The online equation solving service will help you solve any equation. Using our website, you will receive not just the answer to the equation, but also see a detailed solution, that is, a step-by-step display of the process of obtaining the result. Our service will be useful to high school students and their parents. Students will be able to prepare for tests and exams, test their knowledge, and parents will be able to monitor the solution of mathematical equations by their children. The ability to solve equations is a mandatory requirement for schoolchildren. The service will help you educate yourself and improve your knowledge in the field of mathematical equations. With its help, you can solve any equation: quadratic, cubic, irrational, trigonometric, etc. The benefits of the online service are priceless, because in addition to the correct answer, you receive a detailed solution to each equation. Benefits of solving equations online. You can solve any equation online on our website absolutely free. The service is completely automatic, you don’t have to install anything on your computer, you just need to enter the data and the program will give you a solution. Any errors in calculations or typos are excluded. With us, solving any equation online is very easy, so be sure to use our site to solve any kind of equations. You only need to enter the data and the calculation will be completed in a matter of seconds. The program works independently, without human intervention, and you receive an accurate and detailed answer. Solution of the equation in general form. In such an equation, the variable coefficients and the desired roots are interconnected. The highest power of a variable determines the order of such an equation. Based on this, various methods and theorems are used for equations to find solutions. Solving equations of this type means finding the required roots in general form. Our service allows you to solve even the most complex algebraic equation online. You can obtain both a general solution to the equation and a particular one for the numerical values of the coefficients you specify. To solve an algebraic equation on the website, it is enough to correctly fill out only two fields: the left and right sides of the given equation. Algebraic equations with variable coefficients have an infinite number of solutions, and by setting certain conditions, partial ones are selected from the set of solutions. Quadratic equation. The quadratic equation has the form ax^2+bx+c=0 for a>0. Solving quadratic equations involves finding the values of x at which the equality ax^2+bx+c=0 holds. To do this, find the discriminant value using the formula D=b^2-4ac. If the discriminant is less than zero, then the equation has no real roots (the roots are from the field of complex numbers), if it is equal to zero, then the equation has one real root, and if the discriminant is greater than zero, then the equation has two real roots, which are found by the formula: D = -b+-sqrt/2a. To solve a quadratic equation online, you just need to enter the coefficients of the equation (integers, fractions or decimals). If there are subtraction signs in an equation, you must put a minus sign in front of the corresponding terms of the equation. You can solve a quadratic equation online depending on the parameter, that is, the variables in the coefficients of the equation. Our online service for finding general solutions copes well with this task. Linear equations. To solve linear equations (or systems of equations), four main methods are used in practice. We will describe each method in detail. Substitution method. Solving equations using the substitution method requires expressing one variable in terms of the others. After this, the expression is substituted into other equations of the system. Hence the name of the solution method, that is, instead of a variable, its expression is substituted through the remaining variables. In practice, the method requires complex calculations, although it is easy to understand, so solving such an equation online will help save time and make calculations easier. You just need to indicate the number of unknowns in the equation and fill in the data from the linear equations, then the service will make the calculation. Gauss method. The method is based on the simplest transformations of the system in order to arrive at an equivalent triangular system. From it, the unknowns are determined one by one. In practice, you need to solve such an equation online with a detailed description, thanks to which you will have a good understanding of the Gaussian method for solving systems of linear equations. Write down the system of linear equations in the correct format and take into account the number of unknowns in order to accurately solve the system. Cramer's method. This method solves systems of equations in cases where the system has a unique solution. The main mathematical action here is the calculation of matrix determinants. Solving equations using the Cramer method is carried out online, you receive the result instantly with a complete and detailed description. It is enough just to fill the system with coefficients and select the number of unknown variables. Matrix method. This method consists of collecting the coefficients of the unknowns in matrix A, the unknowns in column X, and the free terms in column B. Thus, the system of linear equations is reduced to a matrix equation of the form AxX=B. This equation has a unique solution only if the determinant of matrix A is different from zero, otherwise the system has no solutions, or an infinite number of solutions. Solving equations using the matrix method involves finding the inverse matrix A.
The online fraction calculator allows you to perform simple arithmetic operations with fractions: adding fractions, subtracting fractions, multiplying fractions, dividing fractions. To make calculations, fill in the fields corresponding to the numerators and denominators of the two fractions.
Fractions in mathematics is a number representing a part of a unit or several parts of it.
A common fraction is written as two numbers, usually separated by a horizontal line indicating the division sign. The number above the line is called the numerator. The number below the line is called the denominator. The denominator of a fraction shows the number of equal parts into which the whole is divided, and the numerator of the fraction shows the number of these parts of the whole taken.
Fractions can be regular or improper.
- A fraction whose numerator is less than its denominator is called a proper fraction.
- An improper fraction is when the numerator of a fraction is greater than the denominator.
A mixed fraction is a fraction written as an integer and a proper fraction, and is understood as the sum of this number and the fractional part. Accordingly, a fraction that does not have an integer part is called a simple fraction. Any mixed fraction can be converted to an improper fraction.
In order to convert a mixed fraction into a common fraction, you need to add the product of the whole part and the denominator to the numerator of the fraction:
How to convert a common fraction to a mixed fraction
In order to convert an ordinary fraction to a mixed fraction, you must:
- Divide the numerator of a fraction by its denominator
- The result of division will be the whole part
- The balance of the department will be the numerator
How to convert a fraction to a decimal
In order to convert a fraction to a decimal, you need to divide its numerator by its denominator.
In order to convert a decimal fraction to an ordinary fraction, you must:
How to convert a fraction to a percentage
In order to convert a common or mixed fraction to a percentage, you need to convert it to a decimal fraction and multiply by 100.
How to convert percentages to fractions
In order to convert percentages into fractions, you need to obtain a decimal fraction from the percentage (dividing by 100), then convert the resulting decimal fraction into an ordinary fraction.
Adding Fractions
The algorithm for adding two fractions is as follows:
- Perform addition of fractions by adding their numerators.
Subtracting Fractions
Algorithm for subtracting two fractions:
- Convert mixed fractions to ordinary fractions (get rid of the whole part).
- Reduce fractions to a common denominator. To do this, you need to multiply the numerator and denominator of the first fraction by the denominator of the second fraction, and multiply the numerator and denominator of the second fraction by the denominator of the first fraction.
- Subtract one fraction from another by subtracting the numerator of the second fraction from the numerator of the first.
- Find the greatest common divisor (GCD) of the numerator and denominator and reduce the fraction by dividing the numerator and denominator by GCD.
- If the numerator of the final fraction is greater than the denominator, then select the whole part.
Multiplying fractions
Algorithm for multiplying two fractions:
- Convert mixed fractions to ordinary fractions (get rid of the whole part).
- Find the greatest common divisor (GCD) of the numerator and denominator and reduce the fraction by dividing the numerator and denominator by GCD.
- If the numerator of the final fraction is greater than the denominator, then select the whole part.
Division of fractions
Algorithm for dividing two fractions:
- Convert mixed fractions to ordinary fractions (get rid of the whole part).
- To divide fractions, you need to transform the second fraction by swapping its numerator and denominator, and then multiply the fractions.
- Multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second.
- Find the greatest common divisor (GCD) of the numerator and denominator and reduce the fraction by dividing the numerator and denominator by GCD.
- If the numerator of the final fraction is greater than the denominator, then select the whole part.
Online calculators and converters:
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Let us analyze two types of solutions to systems of equations:
1. Solving the system using the substitution method.
2. Solving the system by term-by-term addition (subtraction) of the system equations.
In order to solve the system of equations by substitution method you need to follow a simple algorithm:
1. Express. From any equation we express one variable.
2. Substitute. We substitute the resulting value into another equation instead of the expressed variable.
3. Solve the resulting equation with one variable. We find a solution to the system.
To solve system by term-by-term addition (subtraction) method need to:
1. Select a variable for which we will make identical coefficients.
2. We add or subtract equations, resulting in an equation with one variable.
3. Solve the resulting linear equation. We find a solution to the system.
The solution to the system is the intersection points of the function graphs.
Let us consider in detail the solution of systems using examples.
Example #1:
Let's solve by substitution method
Solving a system of equations using the substitution method2x+5y=1 (1 equation)
x-10y=3 (2nd equation)
1. Express
It can be seen that in the second equation there is a variable x with a coefficient of 1, which means that it is easiest to express the variable x from the second equation.
x=3+10y
2.After we have expressed it, we substitute 3+10y into the first equation instead of the variable x.
2(3+10y)+5y=1
3. Solve the resulting equation with one variable.
2(3+10y)+5y=1 (open the brackets)
6+20y+5y=1
25y=1-6
25y=-5 |: (25)
y=-5:25
y=-0.2
The solution to the equation system is the intersection points of the graphs, therefore we need to find x and y, because the intersection point consists of x and y. Let's find x, in the first point where we expressed it we substitute y.
x=3+10y
x=3+10*(-0.2)=1
It is customary to write points in the first place we write the variable x, and in the second place the variable y.
Answer: (1; -0.2)
Example #2:
Let's solve using the term-by-term addition (subtraction) method.
Solving a system of equations using the addition method3x-2y=1 (1 equation)
2x-3y=-10 (2nd equation)
1. We choose a variable, let’s say we choose x. In the first equation, the variable x has a coefficient of 3, in the second - 2. We need to make the coefficients the same, for this we have the right to multiply the equations or divide by any number. We multiply the first equation by 2, and the second by 3 and get a total coefficient of 6.
3x-2y=1 |*2
6x-4y=2
2x-3y=-10 |*3
6x-9y=-30
2. Subtract the second from the first equation to get rid of the variable x. Solve the linear equation.
__6x-4y=2
5y=32 | :5
y=6.4
3. Find x. We substitute the found y into any of the equations, let’s say into the first equation.
3x-2y=1
3x-2*6.4=1
3x-12.8=1
3x=1+12.8
3x=13.8 |:3
x=4.6
The intersection point will be x=4.6; y=6.4
Answer: (4.6; 6.4)
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