Fraction Calculator

Fractions can be way difficult to absorb for some students when they first start with the topic. Especially, when dealing with equivalent fractions; it seems that they do not get the head or tail of anything. The concept in reality is very simple; but if the logic still eludes you, you can try using an equivalent fractions calculator, till you get the hang of it.

Fraction Calculator
Fraction Calculator

Your math teacher tells you the equivalent fractions are two or more fractions that have the same value, but have different forms. In simple words, these fractions can be defined as fractions having the same overall value, or the same simplest ratio. These fractions indicate the same part of a whole. The easiest way to explain equivalent fractions is using the example of a round apple pie. Whether you divide a pie into two pieces and take one, or out of four pieces take 2, or further on out of 8 pieces take 4; you still get one-half of the pie to eat. So we can conclude that 1/2 is same as 2/4 or 4/8; they all are equivalent fractions.

The technique to simplify a fraction is very easy; both numerator and denominator must be divided by the same number to reduce the fraction. So remember that the value of a fraction does not change if you multiply or divide the whole fraction by the same number. Remember that the number you use for division must divide without leaving a remainder. Both the numerator and denominator of a fraction must always be whole numbers; so you can know when you have arrived at the simplest answer & cannot reduce the fraction any further. And remember, only multiplication and subtraction is valid when reducing fractions; do not try to perform addition or subtraction while reducing your fractions.

The easiest way when working with conference is to use fraction calculator to check your answers. This will boost your confidence & in the long run help you with your math homework. But remember, that using these calculator will only validate your answer; you still have to learn how to arrive at that answer in the first place.

The prized scientific calculator of your elder sister can act as your equivalent fractions calculator; you can easily check your answers using it. On the other hand, there are many math websites today offering their own version of equivalent fractions calculator, you can easily search & bookmark your favorite one to verify your answers. You can also ask your nerd brother to write a short program for an equivalent fractions calculator; whether he uses C++ or Assembly, the code to develop these calculators is very simple.

It is always important that you make sure that you visit a reliable site to do your calculations. There are some sites that tend to rob your money. It is always important that you do your homework well before choosing a site, to be in a safe situation it is ideal that you go for those sites that have reviews.

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How to Solve For X in Equation

Sometime the equation may contain the letters and not the number. It may be daunting and may students worry when they hear the word algebra.  Sometime algebra can turn to be hard since you have to deal with unknown amounts and the math will not be that concrete anymore. However, the best place to start with is starting with the basic foundation, and you can then learn how to solve for x.  This means that you may figure out how much the unknown amount should be.

Solve for X
Solve for X

The basic rule is that the first step which you have to take to solve for the x is to get the x on its own and alone. At one side of an equation, everything else will be at the one side. You have to keep in mind the rule, what you need to do at one side of an equation, has to be done at another side.  This is to ensure that the equation continues to be equal.

You should start with the simple equation. The basic algebra equation will involve some simple subtraction and addition that have unknown quantity.

As you continue to learn algebra, you will have to go from the simple equation and use an equation that has even more steps. The more difficult equation will have different equations.

As you continue to get more information about how to solve the equation, it will be easier for you to solve for these letters. If you would like to be comfortable by working on algebra problems, then you should take time to practice.

Whenever students are asked to solve for x, they may assume that there is always the solution for x.  However, this is not always the case. When the solution is resolved, sometime the final results may not be achieved.

If you worry about algebra, then you have to know that it is the extension of the basic arithmetic which you are using on a daily basis.  If you know the basic, then it will be easy.  As you practice more, then the rules are going to be automatic.  If you do encounter the problems, you will then find out that rules and tricks to use in order to solve for x.

 You should review the basic mathematics and arithmetic. Even when you remember the negative numbers, you can add the fraction, do the practice sets and this will boost your confidence.  When it comes to algebra, you will need to perform the basic operation, but now there are letters mixed with the equations. The letters are called the variables.   When you have to solve algebra, you will have to find the value of a variable.

When you solve for x, you will have to combine. First the like terms and these are terms that have same variables.  When your multiply or divide a term, you should do it on both sides of the equation. When you reach to the last solution, it will be called factors of a solution.  Factoring in the algebra is breaking down things that seem to become even more complex.  When you break down items in smaller pieces, you will have to apply the math skills and to find answers.

What are a Quadratic Formula Calculator and its Standard Equation?

In elementary algebra, there are various ways of solving a quadratic equation such as completing the square, graphing or factoring. However and whenever you seek for a way to solve these equations the best way which comes to your mind is the Quadratic formula calculator. That is a one-step solution for all kind of quadratic equations. It is one of the simpler, easiest and convenient ways of solving equations. After reading this article, you will become able to identify a quadratic equation. You will learn how to place a quadratic equation into a standard form along with learning the alternative ways to derive a quadratic equation general formula.

Quadratic Formula
Quadratic Formula

A quadratic formula calculator in general terms could be called as a polynomial equation which contains the second degree and no higher degrees of a variable. The standard form of a quadratic equation is –

mx² + nx + k = 0

In this equation, the value of x is always unknown. m, n, and k are constant in which they should be equal to 0 or contains some negative and positive values. On the way to verify whether the quadratic formula is satisfying a quadratic equation or not, you have to insert the former one into the latter. This is known as parameterization. After this, the general quadratic formula is converted into

Math
Math

 

 

known as radical.

All the quadratic equations can be inserted in a standard form. And any equation which can be put into a standard form and can be solved by a quadratic formula solver represents a quadratic equation. The solution of any equation is sometimes known as the root of an equation.

There are various methods for deriving the quadratic formula. Some of these may either be simpler than completing the square method however the method represents interesting applications of the different algebraic techniques. It offers a different view of the field of mathematics.

How the general quadratic formula calculator is derived?

mx² + nx + k = 0

4m²x² + 4mnx + 4mk = 0

4m²x² + 4mnx = -4mk

4m²x² + 4mnx + n² = n² – 4mk

(2mx + n)² = n² – 4mk

equation
equation

 

 

 

 

This is an ancient way of determining the quadratic formula which was known to the people around years ago. When it is compared with other ways of deriving the standard formula, this way of solving and determining the formula is quite simpler. The benefits of this formula derivation are-

  • Simple to solve and is less complicated
  • Less computation of literal coefficients
  • It does not involve fractions until the very last steps.
  • Use of simple math with simple expressions
  • The central theme of algebra is to solve the equations

However solving these equations is not easy for everyone. A lot of times people find a problem get stuck into a particular quadratic equation and do not find the way to solve it. The basic command over mathematics is a must to solve such equations. However, there are various sites which are now offering the services of instantly solving the equations. One such site is the Quick Math which allows you to put down your equation in the available dialogue box to provide the quadratic formula calculator. The whole solution can be displayed along with the answer. It makes your math problems easier and explains the alternative ways to solve an equation.

Learn to Solve a Linear Equation Perfectly

Mathematics is known to be a subject with lots of interesting facts with it. There are many who love to understand the subject deeply and know some more excellent facts about it. Algebra is the most important part of mathematics with some of the most interesting methods and formula. To be perfect in the subject one needs to be perfect with algebra.

Equations constitute some of the basic components, there are many who search out some of the best ways to get perfect in solving equations. If you are able you solve the equations well, then you can handle algebra very easily. Therefore here we are going to deal with the simplest, linear equation and the best ways to solve it correctly.  By the time you will get to know some more interesting tricks while solving such problems.

Linear Equation
Linear Equation

Thorough Basics

Before we move further, everyone should remember the importance of basics. If you are clear with the basics then only you will be able to handle the complex problems perfectly. Therefore it is the best that before moving on to the complex problems learn the basic tricks and formulae well. You need to use the right formula at the right place. You will soon be able to interpret this when you practice the problems regularly. Therefore have a look at your lessons and practice daily. This way you will surely be able to deal with algebra perfectly.

Solving a linear equation

Isolating the variable is the major part in the process of solving the linear equations when you get answers in the form y = 6 or x = 7. Here, the variable is brought to itself or is separated from the rest of the equation. But the question is, How to do this? Well, this may depend on several different factors. We will have to perform exactly the opposite of the operations that are done in the equation. This way you will be able to get the initial equation. Like if something is added we will subtract the same, or if something is multiplied, we will divide the same. All this has to be done considering the LHS and RHS rules. Here is the example of a one-step equation:

Suppose, 4x=8 ; Now to isolate the variable x, we will have to bring it to the other side which will result in the change of operation. Further, it will be:

x=8÷4 ; Therefore, x=2 . Thus isolating the variable will make it easy for you to get the answer.

A two-step equation

Now let’s see a two-step equation say, Solve 2y−7=13. The noticeable fact here is that the variable y is first multiplied by 2 and then 7 is subtracted from it. Therefore to cancel these effects, the solution will move like:

2y-7+7 = 13+7 (Add 7 to both sides as per the LHS and RHS rule) Now,

2y = 20 ; Now solving the equation further,

2y⁄2 = 20⁄2 (Divide 2 on the two sides of the equation) Thus,

y = 10

This way you can easily solve and get perfect with any kind of linear equation.

Subtracting Fractions

The procedure of fraction addition is more or less the same as that used in the subtraction of fractions. This implies that if you have the know-how of adding fractions, you will have an easier time subtracting them. Subtraction of fractions is also one of the most common operations that we are likely to come across in many mathematical computations. All the same, if you have a problem subtracting fractions, there is absolutely no need to worry because what you need is only a few steps and procedure away.

To begin with, it is important to understand the structure of the fraction. A fraction can either be proper improper or mixed. In cases where you are required to perform subtraction of improper fractions, the first step should be to change it into an improper fraction first. A fraction has basically two numbers. One on top and the other at the bottom. The one on top is called the numerator, and the one at the bottom is the denominator. For example:

Given a/b, a is the numerator and b are the denominators.

Having understood the structure of a basic fraction, we shall consider two methods that can be used to subtract fractions basing on the number of fractions being subtracted. These methods require the understanding of the structure of a fraction.

Method of Common Denominator

Method of Least Common Denominator

  1. Method of Common Denominator

This method is well applicable when you are subtracting one fraction from another, meaning, you are dealing with two fractions only. Since by now we know the meaning of a denominator, it will also be-be helpful to understand the meaning of “Common Denominator.” What is a Common Denominator? When the denominators of the two fractions in question are the same or identical, we say that there exists a common denominator.

Therefore, the main aim of this method is to ensure that the denominators of the fractions are the same before performing the subtraction. When the denominators are not the same, subtraction cannot be done. How do we then ensure that the fractions have the same denominators? Multiply each fraction – the numerator and the denominator – by the denominator of the other fraction.

For illustration consider;

a/b – c/d = (a*d)/(b*d) – (c*b)/(d*b)

Once the denominators of the two fractions is now common, (b*d), the ‘new’ numerator are simply added.

Example; 1/2 – 1/3

(1*3)/(2*3) – (1*2)/(3*2) = 3/6 – 2/6 = 5/6

 

  1. Method of Least Common Denominator

This method is used when subtracting two or more fractions. The knowledge of the Least Common Multiple (LCM) is needed in this method. The LCM of the denominators is determined and used in the calculations. To find the LCM of the denominators, follow the steps below;

List the multiples of each denominator

Select the multiples that are common – appearing for all the denominators

Choose the smallest among the common list of the multiples. This is the LCM

After getting the LCM, divide the LCM by each denominator and multiply the result by the numerator of each fraction separately before you proceed to simply subtract the ‘new’ numerators and using the LCM as the denominator. Simplify the resultant fraction.

To clearly illustrate the long theory, we will need an example;

Question; 1/2 – 1/4 – 1/5

List the multiples of each denominator

2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22…

4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40…

5 = 5, 10, 15, 20, 25, 30, 35, 40…

Select the common multiples

20…

Choose the smallest = 20. This is the LCM.

[(1*10) – (1*5) – (1*4)]/20 = 9/20.

When Quadratic Formula is Used

With elementary algebra, quadratic formula is used for the solution of a quadratic equation. You can find many ways that you can use to solve this problem without using the quadratic formula like graphing, completion of the square or factoring while using the quadratic formula maybe most convenient method. The quadratic equation looks like ax2+bx+c=0.  With this equation, x stands for unknown but a, b, with C should be constant, and A should not be zero. Someone may verify that the quadratic formula does satisfy quadratic equation through inserting the first number in the last number.

quadratic formula
quadratic formula

The solution found with the quadratic formula is known as the root for a quadratic equation.  In geometry, such roots can represent the value of x which is the parabola given will cross at the axis of X. The formula can yield zero of different parabola while quadratic formula can give axis to the symmetry of a parabola. This is normally used in order to determine the number of the zero which the quadratic equation does have.

The formula may get derived from the simple application with a technique application needed to complete a square. This is why; a derivation can be sometime left like the exercise of the students who wish to experience the rediscovery of the formula.

A quadratic equation can be in the form to complete a square when it is applied. You may add the constant on the two sides of an equation like the left-hand side which become the complete square.  The terms should be rearranged at a right-hand side so that we can obtain the common denominator. When the square had been completed, then the square root of the two sides have to be found and then isolating the x to get the quadratic formula.

The solution of a quadratic equation can be gotten by using different alternatives of the derivation with the minor differences, and this is through manipulating a. Some of the old sources may use the alternative of parameterization for the equation by using b with a magnitude of the half of a common number.  Even if the results can be different from the first solution, however, they are also equivalent.

Without the need to go in the parabolas like the geometrical objects of the cone, the parabola will be the curve which is being described as the second degree of the polynomial.

The early method to solve the quadratic equation was done in the geometry.   The Babylonian cuneiform tablet had the problems that are reducible in solving a quadratic equation. Egyptian Berlin Papyrus that dated back in the middle kingdom had some solution for a two-term equation.   In Greek, the mathematician Euclid was using the geometric method in order to solve the quadratic equation in the Elements Book 2.  The laws of the quadratic equation do appear in Nine Chapters on Mathematical Art circa from China. A Greek mathematician Diophantus in the work he did on the arthmetica, he solved some quadratic equations which are recognizable to the algebraic done by Euclid. The solution he used was able to give one root, regardless if positive roots were used.

What are the Basic and Right Rules for Dividing Fractions?

Fractions have its set of rules for multiplication, division, subtraction and also for addition. Multiplication of fractions is easy, but the division of fractions it little difficult. However, if you know the rule of dividing fractions, you can easily divide two fractions very easily. Fraction is one of the important concepts of the algebra, and you should know the operations on fractions like the multiplication and the division. It is important as you will come across with fractions while studying the algebraic equation and various problems of algebra. Here, you can get informed about the division as well as multiplication of fractions.

Before you study how to divide the fractions, you should know how to multiply fractions. It will help you in the division also. If you do not know how to multiply two fractions, you can’t divide the fractions. The rule of multiplication is very simple. Multiply the denominator of the first fraction with another fraction and just like multiply the numerators of both fractions. So you will get a new fraction after multiplication.

How to divide the fractions?

The basic rule for the division of fractions is simple. Dividing fractions is followed by the reciprocal and multiplication. It’s the single operation in which you have needed to reciprocal a fraction. You can better get it by reading the simple steps of division listed below.

Step 1: first invert the divisor fraction only and use the inverted divisor.

    Step 2: now, rewrite the problem and replace the multiplication sign “x” to the division sign “÷” and also replace the divisor fraction by its reciprocal.

    Step 3: multiply the numbers at the numerator place of both fractions.

    Step 4: multiply the numbers at the denominator place of both fractions.

Step 5: if possible, reduce the fraction obtained by multiplication into its lowest form.

Example:  

Math
Math

Important thing to consider

But keep in mind that you have only to reciprocal only a single fraction. So, do not reciprocal or invert both the fractions which you are using for the division. So, you have only required inverting the divisor fraction only. There is no need to invert the dividend according to the rule of fraction division. In simple words, only invert the second fraction and use the first fraction as it is to solve fraction division problems. It is the most important consideration for dividing fractions correctly.

The same rule will be followed in the problems of dividing a fraction by a whole number. You have to invert the whole number in this case as the whole number is the divisor. So, the whole number will automatically convert into a fraction. You will get a new fraction and then multiply the numerators and denominators.

In this case, convert the whole number into its reciprocal by putting 1 in the numerator and the number at denominator place. So five becomes 1/5, and it is the reciprocal of that number.

Math
Math

Thus, you can easily get the right solution of the dividing fractions problems. You can divide a fraction by another fraction by following the reciprocal and multiplication rule.