The Rules of Working with Fractions

During the elementary years, one of thing that students should learn about is multiplying fractions. Even if the work at this level is more about dividing, multiplying, subtracting and adding with fraction, it is important in math learning.  Even if working with fraction can be somehow complicated and difficult, it is worth it while creating the math activities that make the learning easy and fun.

When it comes to working with fraction, there are some few rules that someone should keep in mind.

Subtract and add using the same denominators

-        Subtract and add numerators and use one denominator.

Add or subtract fraction using different denominator

-       You can find the common denominator through taking least common multiple for the denominator and through multiplying the denominator.

-       You can convert the fraction by dividing common denominator  and by multiplying the results by  numerator

-       Subtract and add the rule and add the fraction to the same denominator.

Multiply the fraction

-       You can multiply the denominators by the numerators

-       The product of numerators over product of denominators, it will result in the fraction

-       You can simplify resulting fraction when both denominator and numerator are visible  by just one number.

Dividing by the fraction

-       You can multiply the first  numerator by using the fraction of the second denominator for the new numerator

-       You should multiply the second numerator with the fraction numerator for the first denominator of new numerator

-       Multiply the second numerator of faction by using the first fraction denominator and getting the new denominator.

-       When the resulted fraction comes with the numerator which is greater compared to the denominator, you have to divide the numerator by using the denominator so that you may get the mixed number.

Creating of equivalent fraction

-       You should multiply both denominator and numerator using the same number

Convert the mixed number into a faction

-       You should multiply the entire number part using a denominator

-       Add the numerator in order to get  a numerator

-       Use the same denominator as a fraction part of a mixed number 

Convert improper fraction into the mixed number

-       Divide a numerator using a denominator in order to get a part of a whole number

-       The remainder is going to be a numerator to the fractional part

-       The denominator is same as improper fraction denominator

Simplify the fractions

-       You should find greatest common divisor of denominator and numerator

-       You can device both denominator and numerator using greatest common divisor.

If you want to teach your child more about multiplying fractions, you can use available materials to do so.

-       Using the dominoes: you can let the child pick tiles randomly so that she can learn about having different nominators and denominators.  You may also use different cards to teach him about different operations.   You can find more innovative ways to use so that your child can learn more about fraction in a fun way. 

You can also visit different online websites where you can learn more about how to teach math to your child. 

All about Factorization

It is always better to start from scratch and know how the process in-built together and incorporated at places than to start working and return back to the basics.

What does the term Factorization mean?

It is the process of finding out factors of a polynomial or any equation. It is moreover like splitting of a complex term into two other numbers whose multiplication product if equal to the main term.

It can also be defined as the decomposition of a mathematical equation and is not necessarily applicable to polynomials, but also for Matrices and numbers

Why should one Factorize?

The main objective of factorizing is to reduce the complexity of the problem. The end results of Factorizing are something which cannot be further divided, thus breaking the equation to its simpler form.

The factorizing terms in their form can further be multiplied again to retain the original equations. This is also known as the expansion of polynomials. It is the best way to verify the solutions obtained after the factorizing process.

Equation

When should we Factorize?

Before moving on to factorization let us have a look at the factor theorem:

The factor theorem states that when a polynomial f(x) has a factor that is (x-k), it is only when f(x)=0

This means that the value of k that is obtained is a root of the polynomial.

Other uses of the Factor theorem are:

The factor theorem is used to remove known zeros from a polynomial while leaving all unknown zeros fixed, thus producing a lower degree polynomial whose zeros are easier to solve.

The method is:

1.    Use the factor theorem to conclude that the term (x-a) is a factor of f(x).

2.    Solve the polynomial g(x) =f(x)/f(x-a), for example using Long Division method of Polynomials or Synthetic Division method.

3.    Say that any root x is not equal to an of f(x) =0 is a root of g(x)=0.

4.    Since the polynomial degree of g is one less than that of the degree of f, it is "simpler" to find the remaining zeros.

Few Common Methods of Factorization

Listed below are the few commonly used methods for factorization:

Let us have a quick look at them

1. Highest Common Factor

The highest common factor of algebraic expressions is useful in factorization; and it is the product of the common prime factors, which includes both common numerical and algebraic factors.

2. Using the Common factor

ab+bc= b(a+c)

3. Using the Difference of the square formula

a^2-b^2= (a+b)(a-b)

By using the above method, you can easily find the factors of a number.

Real Life applications of Factorization

Finance

Commonly used in finance and accounting where the present value of the assets are determined and for stock evaluation. Its uses are also traced in bond trading and calculations.

Numerical Analysis

For complex and high ordered equations in derivations and formulae method of factorization is needed to reduce the complexity of the problem, thus getting a valid solution or a better and simpler form of the equation. Also, high tech algorithms use the basics of Factorizing.

Quadratic equations

Integration sums and wave equations always end up unexpectedly in a quadratic form and then the only factorization can reach for your help. It is also widely used for solving numerical and calculation unknown values when in higher than or equal to 2nd order format.