radical symbol.

The signs can be positive or negative in nature. Depending on the sign preceding the radical symbol the answer also changes. The positive denotes a positive number and a negative sign denotes a negative number. The magnitude also plays a very important role.

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Get online tutoring and solve tough Mathematical problems in an easy way. Enhance your problem solving skills by taking required learning sessions with expert tutors. Experience the benefits of online learning service and improve your score in exams.

Expert guidance helps students in solving Math problems
                                                                                                                         
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Math Problems and its instant solutions
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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.

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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)