Bottom of the fraction is known as the denominator, and there are numbers like 2 or 3. However, sometimes the denominator can be irrational root. So that the equation can be in its simplest form, it should not be irrational. You should fix this by making the denominator rational, and this is what it is known as rationalizing of the denominator. When the denominator is irrational, it still works, however, this is not simplest form, and it may cost the marks if you are a student. Removing them will help in solving the problem, and this is why you have to know how it works.
Multiply the bottom and the top with a conjugate
You can find another special way of moving the square root starting from the bottom to the top
This is a special way of moving the square root starting from bottom to the fraction which is at the top. This is done by multiplying the bottom and the top using a conjugate of a denominator.
A conjugate is a place where the sign of in a middle of two terms has been changed.
When the number is multiplied using the conjugate, they lead to its square number.
The denominator should never contain the radical, or it will be wrong depending on the level you are on. Rationalizing helps in getting the right answer. You should try everything you can so that you may find the fraction in which the denominator has rational denominator only.
After rationalizing a denominator, you have to check so that you can see that after rationalizing, there will be nothing else that you may simplify.
There is some math in Calculus, and they do take advantage in rationalizing denominator or the numerator. However, rationalizing denominator is important to know before someone can start to learn calculus. Learning the skills needed to rationalize the denominator, is important since it helps to simplify and to evaluate the expression. This is during the period when there were no online calculator needed for doing arithmetic. After rationalizing the equation, it becomes easier in computing without any extra tool. However, through using a powerful calculator, it is no longer required to rationalize the denominator since it is a simple way of doing the arithmetic computation. However, even if the student may be using the calculator, he should be aware of the needed skills to use when there is no calculator around.
Rationalize denominator is required in precalculus and in calculus topic in some case, there may be a need to rationalize a numerator of the fraction.
The greatest common factor is the greatest common number if we factorize the two different numbers and multiply them respectively. Therefore after factorizing, the biggest common number between them is the greatest common factor. In other words, the greatest common factor is also known as the highest common factor which is signified by H.C.F.
Therefore the procedure goes like this if we factories the number if the two numbers are 10 and 25
Step1-divide the number 10 by 2, and you will get 5 and further divide the number 5 with five till you get 1. Therefore the factors are 2*5*1
Step 2-divide the number 25 by 5, if we factories the number then it will be 5 and five will be further divided by the number 5 and we get 1. Therefore the factors are 5*5*1
Step 3- between the factors 2*5*1 and 5*5*1, the greatest number in common is 5 and thus is called as the greatest common factor.
Step 4-Therefore 5 is the greatest common factor or is also known as the HCF or highest common factor.
Linear equations- A linear equation is in such a way because a plane is divided into two parts, the X-axis and the Y-axis. If we wish to identify a line regarding mathematics, then we need two variables and a constant and thus the linear equations is designed as ax+by+c=0 where x and y are variables and c is constant. This the generalized equations regarding mathematics which can further become more complex with the passage of time. Therefore this generalize equation will later be used in solving the equations related to complex lines, lines intersecting in between and many more.
Therefore let's presume two equations 3x+4y+6=0 and 3x+2y+6=0. Now to solve this equation we will have to apply a mathematical trick, we will first multiply the first equation with 1 and which will yield again 3x=4y=6=0 and the second equation by 2 and we will get 6x+4y+12=0. Now after eliminating both the equation we will get 3x+6=0 and x=-1/2.
And now we will put the value of x into the first equation and then we can find the value of y be -15/2 respectively. The entire process can be very exciting if we put the respective values of x and y on the equation we will get the right-hand side value which ultimately defines the value or the position of x and y in the plane sheet.
Math help is the best issue when comes to children. You can get the best software when comes to solving mathematical problems as there are much mathematical software. The beautiful part of the software is that it can help solve all the problems in the equations and thus can easily entice people. There are even endless numbers of software which can easily help children learn mathematics. The software includes learning abacus and playing with the calculation and thus finally figuring out the exact value of the question. Thus the significance can’t be overlooked. Mathematics is the very fabric which helps in understanding the very fabric of life and how it’s been made.
Addition and subtraction are the most common mathematical term. Addition and subtraction of two numbers are easy, and each can solve the problem. Instead of it, primary school students feel some difficulties while solving large numerical values. Though students can solve largest numerical subtraction, but they need help while they are solving fractional values. Addition and subtraction of fractional values are quite difficult. Adding and subtracting fractions seems tricky, but you follow simple steps then you need to practice more and more.
Here you can find some steps to follow. The adding and subtracting fraction values depends on the denominators. Check if the denominator of all fraction values or same or unequal. If the denominators are not same, then you need to make it equal or find out the LCM of the denominators. If the denominator is similar, then you just need to add the numerator. On the other hand, by making the denominator same, you can add numerator simply. Now, write the numerator after adding or subtracting over the denominator.
To understand both the methods, you should have to check some examples below-
If the denominator is same,
If the denominator is different from another fraction value
When the denominator is not same, then you can solve the fractional problem with two different methods. One is using the LCM of a denominator, or another one is a direct method. For example-
Here, 12 is the LCM of the denominator. Now, you will get the result as
Hence, the LCM method is quite difficult as compared to the direct method because you have to find out LCM first. If using the direct method, you simply need to multiply the numerator of the first fraction to the denominator of second fraction and numerator of the second fraction to the denominator of the first fraction. The example given below that can better help you to understand subtracting fractions.
Now, multiply the numerator of the first fraction by the denominator of the second fraction and vice versa then multiply both denominators.
Now, you get the solution as
It is a simple method as compare of taking the LCM of denominators. Subtracting fractions is basically the simple mathematical problem, but it becomes difficult when there is more than two fractions are available in the problem. When there is more than two fractions are available, then the direct method becomes more complex and LCM method as well. There is no direct trick to solve the complex subtracting fractions.
To overcome the problem, you can buy the software or use the website to solve the fraction values directly. You can find hundreds of websites or software that helps in solving mathematical problems. In the software or website, you just need to fill the problem then press on next step. Either you choose a direct answer or solve the problem step by step. Basically, it is not an online/offline tutorial but the software that helps in solving the adding and subtracting fractions. It is quite simple to use the software. You can buy CD relevant to the software and install on your PC. Now, you can learn how to solve fractions or help others.
There are many children who don’t like to learn math at all but math is a very important subject. There are many parents who are worried because their children are very week in math. Parents spend a lot of money just to make sure that their children are learning to solve the problems and what the things they have to keep in mind. But here we come up with the new formula that will help you in solving math very easily with the help of simplify calculator.
This calculator helps you in solving the entire mathematical problem. It helps you in solving all your doubts and will be providing the solution to the problem. Simplify calculator is very useful for the school, college going students, parents, and people who want to learn math. Simplify calculator will you in doing your homework. With the help of this calculator you can do your homework, prepare for your exams and you can also refresh your memory.
You just have to write the question in the simplify calculator, and it will help you in providing with the solution of the question. The solution that is provided by the calculator has explained in step wise manner that so that you do not have any problem in understanding the solution to the problem and know how it is done.
The solution provided to you is in a very explanatory form you can see the entire demo and the related questions as well. You can know all the step by step solution, therefore, you can learn with more perfection. The simplify calculator convert the improper fraction to mixed in the simple form. This calculator helps you in simplifying the proper fraction by deducting the lowest term it also helps you in showing the work involved.
The benefits of simplify calculator are:
It helps you in solving all types of questions whatever they may be like algebra, quadratic or any mathematical problem. All the solution of the problem can be easily solved very easily. This will provide you with the solution of the problems in few seconds.
All the complex problems can be easily solved; they help you in providing all the problems of the solution weather they are quadratic, algebra, linear equation, polynomial and much more all the solution of the problem can be easily provided to you.
All the complex questions can be solved in a simplified form. Like all the improper fractions into a proper fraction for the solution. As when you can solve the problem by converting them into proper form Therefore with the help of the simplify calculator, you can put the question, and it will help you in providing the solution for the problem.
When you have the simplify calculator, then parents will not have to spend a lot of money on tutors. As this simplify calculators will help you in solving the entire problem as it is done by the tutor it selves.
These are some of the benefits of simplify calculator.
Different types of mathematical equations you can find in which linear, as well as quadratic equations, are common. These are the part of algebraic equations. The algebra is the part or branch of mathematics, and you can find its importance in mathematics. The algebraic system of equation contains different equations. Before learning about the system of equations, you must know some basics as-
Algebraic equations: The algebraic equation is the major part of mathematics in which various unknown values, mathematical signs, and constant values used to represent any number. While solving the algebraic expressions, you can get the values of unknown. More than one solution is possible for same variable value according to the equation.
Linear equation: liner equation includes one or more than one variable, but the variable does not include any higher degree. It means the variable has a first-order degree and you can find only one value for unknown.
Ex: x + 6 = 12
In result, you will get the value of x = 6
Quadratic equation: It comes under the algebraic equation in which you can find the second order degree of a variable. In a quadratic equation, you get two results for same variable or unknown value. For example- x² + 5x + 6 = 0
In which you can find values of x = -2 and -3
Exponential equation: It is another type of algebraic equation. In the system of equation in mathematics, exponential equations place an important role. The exponential equation shows successive increasing and decreasing variables.
Along with them, you can find various algebraic equations. Solving this algebraic equation becomes difficult when you do not have adequate knowledge of equations. Then, you need to join an online tutor to get adequate knowledge of it. On the other hand, you can choose the online platform that automatically solves the algebraic equations. You can also find the software which works offline.
How does the offline platform work?
You can choose either the website or the software for algebraic equation then you can easily solve it. First, you need to download the software on your PC. You can also buy CD to install the software on your personal computer. Now, you can use your PC to solve an algebraic equation. Some important formulas are preloaded into the software. It is not an offline tutor but solves the problem due to a pre-loaded program.
The user just needs to fill the question then press on the next tab. Now, you can get step by step solution of the equation. You can either choose the direct formula method to apply different method. The major benefit of choosing the software is that you can get the answer in few seconds. You can help your kid to solve their homework. The step by step solution of particular equation helps to understand the system of equations. Now, you can understand each operation, note down each step and understand what operations were used in the solution.
The system of equations is not difficult with the right mathematical software. It is your choices either use the particular website or download the software to solve an algebraic solution.
The solution of an algebraic equation is nothing but finding a number or quantity that can balance the equation. The algebra equation is basically a combination of constant value, coefficients, and variables. The total sum of all the quantities given above is equal to zero. The standard form of an algebraic equation is constituted coefficient, one or more than one variable, and the content value. Basically, the algebraic equation denotes a line which is parallel, perpendicular or cuts the X and Y-axis. Some of the algebraic equations types are given below-
A Linear equation is a type of algebraic equation in which the variable only has degree =1. The linear equitation is denoted as-
If we put a single number in place of x, we will get a number of y and vice versa. It is the most common method to solve the linear algebraic equation.
It is also the type of algebra equation which has two higher degrees of a variable. You can better understand the quadratic equation with right example as-
y = 2x² + 10x + 8
If we put y = 0, then we will get
2x² + 10x + 8 = 0
Now you can solve the above equation by using the formula method. Also, there are different methods available to solve the equation, but formula method is usually used more than other.
The cubic algebraic equation has three higher degrees of a variable. That means you will get three values of a variable. When one of the values of a variable puts on the equation, the equation becomes zero. Hence, you have achieved the right quantity of a variable. Consider an example to understand the cubic equation-
7x³ + 2x² + 10x + 8 = 0
With the specific method, the cubic algebraic equation can be easily solved.
Quartic equation with degree = 4
The quadratic equation is a part of the algebraic equation which includes four higher degree variables. Basically, it is simple to solve the as compared to the cubic equation. To better understand the example explains better-
It can be solved as the quadratic equation by putting the variable equal to x².
Quantic equation includes 5 higher degrees on a variable. It is also taught to solve the quantic equation.
You can use various methods to solve this equation which is complicated.
It is the algebraic equation that includes 6 higher degree of a variable. The example is given below-
Also, there are higher order degrees are available in an algebraic equation, but less than 5-degree algebraic equations are common in algebraic homework.
To get the math help or homework help by the algebra software, you need to visit the proper website. This website includes the program that provides an accurate answer about the variable. You do not need to feel any trouble with solving the algebra equation. The algebraic calculator helps you out with ease.
Mathematical has been one of the interesting subjects for many students since school years. Some of the students are afraid of its complexity and the numerical values. Simple mathematical rules such as addition, subtraction, multiplication, and division are really simple. But adding some unknown values into these expressions cause complexity in a mathematics calculation. These unknown values are basically expressed as X or Y. also other letters can be taken as the unknown. These unknown values are variables whose value varies with some numerical values. The entire expression is known as an algebra equation.
Algebra equation contains three terms namely variables, coefficients, and the constant value. Different type of algebraic equation and its form is available. You can analyze its type as-
Some digital platforms are available where the mathematical expert helps you in solving the exponential problems. Exponential expressions are one of the intimidating mathematical problems. To solve the algebra equation without graph calculator, you need to learn from basic. There is some basic function of algebra are-
Factors, base and exponential
In simple mathematical expression where you are instructed to multiply numbers and find out the single result. These numbers are known as factors. To understand better, consider an example as
3 x 5 = 15
Here 3 and 5 are the factors of 15 and the 15 is the product of 3 and 5. If you are going to find the factor of 49, then there are two factors i.e. 7 and 7. Consider one more example as to find a factor of 63. Here 7 and 9 are the factors and 3 and 3 are the factor of 9. So, you have 7, 3 and 3 factors of 63. The mathematical expression can be written as
3 x 5 = 15
7 x7 = 49
7 x 3 x 3 = 63
The last expression can be written as 7×3² = 63
The product of 3 x 3 can be written as 3² , and it is pronounced as three squared. Here the superscript is known as an exponent, and a lower number is called base. Now we know about base, factors, and exponent.
To add any number in which each has exponent value you have to find out the power of numerical term then multiply the number. Now you can easily add it. Similarly, if the math problem includes addition, multiplication, subtraction, and division then need to know the variable power then solve it.
3² + 4⁴ = 9 + 64 = 73
6x²+3x² = 9x²
This is the common rule to solve the exponential mathematical equation. The exponential calculator works similar but provides an instant result.
Do you dislike mathematics subject and feel sleepy in the classroom while the teachers are delivering the mathematics concepts? Then, you can start loving the subject by learning mathematics at your pace using math software that is available in online. This helps both the students and the parents while the former can learn the concepts of mathematics from the scratch and the latter will save a lot of money from hiring a tutor for their kids. Ideally, this software will let the students learn the step by step procedure in solving the math problem. So, when students gain a grip over the concepts and formulas, they will be able to solve any complicated problem with ease. But, for that, it is imperative for the students to understand the concepts from scratch.
Mathematics is the complicated subject for many students. Also, in the entire universe, the most crucial characters are numbers. To solve a problem, people have to learn many concepts in mathematics. For instance, if you want to solve a problem in algebra, then you would need to carry out factorization and simplification. Undeniably, mathematics is the toughest subject in school and understanding the concepts make it the easiest of all. For that, there need a lot of dedication, hard work, and will to learn new concepts. Solving a complicated problem is challenging for the people, however, if you understand the methodologies and procedure, then it would be a piece of cake.
However, if you want to solve the math problem with ease, then here are a few tips you need to embrace
Examine the problem: Prior to putting your pen on the paper to solve the problem; you first need to understand the way you can solve it. You need to extract the data required for you to solve the problem. Subsequently, you need to take your time to thoroughly understand the problem. You need to break the complicated problem into small parts to solve it without making blunders and to get an accurate result. When reading the problem, you need to break the sentences and understand each sentence clearly. You can also take the help of the hints given in the problem. This helps you to attempt the problem and get the correct result.
Use the right formulas: It is crucial for a student to learn the mathematical formulas. These are important to solve the problem with ease. Applying of a right formula will help you get an accurate result. If you are doing homework, then you need to check the math formula in the textbook. Also, you can take the examples given in the text book as a reference to solve similar kind of unsolved problems. Ideally, mathematical problems are explained by multiple variables. You need to identify the formula that applies to solve a problem.
Be careful while solving the problem: Math problems should be solved in step by step manner to get the right output. You need to break the problem and solve each part of the problem carefully. A single mistake made in a problem would continue throughout the problem and at the end, it gives a wrong output. Ideally, this kind of challenge is faced by the students with complicated problems. If you have any doubts, then you can refer to the procedure to solve the problem.
Algebra expression is directly related to the algebraic equations and polynomial equations. In the equation, you have one or more than one unknown, but the values cannot be determined when there is no equation including same unknown. The algebraic equations are most probably used to find the variables values to make both the side equal. For example, you have algebraic equation such as
4x + 8y = 18
And other one is, 3x+ 4y = 14,
Now, you have to find the value of x and y respectively. To find the values of unknown, you must know mathematical operations such as addition, subtraction, multiplication, and division.
To solve this algebra expression, apply subtraction operation on the both. In subtraction, only same variables can subtract. That means the 4x may subtract from 3x and similarly, 8y subtract from 4y. The constant value subtracts from a constant value of other equation.
Note that, before subtracting the equation, it needs to make the variables same. That means if we do not make the values same, then we have the equation in which both unknown are available. Then we can never find the value. To avoid this complexity in algebra expression, multiply the number with both the equation. It is not difficult to find the number to multiply in an equation. Find the unknown which you want to eliminate. Then select the number according to it. You want to eliminate x from both the equation then multiply equation one by 3, and another one is 4.
Now you have new equations as,
12x + 24y = 54
And, second one becomes, 12x + 16y = 56
Now you have the option to eliminate the variable x from the equation. For this, you need to subtract equation one from two. Then you have a new equation which has only one unknown because the second one has eliminated.
You have, 8y = -2,
Don’t you worry if you have answered in negative because in algebra expression; you have to face lots of questions that include negative value? It is easy to find the unknown if you have only one unknown. Divide both the side of an equation by 8, and you will get the value of y.
You have, y = -1/4
After getting the one variable’s value, you have to find another one. Now put Y’s value on anyone equation in which x is present. Consider equation one,
4x + 8y = 18,
When putting the value of y,
You have, 4x – 2 = 18
Not transfer the constant value to the right side. Then you have,
4x = 20,
Divide both the side by 4, and you have x = 5
In algebra expression, you need to face various difficulties which are solved by considering important factors. The application of algebraic equation helps to know the certain results. To solve the difficult expression, you need to practice more and more. More the practice takes you to be expert in solving the algebraic equations. The basic of algebra is simple but difficult to solve their application. Regular practicing can make you perfect in algebra expression-solving.
Mathematics is the subject that is tough, but interesting. Many people face a problem with many topics of the mathematics. If you found it difficult to solve the fraction to decimal problems, you should read the steps explained further to solve such problems. Firstly, you should know what is a decimal or fraction number. A decimal number is a number that has a decimal point, and it is a number of base-10 number system. For example 10.0, 0.45, 1.75 is the decimal numbers.
There are commonly three types of the fraction. It includes a proper fraction, improper fraction, and the mixed fraction. If the numerator is less than the denominator, then it is called as a proper fraction, for example, 5/8. On the other hand, if the numerator is greater than the denominator, then it is called as the improper fraction, for example, 4/3. Mixed fraction has a whole number as well as a fraction.
It is true that we are living in a modern world and we have the calculators in computers and mobile phones. Anyone can easily calculate the fraction form of a decimal number. But you should know the manual method of solving the fraction to decimal problems. You can easily solve such problems by following these easy steps.
The easy steps to convert a fraction to decimal number with an example
• Step 1: you must have to find a number that you can multiply by the number at the denominator place of the fraction. So, it can convert the number at denominator to 10, or 100, or 1000 and so on. We will take an example here as 5/4. So, you should find the right number that will make the denominator of this fraction that is 4 to 100 on multiplication. You can’t make it 10 as it is not a multiple of 4. So you have to find a number which you can multiply to 4 to make 100 at the denominator. You can multiply 25 by 4 so you can make it 100.
• Step 2: The next step is to multiply both the numerator and denominator by that number. In this example, you have to multiply 5 and 4 by 25 so you will get a result as 125/100. It is an important step to finding a correct answer of any fraction to the decimal problem. If you want a proper solution, you must multiply correctly.
• Step 3: the last step is just to right down the numerator number by correctly putting the decimal point in the right spot. In this example, you have to place a decimal point after two spaces from the right side due to the reason that there are two zeros in the denominator. So the correct decimal of the fraction 5/4 is 1.25.
Thus, these are the simple steps that are applicable for both the improper and proper fractions. The example given with these steps helps to get a good idea about it. If you practice some more problems of the fraction to a decimal by using these steps, your concept will be clear. You can then easily solve any problem on this topic.
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