# Math Problem Solver

This free calculator will try to solve any math problem: algebra (equation solver, system of equations solver, least common multiple, greatest common divisor, synthetic division, polynomial long division, partial fraction decomposition, polynomial calculator, factoring calculator), calculus (derivative, integral, Taylor series, tangent line, graphing calculator, implicit differentiation, Riemann sum), differential equations (direct and inverse Laplace transforms) and much more, with steps shown (if possible).

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## Prime Factorization Calculator

This calculator will find the prime factorization of the given number, with steps shown.

## Mixed Number to Improper Fraction Calculator

The calculator will convert the given mixed number into an improper fraction, with steps shown.

## Improper Fraction to Mixed Number Calculator

The calculator will convert the given improper fraction into a mixed number, with steps shown.

## Decimal to Fraction Calculator

The calculator will convert decimal (simple, repeating or recurring) into fraction (and, if possible, into mixed number), with steps shown.

## Fraction to Decimal Calculator

The calculator will convert the given fraction (proper or improper) or mixed number into a decimal (possibly, repeating or recurring), with steps shown.

## Percent to Fraction Calculator

The calculator will convert percent into fraction (proper, improper, mixed number), with steps shown.

## Fraction to Percent Calculator

The calculator will convert the given fraction (proper, improper, or mixed number) into a percent, with steps shown.

## Decimal to Percent Calculator

The calculator will convert decimal into percent, with steps shown.

## Percent to Decimal Calculator

The calculator will convert percent into decimal, with steps shown.

## Fractions Calculator

The calculator will find (with steps shown) the sum, difference, product and result of the division of fractions or mixed numbers. It will also convert fraction into decimal number and into improper fraction (if possible).

## Square Root Calculator

The calculator will find the square root of the number `n` (i.e. such number `x`, that `x^2=n`) to the given precision.

## Cube Root Calculator

The calculator will find the cube root of the number `n` (i.e. such number `x`, that `x^3=n`) to the given precision.

## Greatest Common Divisor/Factor (GCD) Calculator

The calculator will find the greatest common factor/divisor (GCF) of the given positive numbers, with steps shown, using either the factoring method or the prime factorization method.

## Least Common Multiple (LCM) Calculator

The calculator will find the least (smallest) common multiple of the given positive numbers, with steps shown, using either the factoring method or the prime factorization method.

## Long Division Calculator

The calculator will divide any two numbers (positive or negative, integer or decimal), with steps shown. Enter the dividend and the divisor and get the quotient to the given precision without remainder or quotient with remainder.

## Scientific Notation Calculator

The calculator will convert the given number into scientific notation.

## Quadratic Equation Calculator

The calculator will solve the quadratic equation step by step either by completing the square or using the quadratic formula. It will find both the real and the imaginary (complex) roots.

## Synthetic Division Calculator

The calculator will divide the polynomial by the binomial using synthetic division, with steps shown.

## Polynomial Long Division Calculator

The calculator will perform the long division of polynomials, with steps shown.

## Polynomial Calculator

The calculator will find (with steps shown) the sum, difference, product and result of the division of two polynomials (quadratic, binomial, trinomial, etc.). It will also calculate the roots of the polynomials and factor them. Both univariate and multivariate polynomials are accepted.

## Slope Intercept Form Calculator with Two Points

The slope intercept form calculator will find the slope of the line passing through the two given points, its y-intercept and slope-intercept form of the line, with steps shown.

## Factoring Polynomials Calculator

The calculator will try to factor any polynomial (binomial, trinomial, quadratic, etc.), with steps shown. The following methods are used: factoring monomials (common factor), factoring quadratics, grouping and regrouping, square of sum/difference, cube of sum/difference, difference of squares, sum/difference of cubes, Rational Zeros Theorem. The calculator accepts both univariate and multivariate polynomials.

## Order of Operations Calculator

The calculator will evaluate the given expression, showing the order of operations PEMDAS.

## Parallel and Perpendicular Line Calculator

The calculator will find the equation of the parallel/perpendicular line to the given line, passing through the given point, with steps shown.

For drawing lines, use graphing calculator.

## FOIL Calculator

The calculator will multiply two binomials using the FOIL method, with steps shown.

## Multiplying Polynomials Calculator

The calculator will multiply two polynomials (quadratic, binomial, trinomial etc.), with steps shown.

## Dividing Polynomials Calculator

The calculator will divide two polynomials (quadratic, binomial, trinomial etc.), with steps shown.

## Rational Zeros Theorem Calculator

The calculator will find all possible rational roots of the polynomial, using the Rational Zeros Theorem. After this, it will decide which possible roots are actually the roots. This is a more general case of the Integer (Integral) Root Theorem (when leading coefficient is `1` or `-1`). Steps are available.

## Descartes' Rule of Signs Calculator

The calculator will find the maximum number of positive and negative real roots of the given polynomial using the Descartes' Rule of Signs, with steps shown.

## Completing the Square Calculator

The calculator will try to complete the square for the given quadratic expression, ellipse, hyperbola or any polynomial expression, with steps shown.

## Remainder Theorem Calculator

The calculator will calculate `f(a)` using the remainder (little BÃ©zout's) theorem, with steps shown.

## Partial Fraction Decomposition Calculator

This online calculator will find the partial fraction decomposition of the rational function, with steps shown.

## Factoring Calculator

The calculator will try to factor any expression (polynomial, binomial, trinomial, quadratic, rational, irrational, exponential, trigonometric, or mix of them), with steps shown. To do this, some substitutions are first applied to convert the expression into a polynomial, and then the following techniques are used: factoring monomials (common factor), factoring quadratics, grouping and regrouping, square of sum/difference, cube of sum/difference, difference of squares, sum/difference of cubes, and Rational Zeros Theorem.

## Equation Solver

The calculator will find the roots (exact and numerical, real and complex), i.e. solve for `x`, `y` or any other variable, of any equation (linear, quadratic, polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value) on the given interval.

## System of Equations Calculator

This solver (calculator) will try to solve a system of 2, 3, 4, 5 equations of any kind, including polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value, etc. It can find both real and complex solutions. To solve a system of linear equations with steps, use the system of linear equations calculator.

## Simplify Expression Calculator

This calculator will simplify fractions, polynomial, rational, radical, exponential, logarithmic, trigonometric, and hyperbolic expressions.

## Inverse Function Calculator

The calculator will find the inverse of the given function, with steps shown. If the function is one-to-one, there will be a unique inverse.

## Parabola Calculator

This calculator will find either the equation of the parabola from the given parameters or the axis of symmetry, focus, vertex, directrix, focal parameter, x-intercepts, y-intercepts of the entered parabola.

To graph a parabola, visit parabola grapher (choose the implicit option).

## Circle Calculator

This calculator will find either the equation of the circle from the given parameters or the center, radius, diameter, area, circumference (perimeter), eccentricity, x-intercepts, y-intercepts, domain, and range of the entered circle.

To graph a circle, visit circle graphing calculator (choose implicit option).

## Ellipse Calculator

This calculator will find either the equation of the ellipse (standard form) from the given parameters or the center, vertices, co-vertices, foci, area, circumference (perimeter), focal parameter, eccentricity, (semi)major axis length, (semi)minor axis length, x-intercepts, y-intercepts, domain, and range of the entered ellipse.

To graph an ellipse, visit ellipse graphing calculator (choose the implicit option).

## Hyperbola Calculator

This calculator will find either the equation of the hyperbola (standard form) from the given parameters or the center, vertices, co-vertices, foci, asymptotes, focal parameter, eccentricity, (semi)major axis length, (semi)minor axis length, x-intercepts, and y-intercepts of the entered hyperbola.

To graph a hyperbola, visit hyperbola graphing calculator (choose the implicit option).

## Distance between Two Points Calculator

For two given points, the calculator will find the distance between them, with steps shown.

## Inverse Sine Calculator

The calculator will find the inverse sine of the given value in radians and degrees.

The inverse sine `y=sin^(-1)(x)` or `y=asin(x)` or `y=arcsin(x)` is such a function that `sin(y)=x`.

The domain of the inverse sine is `[-1,1]`, the range is `[-pi/2,pi/2]`.

It is an odd function.

## Inverse Cosine Calculator

The calculator will find the inverse cosine of the given value in radians and degrees.

The inverse cosine `y=cos^(-1)(x)` or `y=acos(x)` or `y=arccos(x)` is such a function that `cos(y)=x`.

The domain of the inverse cosine is `[-1,1]`, the range is `[0,pi]`.

It is an even function.

## Inverse Tangent Calculator

The calculator will find the inverse tangent of the given value in radians and degrees.

The inverse tangent `y=tan^(-1)(x)` or `y=atan(x)` or `y=arctan(x)` is such a function that `tan(y)=x`.

The domain of the inverse tangent is `(-oo,oo)`, the range is `(-pi/2,pi/2)`.

It is an odd function.

## Inverse Cotangent Calculator

The calculator will find the inverse cotangent of the given value in radians and degrees.

The inverse cotangent `y=cot^(-1)(x)` or `y=acot(x)` or `y=arccot(x)` is such a function that `cot(y)=x`.

The domain of the inverse cotangent is `(-oo,oo)`, the range is `(0,pi)`.

It is an odd function.

## Inverse Secant Calculator

The calculator will find the inverse secant of the given value in radians and degrees.

The inverse secant `y=sec^(-1)(x)` or `y=asec(x)` or `y=arcsec(x)` is such a function that `sec(y)=x`.

The domain of the inverse secant is `(-oo,-1]uu[1,oo)`, the range is `[0,pi/2)uu(pi/2,pi]`.

This function is neither even nor odd.

## Inverse Cosecant Calculator

The calculator will find the inverse cosecant of the given value in radians and degrees.

The inverse secant `y=csc^(-1)(x)` or `y=acsc(x)` or `y=arccsc(x)` is such a function that `csc(y)=x`.

The domain of the inverse cosecant is `(-oo,-1]uu[1,oo)`, the range is `[-pi/2,0)uu(0,pi/2]`.

This function is neither even nor odd.

## Binomial Expansion Calculator

The calculator will find the binomial expansion of the given expression, with steps shown.

## Logarithm Calculator

The calculator will find the logarithm (natural, decimal, etc.) of the given value to the given base (e, 10, etc.).

The domain of the logarithm is `(0,oo)`, the range is `(-oo,oo)`.

It is neither an even nor an odd function.

## Inequality Calculator

This calculator will solve the linear, quadratic, polynomial, rational and absolute value inequalities. It can handle compound inequalities and systems of inequalities as well.

To graph inequalities, use graphing calculator.

## Composite Function Calculator

The calculator will find the composition of the functions, with steps shown. It will also evaluate the composition at the specified point, if needed.

## Evaluate Calculator

The calculator will find the value of the given expression, plugging the values of the given variables, if needed.

## Solve for X Calculator

The calculator will find the `x` (exact and numerical, real and complex) in the given equation.

## Zeros Calculator

The calculator will find zeros (exact and numerical, real and complex) of the linear, quadratic, cubic, quartic, polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, and absolute value function on the given interval.

## Simultaneous Equation Solver

This calculator will try to solve the system of 2, 3, 4, 5 simultaneous equations of any kind, including polynomial, rational, irrational, exponential, logarithmic, trigonometric, hyperbolic, absolute value, etc. It can find both real and complex solutions.

## Trigonometry Calculator

This calculator can solve trigonometric equations, simplify and evaluate expressions. It can handle trigonometric and inverse trigonometric functions.

## Complex Number Calculator

The calculator will simplify any complex expression, with steps shown. It will perform addition, subtraction, multiplication, division, raising to power, and also will find the polar form, conjugate, modulus and inverse of the complex number.

## Intercepts Calculator

The calculator will find the x- and y-intercepts of the given function, expression or equation.

## Roots of Complex Number Calculator

The calculator will find the `n`-th roots of the given complex number, using de Moivre's Formula, with steps shown.

## Cubic Equation Calculator

The calculator will find the roots of the cubic equation in both the analytic and the approximate forms.

## Quartic Equation Calculator

The calculator will find the roots of the quartic equation in both the analytic and the approximate forms.

## Exponential Function Calculator

This calculator will calculate the exponential function with the given base and exponent.

## System of Linear Equations Calculator

This calculator will solve the system of linear equations of any kind, with steps shown, using either the Gauss-Jordan Elimination method or the Cramer's Rule. To solve any system, use system of equations calculator.

## End Behavior Calculator

This calculator will determine the end behavior of the given polynomial function, with steps shown.

## Degree and Leading Coefficient Calculator

The calculator will find the degree, leading coefficient, and leading term of the given polynomial function.

## Triangle Calculator

The calculator will try to find all sides and angles of the triangle (right triangle, obtuse, acute), as well as its perimeter and area.

## Pythagorean Theorem (Right Triangle) Calculator

The calculator will try to find all sides of the right-angled triangle using the Pythagorean Theorem. It will also find all angles, as well as perimeter and area.

## MathGrapher: Graphing Calculator-Function Grapher

A free online 2D graphing calculator (plotter), or curve calculator, that can plot piecewise, linear, quadratic, cubic, quartic, polynomial, trigonometric, hyperbolic, exponential, logarithmic, inverse functions given in different forms: explicit, implicit, polar, and parametric. It can also graph conic sections, arbitrary inequalities or systems of inequalities, slope fields (vector fields or direction fields), and visualize the Riemann Sum. Plots can be styled and customized according to needs.

To plot a 3d graph, use 3d grapher.

## Online Derivative Calculator with Steps

The online calculator will calculate the derivative of any function, with steps shown. Also, it will evaluate the derivative at the given point, if needed. It also supports computing the first, second and third derivatives, up to 10.

## Limit Calculator

This free calculator will find the limit (two-sided or one-sided, including left and right) of the given function at the given point (including infinity).

## Tangent Line Calculator

The calculator will find the tangent line to the explicit, polar, parametric and implicit curve at the given point, with steps shown.

It can handle horizontal and vertical tangent lines as well.

## Taylor and Maclaurin (Power) Series Calculator

The calculator will find the Taylor (or power) series expansion of the given function around the given point, with steps shown. You can specify the order of the Taylor polynomial. If you want the Maclaurin polynomial, just set the point to `0`.

## Implicit Differentiation Calculator

The implicit differentiation calculator will find the derivative of an implicit function treating either `y` as a function of `x` or `x` as a function of `y`.

## Asymptote Calculator

The calculator will find the vertical, horizontal and slant asymptotes of the function, with steps shown.

## Linear Approximation Calculator

The calculator will find the linear approximation to the explicit, polar, parametric and implicit curve at the given point, with steps shown.

## Quadratic Approximation Calculator

The calculator will find the quadratic approximation to the given function at the given point, with steps shown.

## Function Calculator

The calculator will find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical points, extrema (minimum and maximum, local, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the single variable function. The interval can be specified. Parity will also be determined.

## Domain and Range Calculator

The calculator will find the domain and range of the single-variable function.

## Critical Points and Extrema Calculator

The calculator will find the critical points, local and absolute (global) maxima and minima of the single variable function. The interval can be specified.

## Mean Value Theorem Calculator

The calculator will find all numbers `c` (with steps shown) that satisfy the conclusions of the Mean Value Theorem for the given function on the given interval.

## Difference Quotient Calculator

The calculator will find the difference quotient for the given function, with steps shown.

## Average Rate of Change Calculator

The calculator will find the average rate of change of the given function on the given interval, with steps shown.

## Inflection Points and Concavity Calculator

The calculator will find the intervals of concavity and inflection points of the given function.

## Integral (Antiderivative) Calculator with Steps

This online calculator will find the indefinite integral (antiderivative) of the given function, with steps shown (if possible).

## Definite and Improper Integral Calculator

The calculator will evaluate the definite (i.e. with bounds) integral, including improper, with steps shown.

## Area between Curves Calculator

The calculator will find the area between two curves, or just under one curve.

## Riemann Sum Calculator

The calculator will approximate the definite integral using the Riemann sum and sample points of your choice: left endpoints, right endpoints, midpoints, and trapezoids.

## Trapezoidal Rule Calculator

The calculator will approximate the integral using the Trapezoidal Rule, with steps shown.

## Midpoint Rule Calculator

An online calculator for approximating a definite integral using the Midpoint (Mid ordinate) Rule, with steps shown.

## Simpson's (Parabolic) Rule Calculator

An online calculator for approximating the definite integral using the Simpson's (Parabolic) rule, with steps shown.

## Series and Sum Calculator

This calculator will find the sum of arithmetic, geometric, power, infinite, and binomial series, as well as the partial sum.

## Arc Length Calculator for Curve

The calculator will find the arc length of the explicit, polar or parametric curve on the given interval, with steps shown.

## Radius and Interval of Convergence Calculator

The calculator will find the radius and interval of convergence of the given power series.

## Area of Surface of Revolution Calculator

The calculator will find the area of the surface of revolution (around the given axis) of the explicit, polar or parametric curve on the given interval, with steps shown.

## Average Value of a Function Calculator

The calculator will find the average value of the function on the given interval, with steps shown.

## Polar/Rectangular Coordinates Calculator

The calculator will convert the polar coordinates to rectangular (Cartesian) and vice versa, with steps shown.

## Partial Derivative Calculator

This online calculator will calculate the partial derivative of the function, with steps shown. You can specify any order of integration.

## Multiple (Double, Triple) Integral Calculator

The calculator will calculate the multiple integral (double, triple).

## Divergence Calculator

The calculator will find the divergence of the given vector field, with steps shown.

## Gradient of Function Calculator

The calculator will find the gradient of the given function (at the given point if needed), with steps shown.

## Directional Derivative Calculator

The calculator will find the directional derivative (with steps shown) of the given function at the point in the direction of the given vector.

## Curvature Calculator

The calculator will find the curvature of the given explicit, parametric or vector function at a specific point, with steps shown.

## Unit Tangent Vector Calculator

The calculator will find the unit tangent vector of a vector-valued function at the given point, with steps shown.

## Unit Normal Vector Calculator

The calculator will find the principal unit normal vector of the vector-valued function at the given point, with steps shown.

## 3D Function Grapher

A free online 3D graphing calculator for plotting linear, quadratic, cubic, quartic, polynomial, trigonometric, hyperbolic, exponential, and logarithmic curves. Plots can be styled and customized according to the needs.

To plot a 2d graph, use 2d grapher.

## Laplace Transform Calculator

The calculator will find the Laplace Transform of the given function.

Recall that the Laplace transform of a function is $$$F(s)=L(f(t))=\int_0^{\infty} e^{-st}f(t)dt$$$.

Usually, to find the Laplace Transform of a function, one uses partial fraction decomposition (if needed) and then consults the table of Laplace Transforms.

## Inverse Laplace Transform Calculator

The calculator will find the Inverse Laplace Transform of the given function.

Recall, that $$$\mathcal{L}^{-1}\left(F(s)\right)$$$ is such a function `f(t)` that $$$\mathcal{L}\left(f(t)\right)=F(s)$$$.

Usually, to find the Inverse Laplace Transform of a function, we use the property of linearity of the Laplace Transform. Just perform partial fraction decomposition (if needed), and then consult the table of Laplace Transforms.

## Wronskian Calculator

The calculator will find the Wronskian of the set of functions, with steps shown. Supports up to 5 functions, 2x2, 3x3, etc.

## Differential Equation Calculator

The calculator will find the solution of the given ODE: first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous.

Initial conditions are also supported.

## Euler's Method Calculator

The calculator will find the approximate solution of the first-order differential equation using the Euler's method, with steps shown.

## Improved Euler (Heun's) Method Calculator

The calculator will find the approximate solution of the first-order differential equation using the Improved Euler (Heun's) method, with steps shown.

## Half-Life Calculator

This calculator will calculate the half-life, initial quantity, quantity remained and time, with steps shown.

## Inverse of Matrix Calculator

The calculator will find the inverse of the square matrix using the Gaussian elimination method, with steps shown.

## Cross Product Calculator

An online calculator for finding the cross product of two vectors, with steps shown.

## Dot (Inner) Product Calculator

An online calculator for finding the dot (inner) product of two vectors, with steps shown.

## Matrix Multiplication Calculator

The calculator will find the product of two matrices (if possible), with steps shown. It multiplies matrices of any size up to 10x10.

## Matrix Determinant Calculator

The calculator will find the determinant of the matrix (2x2, 3x3, etc.), with steps shown.

## Reduced Row Echelon Form (RREF) Caclulator

The calculator will find the row echelon form (simple or reduced - RREF) of the given (augmented) matrix (with variables if needed), with steps shown.

## Eigenvalue and Eigenvector Calculator

The calculator will find the eigenvalues and eigenvectors of the given square matrix, with steps shown.

## Matrix Calculator

This solver will add, subtract, multiply, divide, and raise to power two matrices, with steps shown. It will also find the determinant, inverse, rref (reduced row echelon form), null space, rank, eigenvalues and eigenvectors.

## Matrix Null Space Calculator

The calculator will find the null space of the given matrix, with steps shown.

## Angle between Vectors Calculator

The calculator will find the angle (in radians and degrees) between the two vectors, and will show the work.

## Gauss-Jordan Elimination Calculator

The calculator will perform the Gaussian elimination on the given augmented matrix, with steps shown. Complete reduction is available optionally.

## Characteristic Polynomial Calculator

The calculator will find the characteristic polynomial of the given matrix, with steps shown.

## Cofactor Matrix Calculator

The calculator will find the matrix of cofactors of the given square matrix, with steps shown.

## Adjoint Matrix Calculator

The calculator will find the adjoint (adjugate, adjunct) matrix of the given square matrix, with steps shown.

## Matrix Transpose Calculator

The calculator will find the transpose of the given matrix, with steps shown.

## Diagonalize Matrix Calculator

The calculator will diagonalize the given matrix, with steps shown.

## Gram-Schmidt Calculator

This calculator will orthonormalize the set of vectors using the Gram-Schmidt process, with steps shown.

## P-Value Calculator

The calculator will find the p-value for two-tailed, right-tailed and left-tailed tests from normal, Student's (T-distribution), chi-squared and Fisher (F-distribution) distributions.

## Average (Mean) Calculator

For the given group of numbers, the calculator will find their average (mean), with steps shown.

## Sample/Population Standard Deviation Calculator

For the given set of observations, the calculator will find their standard deviation (either sample or population), with steps shown.

## Sample/Population Variance Calculator

For the given set of values, the calculator will find their variance (either sample or population), with steps shown.

## Median Calculator

The calculator will find the median for the given sample data, with steps shown.

## Mode Calculator

For the given set of data, the calculator will find the mode, with steps shown.

## Percentile Calculator

For the given set of data, the calculator will find the `p`^{th} percentile, with steps shown.

## Binomial Distribution Calculator

The calculator will find the binomial and cumulative probabilities, as well as the mean, variance and standard deviation of the binomial distribution.

## Poisson Distribution Calculator

The calculator will find the Poisson and cumulative probabilities, as well as the mean, variance and standard deviation of the Poisson distribution.

## Hypergeometric Distribution Calculator

The calculator will find the hypergeometric and cumulative probabilities, as well as the mean, variance and standard deviation of the hypergeometric distribution.

## Z-Score Calculator

The calculator will find the Z-Score (standardized score), given the unstandardized value, mean and standard deviation of the population, with steps shown.

## Margin of Error Calculator

The calculator will find the margin of error from the given sample size and distribution, with steps shown.

## Normal Distribution Calculator

For the given mean and standard deviation, the calculator will find various probabilities for the random variable, and vice versa: for the specified probability, it will find the values of the random variable.

## Geometric Distribution Calculator

The calculator will find the simple and cumulative probabilities, as well as mean, variance and standard deviation of the geometric distribution.

## Percentile Rank, Class Rank Calculator

For the given set of data and score, the calculator will find the percentile class rank, with steps shown.

## Metric Conversion Charts and Calculators

The calculator will find the conversion for different metrics: volume, temperature, weight, speed, area, and length.

## Algebra Calculators

A collection of calculators to solve virtually any algebra problem step-by-step. Solve equations (quadratic, polynomial, trigonometric, etc.), factor polynomials, perform synthetic division and partial fraction decomposition, discover conic sections, and many more.

## Calculus Calculators

A collection of calculators to solve virtually any calculus problem step-by-step. Find derivatives, limits, integrals, asymptotes, Taylor series, plot graphs, and many more.

## Four-Function (Ten-Key) Calculator

This online calculator is basic, and can perform only 4 operations: addition, subtraction, multiplication, and division. It has approximately 10 keys.