- Solve equations and inequalities
- Simplify expressions
- Factor polynomials
- Graph equations and inequalities
- Advanced solvers
- All solvers
- Arithmetics
- Determinant
- Percentages
- Scientific Notation
- Inequalities

## What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

- The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
- The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
- The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
- The calculus section will carry out differentiation as well as definite and indefinite integration.
- The matrices section contains commands for the arithmetic manipulation of matrices.
- The graphs section contains commands for plotting equations and inequalities.
- The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

## Math Topics

More solvers.

- Add Fractions
- Simplify Fractions

Examples for

## Mathematics

Wolfram|Alpha has broad knowledge and deep computational power when it comes to math. Whether it be arithmetic, algebra, calculus, differential equations or anything in between, Wolfram|Alpha is up to the challenge. Get help with math homework, solve specific math problems or find information on mathematical subjects and topics.

Do basic arithmetic. Work with fractions, percentages and similar fundamentals. Solve place value and word problems.

## Do basic arithmetic:

Do exact arithmetic with fractions:.

Compute the properties of geometric objects of various kinds in 2, 3 or higher dimensions. Explore and apply ideas from many subfields of geometry.

## Compute properties of a geometric figure:

Plot a conic section and identify its type:, compute properties of a polyhedron:.

Work with various kinds of numbers. Check for membership in larger sets, such as the rationals or the transcendental numbers. Convert between bases.

## Compute a decimal approximation to a specified number of digits:

Convert a decimal number to another base:.

Analyze integers; subsets of the integers, including the prime numbers; and related ideas.

## Compute a prime factorization:

Solve a diophantine equation:.

Perform numerical analysis and optimization of systems and objects, including packing and covering of objects and control systems.

## Minimize or maximize a function:

Numerically integrate functions that cannot be integrated symbolically:.

Make queries about various definitions and descriptions in mathematics.

## Find information about a math concept:

Get a brief definition:.

Compute properties of datasets, perform statistical inference or model data. Work with probability distributions and random variables.

## Calculate basic descriptive statistics for a data set:

Find the sample size needed to estimate a binomial parameter:.

Find roots of and expand, factor or simplify mathematical expressions—everything from polynomials to fields and groups.

## Solve an equation:

Factor a polynomial:, simplify an expression:.

Solve differential equations of any order. Examine solutions and plots of the solution families. Specify initial conditions to find exact solutions.

## Solve a linear ordinary differential equation:

Specify initial values:, solve a nonlinear equation:.

Perform trigonometric calculations and explore properties of trigonometric functions and identities.

## Compute values of trigonometric functions:

Solve a trigonometric equation:.

Explore sequences and recurrences, solve common problems in combinatorics and compute properties of graphs and lattices.

## Compute a possible formula and continuation for a sequence:

Analyze a graph specified by adjacency rules:, solve a recurrence:.

Evaluate Boolean logic expressions and expressions involving sets and set operators. Solve Boolean equations. Compute truth tables. Generate Venn diagrams.

## Compute a truth table:

Generate a venn diagram:.

Gather information about famous problems, conjectures, theorems and paradoxes. Learn about them and their formulators.

## Get information about a mathematical conjecture:

Get historical information about a theorem:.

Compute the probabilities of certain events occurring. Compute joint, disjoint or conditional probabilities and apply them to real-world situations.

## Compute the probability of a union of events:

Compute coin‐toss probabilities:.

Compute integrals, derivatives and limits as well as analyze sums, products and series.

## Compute an integral:

Calculate a derivative:, solve an ordinary differential equation:.

Visualize functions, equations and inequalities. Do so in 1, 2 or 3 dimensions. Make polar and parametric plots.

## Plot a function:

Plot a region satisfying multiple inequalities:.

Explore and compute properties of vectors, matrices and vector spaces.

## Compute properties of a vector:

Calculate properties of a matrix:, determine whether a set of vectors is linearly independent:.

Analyze functions and expressions containing imaginary numbers or complex variables.

## Compute properties of a function of a complex variable (use the variable z ):

Compute the residue of a function at a point:.

Examine the properties of mathematical functions, such as continuity, surjectivity and parity. Utilize notable special functions or number theoretic functions.

## Do computations with special functions:

Do computations with number theoretic functions:, find representations for a function:.

Compute; learn about algorithms, definitions and theorems involving; or find properties of continued fractions.

## Find the continued fraction representation of a number:

Find definitions of continued fraction terminology:, find continued fraction papers by author:.

Get information about math Common Core Standards for kindergarten through eighth grade.

## Evaluate an expression (CCSS.Math.Content.6.EE.A.2c):

Perform multiple operations with rational numbers (ccss.math.content.7.ns.a.2c):.

## Upload a screenshot and solve any math problem instantly with MathGPT!

Drag & drop an image file here, or click to select an image.

## Supercharge your math learning

Use our ai-powered math solver to learn math step-by-step., free examples solved step-by-step, trigonometry, derivatives, differential equations, youtube channel.

## Enter a Problem. Solve and Learn!

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## Over 5 Billion Problems Solved

Step-by-step examples.

- Adding Using Long Addition
- Long Subtraction
- Long Multiplication
- Long Division
- Dividing Using Partial Quotients Division
- Converting Regular to Scientific Notation
- Arranging a List in Order
- Expanded Notation
- Prime or Composite
- Comparing Expressions
- Converting to a Percentage
- Finding the Additive Inverse
- Finding the Multiplicative Inverse
- Reducing Fractions
- Finding the Reciprocal
- Converting to a Decimal
- Converting to a Mixed Number
- Adding Fractions
- Subtracting Fractions
- Multiplying Fractions
- Dividing Fractions
- Converting Ratios to Fractions
- Converting Percents to Decimal
- Converting Percents to Fractions
- Converting the Percent Grade to Degree
- Converting the Degree to Percent Grade
- Finding the Area of a Rectangle
- Finding the Perimeter of a Rectangle
- Finding the Area of a Square
- Finding the Perimeter of a Square
- Finding the Area of a Circle
- Finding the Circumference of a Circle
- Finding the Area of a Triangle
- Finding the Area of a Trapezoid
- Finding the Volume of a Box
- Finding the Volume of a Cylinder
- Finding the Volume of a Cone
- Finding the Volume of a Pyramid
- Finding the Volume of a Sphere
- Finding the Surface Area of a Box
- Finding the Surface Area of a Cylinder
- Finding the Surface Area of a Cone
- Finding the Surface Area of a Pyramid
- Converting to a Fraction
- Simple Exponents
- Prime Factorizations
- Finding the Factors
- Simplifying Fractions
- Converting Grams to Kilograms
- Converting Grams to Pounds
- Converting Grams to Ounces
- Converting Feet to Inches
- Converting to Meters
- Converting Feet to Miles
- Converting Feet to Yards
- Converting to Feet
- Converting to Yards
- Converting Miles to Feet
- Converting Miles to Kilometers
- Converting Miles to Yards
- Converting Kilometers to Miles
- Converting Kilometers to Meters
- Converting Meters to Feet
- Converting Meters to Inches
- Converting Ounces to Grams
- Converting Ounces to Pounds
- Converting Ounces to Tons
- Converting Pounds to Grams
- Converting Pounds to Ounces
- Converting Pounds to Tons
- Converting Yards to Feet
- Converting Yards to Millimeters
- Converting Yards to Inches
- Converting Yards to Miles
- Converting Yards to Meters
- Converting Fahrenheit to Celsius
- Converting Celsius to Fahrenheit
- Finding the Median
- Finding the Mean (Arithmetic)
- Finding the Mode
- Finding the Minimum
- Finding the Maximum
- Finding the Lower or First Quartile
- Finding the Upper or Third Quartile
- Finding the Five Number Summary
- Finding a Point's Quadrant
- Finding the Midpoint of a Line Segment
- Distance Formula
- Arithmetic Operations
- Combining Like Terms
- Determining if the Expression is a Polynomial
- Distributive Property
- Simplifying
- Multiplication
- Polynomial Addition
- Polynomial Subtraction
- Polynomial Multiplication
- Polynomial Division
- Simplifying Expressions
- Evaluate the Expression Using the Given Values
- Multiplying Polynomials Using FOIL
- Identifying Degree
- Operations on Polynomials
- Negative Exponents
- Evaluating Radicals
- Solving by Adding/Subtracting
- Solving by Multiplying/Dividing
- Solving Containing Decimals
- Solving for a Variable
- Solving Linear Equations
- Solving Linear Inequalities
- Finding the Quadratic Constant of Variation
- Converting the Percent Grade to Slope
- Converting the Slope to Percent Grade
- Finding Equations Using Slope-Intercept
- Finding the Slope
- Finding the y Intercept
- Calculating Slope and y-Intercept
- Rewriting in Slope-Intercept Form
- Finding Equations Using the Slope-Intercept Formula
- Finding Equations Using Two Points
- Finding a Perpendicular Line Containing a Given Point
- Finding a Parallel Line Containing a Given Point
- Finding a Parallel Line to the Given Line
- Finding a Perpendicular Line to the Given Line
- Finding Ordered Pair Solutions
- Using a Table of Values to Graph an Equation
- Finding the Equation Using Point-Slope Form
- Finding the Surface Area of a Sphere
- Solving by Graphing
- Finding the LCM of a List of Expressions
- Finding the LCD of a List of Expressions
- Determining if the Number is a Perfect Square
- Finding the Domain
- Evaluating the Difference Quotient
- Solving Using the Square Root Property
- Determining if True
- Finding the Holes in a Graph
- Finding the Common Factors
- Expand a Trinomial with the Trinomial Theorem
- Finding the Start Point Given the Mid and End Points
- Finding the End Point Given the Start and Mid Points
- Finding the Slope and y-Intercept
- Finding the Equation of the Parabola
- Finding the Average Rate of Change
- Finding the Slope of the Perpendicular Line to the Line Through the Two Points
- Rewriting Using Negative Exponents
- Synthetic Division
- Maximum Number of Real Roots/Zeros
- Finding All Possible Roots/Zeros (RRT)
- Finding All Roots with Rational Root Test (RRT)
- Finding the Remainder
- Finding the Remainder Using Long Polynomial Division
- Reordering the Polynomial in Ascending Order
- Reordering the Polynomial in Descending Order
- Finding the Leading Term
- Finding the Leading Coefficient
- Finding the Degree, Leading Term, and Leading Coefficient
- Finding the GCF of a Polynomial
- Factoring Out Greatest Common Factor (GCF)
- Identifying the Common Factors
- Cancelling the Common Factors
- Finding the LCM using GCF
- Finding the GCF
- Factoring Trinomials
- Trinomial Squares
- Factoring Using Any Method
- Factoring a Difference of Squares
- Factoring a Sum of Cubes
- Factoring by Grouping
- Factoring a Difference of Cubes
- Determine if an Expression is a Factor
- Determining if Factor Using Synthetic Division
- Find the Factors Using the Factor Theorem
- Determining if Polynomial is Prime
- Determining if the Polynomial is a Perfect Square
- Expand using the Binomial Theorem
- Factoring over the Complex Numbers
- Finding All Integers k Such That the Trinomial Can Be Factored
- Determining if Linear
- Rewriting in Standard Form
- Finding x and y Intercepts
- Finding Equations Using the Point Slope Formula
- Finding Equations Given Point and y-Intercept
- Finding the Constant Using Slope
- Finding the Slope of a Parallel Line
- Finding the Slope of a Perpendicular Line
- Simplifying Absolute Value Expressions
- Solving with Absolute Values
- Finding the Vertex for the Absolute Value
- Rewriting the Absolute Value as Piecewise
- Calculating the Square Root
- Simplifying Radical Expressions
- Rationalizing Radical Expressions
- Solving Radical Equations
- Rewriting with Rational (Fractional) Exponents
- Finding the Square Root End Point
- Operations on Rational Expressions
- Determining if the Point is a Solution
- Solving over the Interval
- Finding the Range
- Finding the Domain and Range
- Solving Rational Equations
- Adding Rational Expressions
- Subtracting Rational Expressions
- Multiplying Rational Expressions
- Finding the Equation Given the Roots
- Finding the Asymptotes
- Finding the Constant of Variation
- Finding the Equation of Variation
- Substitution Method
- Addition/Elimination Method
- Graphing Method
- Determining Parallel Lines
- Determining Perpendicular Lines
- Dependent, Independent, and Inconsistent Systems
- Finding the Intersection (and)
- Using the Simplex Method for Constraint Maximization
- Using the Simplex Method for Constraint Minimization
- Finding the Union (or)
- Finding the Equation with Real Coefficients
- Solving in Terms of the Arbitrary Variable
- Finding a Direct Variation Equation
- Finding the Slope for Every Equation
- Finding a Variable Using the Constant of Variation
- Quadratic Formula
- Solving by Factoring
- Solve by Completing the Square
- Finding the Perfect Square Trinomial
- Finding the Quadratic Equation Given the Solution Set
- Finding a,b, and c in the Standard Form
- Finding the Discriminant
- Finding the Zeros by Completing the Square
- Quadratic Inequalities
- Rational Inequalities
- Converting from Interval to Inequality
- Converting to Interval Notation
- Rewriting as a Single Interval
- Determining if the Relation is a Function
- Finding the Domain and Range of the Relation
- Finding the Inverse of the Relation
- Finding the Inverse
- Determining if One Relation is the Inverse of Another
- Determining if Surjective (Onto)
- Determining if Bijective (One-to-One)
- Determining if Injective (One to One)
- Rewriting as an Equation
- Rewriting as y=mx+b
- Solving Function Systems
- Find the Behavior (Leading Coefficient Test)
- Determining Odd and Even Functions
- Describing the Transformation
- Finding the Symmetry
- Arithmetic of Functions
- Domain of Composite Functions
- Finding Roots Using the Factor Theorem
- Determine if Injective (One to One)
- Determine if Surjective (Onto)
- Finding the Vertex
- Finding the Sum
- Finding the Difference
- Finding the Product
- Finding the Quotient
- Finding the Domain of the Sum of the Functions
- Finding the Domain of the Difference of the Functions
- Finding the Domain of the Product of the Functions
- Finding the Domain of the Quotient of the Functions
- Finding Roots (Zeros)
- Identifying Zeros and Their Multiplicities
- Finding the Bounds of the Zeros
- Proving a Root is on the Interval
- Finding Maximum Number of Real Roots
- Function Composition
- Rewriting as a Function
- Determining if a Function is Rational
- Determining if a Function is Proper or Improper
- Maximum/Minimum of Quadratic Functions
- Finding All Complex Number Solutions
- Rationalizing with Complex Conjugates
- Vector Arithmetic
- Finding the Complex Conjugate
- Finding the Magnitude of a Complex Number
- Simplifying Logarithmic Expressions
- Expanding Logarithmic Expressions
- Evaluating Logarithms
- Rewriting in Exponential Form
- Converting to Logarithmic Form
- Exponential Expressions
- Exponential Equations
- Converting to Radical Form
- Find the Nth Root of the Given Value
- Simplifying Matrices
- Finding the Variables
- Solving the System of Equations Using an Inverse Matrix
- Finding the Dimensions
- Multiplication by a Scalar
- Subtraction
- Finding the Determinant of the Resulting Matrix
- Finding the Inverse of the Resulting Matrix
- Finding the Identity Matrix
- Finding the Scalar multiplied by the Identity Matrix
- Simplifying the Matrix Operation
- Finding the Determinant of a 2x2 Matrix
- Finding the Determinant of a 3x3 Matrix
- Finding the Determinant of Large Matrices
- Inverse of a 2x2 Matrix
- Inverse of an nxn Matrix
- Finding Reduced Row Echelon Form
- Finding the Transpose
- Finding the Adjoint
- Finding the Cofactor Matrix
- Finding the Pivot Positions and Pivot Columns
- Finding the Basis and Dimension for the Row Space of the Matrix
- Finding the Basis and Dimension for the Column Space of the Matrix
- Finding the LU Decomposition of a Matrix
- Identifying Conic Sections
- Identifying Circles
- Finding a Circle Using the Center and Another Point
- Finding a Circle by the Diameter End Points
- Finding the Parabola Equation Using the Vertex and Another Point
- Finding the Properties of the Parabola
- Finding the Vertex Form of the Parabola
- Finding the Vertex Form of an Ellipse
- Finding the Vertex Form of a Circle
- Finding the Vertex Form of a Hyperbola
- Finding the Standard Form of a Parabola
- Finding the Expanded Form of an Ellipse
- Finding the Expanded Form of a Circle
- Finding the Expanded Form of a Hyperbola
- Vector Addition
- Vector Subtraction
- Vector Multiplication by a Scalar
- Finding the Length
- Finding the Position Vector
- Determining Column Spaces
- Finding an Orthonormal Basis by Gram-Schmidt Method
- Rewrite the System as a Vector Equality
- Finding the Rank
- Finding the Nullity
- Finding the Distance
- Finding the Plane Parallel to a Line Given four 3d Points
- Finding the Intersection of the Line Perpendicular to Plane 1 Through the Origin and Plane 2
- Finding the Eigenvalues
- Finding the Characteristic Equation
- Finding the Eigenvectors/Eigenspace of a Matrix
- Proving a Transformation is Linear
- Finding the Kernel of a Transformation
- Projecting Using a Transformation
- Finding the Pre-Image
- Finding the Intersection of Sets
- Finding the Union of Number Sets
- Determining if a Set is a Subset of Another Set
- Determining if Two Sets are Mutually Exclusive
- Finding the Set Complement of Two Sets
- Finding the Power Set
- Finding the Cardinality
- Finding the Cartesian Product of Two Sets
- Determining if a Set is a Proper Subset of Another Set
- Finding the Function Rule
- Finding the Square or Rectangle Area Given Four Points
- Finding the Square or Rectangle Perimeter Given Four Points
- Finding the Square or Rectangle Area Given Three Points
- Finding the Square or Rectangle Perimeter Given Three Points
- Finding the Equation of a Circle
- Finding the Equation of a Hyperbola
- Finding the Equation of an Ellipse
- Partial Fraction Decomposition
- Finding an Angle Using another Angle
- Pythagorean Theorem
- Finding the Sine
- Finding the Cosine
- Finding the Tangent
- Finding the Trig Value
- Converting to Degrees, Minutes, and Seconds
- Finding Trig Functions Using Identities
- Finding Trig Functions Using the Right Triangle
- Converting Radians to Degrees
- Converting Degrees to Radians
- Finding a Reference Angle
- Finding a Supplement
- Finding a Complement
- Converting RPM to Radians per Second
- Finding the Quadrant of the Angle
- Graphing Sine & Cosine Functions
- Graphing Other Trigonometric Functions
- Amplitude, Period, and Phase Shift
- Finding the Other Trig Values in a Quadrant
- Finding the Exact Value
- Finding the Value Using the Unit Circle
- Expanding Trigonometric Expressions
- Expanding Using Double-Angle Formulas
- Expanding Using Triple-Angle Formulas
- Expanding Using Sum/Difference Formulas
- Simplify Using Pythagorean Identities
- Simplify by Converting to Sine/Cosine
- Inverting Trigonometric Expressions
- Finding the Trig Value of an Angle
- Expanding Using De Moivre's Theorem
- Verifying Trigonometric Identities
- Using Fundamental Identities
- Solving Standard Angle Equations
- Complex Trigonometric Equations
- Solving the Triangle
- Find the Roots of a Complex Number
- Complex Operations
- Trigonometric Form of a Complex Number
- Converting to Polar Coordinates
- Identifying and Graphing Circles
- Identifying and Graphing Limacons
- Identifying and Graphing Roses
- Identifying and Graphing Cardioids
- Difference Quotient
- Finding Upper and Lower Bounds
- Evaluating Functions
- Right Triangle Trigonometry
- Arithmetic Sequences/Progressions
- Geometric Sequences/Progressions
- Finding the Next Term of the Sequence
- Finding the nth Term Given a List of Numbers
- Finding the nth Term
- Finding the Sum of First n Terms
- Expanding Series Notation
- Finding the Sum of the Series
- Finding the Sum of the Infinite Geometric Series
- Converting to Rectangular Coordinates
- Evaluating Limits Approaching a Value
- Evaluating Limits Approaching Infinity
- Finding the Angle Between the Vectors
- Determining if the Point is on the Graph
- Finding the Antiderivative
- Checking if Continuous Over an Interval
- Determining if a Series is Divergent
- Using the Integral Test for Convergence
- Determining if an Infinite Series is Convergent Using Cauchy's Root Test
- Using the Limit Definition to Find the Tangent Line at a Given Point
- Finding the nth Derivative
- Finding the Derivative Using Product Rule
- Finding the Derivative Using Quotient Rule
- Finding the Derivative Using Chain Rule
- Use Logarithmic Differentiation to Find the Derivative
- Finding the Derivative
- Implicit Differentiation
- Using the Limit Definition to Find the Derivative
- Evaluating the Derivative
- Finding Where dy/dx is Equal to Zero
- Finding the Linearization
- Finding a Tangent Line to a Curve
- Checking if Differentiable Over an Interval
- The Mean Value Theorem
- Finding the Inflection Points
- Find Where the Function Increases/Decreases
- Finding the Critical Points of a Function
- Find Horizontal Tangent Line
- Evaluating Limits with L'Hospital Rule
- Local Maxima and Minima
- Finding the Absolute Maximum and Minimum on the Given Interval
- Finding Concavity using the Second Derivative
- Finding the Derivative using the Fundamental Theorem of Calculus
- Find the Turning Points
- Finding the Integral
- Evaluating Definite Integrals
- Evaluating Indefinite Integrals
- Substitution Rule
- Finding the Arc Length
- Finding the Average Value of the Derivative
- Finding the Average Value of the Equation
- Finding Area Between Curves
- Finding the Volume
- Finding the Average Value of the Function
- Finding the Root Mean Square
- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitution
- Integration by Partial Fractions
- Eliminating the Parameter from the Function
- Verify the Solution of a Differential Equation
- Solve for a Constant Given an Initial Condition
- Find an Exact Solution to the Differential Equation
- Verify the Existence and Uniqueness of Solutions for the Differential Equation
- Solve for a Constant in a Given Solution
- Solve the Bernoulli Differential Equation
- Solve the Linear Differential Equation
- Solve the Homogeneous Differential Equation
- Solve the Exact Differential Equation
- Approximate a Differential Equation Using Euler's Method
- Finding Elasticity of Demand
- Finding the Consumer Surplus
- Finding the Producer Surplus
- Finding the Gini Index
- Finding the Geometric Mean
- Finding the Quadratic Mean (RMS)
- Find the Mean Absolute Deviation
- Finding the Mid-Range (Mid-Extreme)
- Finding the Interquartile Range (H-Spread)
- Finding the Midhinge
- Finding the Standard Deviation
- Finding the Skew of a Data Set
- Finding the Range of a Data Set
- Finding the Variance of a Data Set
- Finding the Class Width
- Solving Combinations
- Solving Permutations
- Finding the Probability of Both Independent Events
- Finding the Probability of Both Dependent Events
- Finding the Probability for Both Mutually Exclusive Events
- Finding the Conditional Probability for Independent Events
- Determining if Given Events are Independent/Dependent Events
- Determining if Given Events are Mutually Exclusive Events
- Finding the Probability of Both not Mutually Exclusive Events
- Finding the Conditional Probability Using Bayes' Theorem
- Finding the Probability of the Complement
- Describing Distribution's Two Properties
- Finding the Expectation
- Finding the Variance
- Finding the Probability of a Binomial Distribution
- Finding the Probability of the Binomial Event
- Finding the Mean
- Finding the Relative Frequency
- Finding the Percentage Frequency
- Finding the Upper and Lower Class Limits of the Frequency Table
- Finding the Class Boundaries of the Frequency Table
- Finding the Class Width of the Frequency Table
- Finding the Midpoints of the Frequency Table
- Finding the Mean of the Frequency Table
- Finding the Variance of the Frequency Table
- Finding the Standard Deviation of the Frequency Table
- Finding the Cumulative Frequency of the Frequency Table
- Finding the Relative Frequency of the Frequency Table
- Finding the Median Class Interval of the Frequency Table
- Finding the Modal Class of the Frequency Table
- Creating a Grouped Frequency Distribution Table
- Finding the Data Range
- Finding a z-Score for a Normal Distribution
- Approximating Using Normal Distribution
- Finding the Probability of the z-Score Range
- Finding the Probability of a Range in a Nonstandard Normal Distribution
- Finding the z-Score Using the Table
- Finding the z-Score
- Testing the Claim
- Finding a t-Value for a Confidence Level
- Finding the Critical t-Value
- Setting the Alternative Hypothesis
- Setting the Null Hypothesis
- Determining if Left, Right, or Two Tailed Test Given the Null Hypothesis
- Determining if Left, Right, or Two Tailed Test Given the Alternative Hypothesis
- Finding Standard Error
- Finding the Linear Correlation Coefficient
- Determining if the Correlation is Significant
- Finding a Regression Line
- Cramer's Rule
- Solving using Matrices by Elimination
- Solving using Matrices by Row Operations
- Solving using an Augmented Matrix
- Finding the Simple Interest Received
- Finding the Present Value with Compound Interest
- Finding the Simple Interest Future Value
- Finding the Future Value with Continuous Interest
- Finding the Norm in Real Vector Space
- Finding the Direction Angle of the Vector
- Finding the Cross Product of Vectors
- Finding the Dot Product of Vectors
- Determining if Vectors are Orthogonal
- Finding the Distance Between the Vectors
- Finding a Unit Vector in the Same Direction as the Given Vector
- Finding the Angle Between Two Vectors Using the Cross Product
- Finding the Angle Between Two Vectors Using the Dot Product
- Finding the Projection of One Vector Onto another Vector
- Matrices Addition
- Matrices Subtraction
- Matrices Multiplication
- Finding the Trace
- Finding the Basis
- Matrix Dimension
- Convert to a Linear System
- Diagonalizing a Matrix
- Determining the value of k for which the system has no solutions
- Linear Independence of Real Vector Spaces
- Finding the Null Space
- Determining if the Vector is in the Span of the Set
- Finding the Number of Protons
- Finding the Number of Electrons
- Finding the Number of Neutrons
- Finding the Mass of a Single Atom
- Finding the Electron Configuration
- Finding the Atomic Mass
- Finding the Atomic Number
- Finding the Mass Percentages
- Finding Oxidation Numbers
- Balancing Chemical Equations
- Balancing Burning Reactions
- Finding the Density at STP
- Determining if the Compound is Soluble in Water
- Finding Mass
- Finding Density
- Finding Weight
- Finding Force
- Finding the Work Done
- Finding Angular Velocity
- Finding Centripetal Acceleration
- Finding Final Velocity
- Finding Average Acceleration
- Finding Displacement
- Finding Voltage Using the Ohm's Law
- Finding Electrical Power
- Finding Kinetic Energy
- Finding Power
- Finding Wavelength
- Finding Frequency
- Finding Pressure of the Gas

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Mathway is the world’s smartest math calculator for algebra, graphing, calculus and more! Mathway gives you unlimited access to math solutions that can help you understand complex concepts. Simply point your camera and snap a photo or type your math homework question for step-by-step answers. If a premium subscription option is selected: • Payment will be charged to iTunes Account at confirmation of purchase • Subscription automatically renews unless auto-renew is turned off at least 24-hours before the end of the current period • Account will be charged for renewal within 24-hours prior to the end of the current period, at the same monthly or annual rate selected at the beginning of the subscription • Subscriptions may be managed by the user and auto-renewal may be turned off by going to the user's Account Settings after purchase Terms of Use: https://www.mathway.com/terms Privacy Policy: https://www.mathway.com/privacy

Version 5.3.3

Powered by Chegg, Mathway is your one-stop shop for homework help. Is your equation too complex to type? Save time with our snap and solve feature! Just take a photo and instantly see the solution. Our interactive calculator also allows you to select your class subject (now including physics!) to generate all the functions you need to solve that equation. Need more than an answer? Upgrade your subscription and get unlimited access to detailed equation breakdowns, helping you learn how to solve it one step at a time.

## Ratings and Reviews

414.6K Ratings

## Recommend!!!!!!?

Once I was doing my homework I couldn’t figure it out I asked my mom to help me and I showed her and she fell asleep so I kind of started panicking Went downstairs to the table I started struggling and thinking and thinking so I went to the App Store looked and looked and looked and looked left to right for helping your homeworkIs the best I really do recommend it it is the best it will save your life and when I mean save your life I mean really save your life nobody really understands when they say that they saved their lifeThey never understand how much that person means they don’t even know how serious the persons like saying I really do recommend this app messed up in the world five star review amazing helpful save your life get it get it now get it now it’s the best app ever students allowed teacher teachers not allowed can students really need this app so don’t get mad at them if they have this app it’s the best time with them so hope you get it

## All it does is give the answer

Seriously saying, this app is literally just useless unless if you know the answer to math problems and want to check your answers. Otherwise, paying wouldn’t be a consideration for me. For those who are on a tight budget, and have a strong desire to reach their future career, I’d say paying wouldn’t be worth it, especially if you are just doing a living only as a student with no career and if you do not have enough financial support. I’ve lived a long way with this app studying all day and all night and yet there is high demand for paying just to get the work shown to get the idea why a question is answered in a certain way. This is why nowadays I read reviews from various books titled for math and read books that give a full explanation of how an answer is earned. As a life lesson it’s just good to say the fact that spending is not worth it for this app since there are various places and apps to ask questions related to learning math (at least in my area). This app should be like a substitute teacher or tutor for those who are having trouble, but the fact that there is such huge fee just ruins the reason why I should install this app. Teachers ask for showing work, and yet I’m stuck, having no idea what to do to get the right answers. This also goes to understanding how an answer is caught as well.

## It works but the full version hasn’t for me

I have been using this a lot this semester so I decided to pay for the monthly subscription then I could cancel the membership at the end of the semester, but it doesn’t even work. The subscription shows in my subscriptions list in my settings but I still can’t view the steps, and when I attempt to see how the problem is solved it brings me to the menu to subscribe to the paid part of the app. Honestly though, other than that. This app works pretty great, solves problems the right way and you can select the method of how you want the problem solved. You can change what kind of math you are trying to solve, and the answers are pretty spot on. The predictive text is even really good on this, it’ll help solve word problems and you kind of don’t em have to type anything in sometimes. However, the keyboard is very buggy and you can’t type very fast. It’s also kind of hard to navigate as there are like 4 different keyboard menus to choose from, I always forget where to find things and it kind of takes a while to load the text sometimes. But it does solve the problems.

## Developer Response ,

Sorry to hear of the issues you're having - please select 'restore subscription' from the settings of your Mathway account. This should turn the steps "ON". For further assistance you can reach Mathway customer support by emailing: [email protected].

## App Privacy

The developer, Chegg, Inc. , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

## Data Used to Track You

The following data may be used to track you across apps and websites owned by other companies:

- Contact Info
- Identifiers

## Data Linked to You

The following data may be collected and linked to your identity:

- User Content

## Data Not Linked to You

The following data may be collected but it is not linked to your identity:

Privacy practices may vary, for example, based on the features you use or your age. Learn More

## Information

English, Arabic, French, German, Hindi, Indonesian, Italian, Japanese, Korean, Portuguese, Russian, Simplified Chinese, Spanish, Turkish, Vietnamese

- Steps (Monthly) $9.99
- Steps (Monthly) $19.99
- Steps (Annual) $39.99
- Steps (Annual) $79.99
- Developer Website
- App Support
- Privacy Policy

## More By This Developer

Chegg Study - Homework Helper

Chegg eReader - study eBooks

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## AI Math Problem Solver

Instant step by step answers to your math homework problems. Improve your math grades today with unlimited math solutions. Try for Free

## Top organizations trust our math lessons and content

## 5 Million Students Helped Each Year

Interactive Mathematics helps over 5 Million students each year, who use our free lessons to help get ahead in math. We've taken that expertise and paired it with AI to provide a free to try AI math problem solver and math tutoring chat platform.

## Math Problems, meet Math Solutions.

We've combined a powerful mathematical computational engine with large language model artificial intelligence to create a state of the art math problem solver and AI math calculator. More accurate than ChatGPT, more powerful than a math calculator, and faster than a math tutor! Whether it's a tough word problem, algebra equation or advanced calculus, our AI math problem solver and calculator can solve it.

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Math calculators and online math solver apps aren't built to handle math word problems. We've fixed that! Our solver can interpret math word problems and determine what mathematical operations needs to be used to solve the problem.

## Step-by-Step Solutions

Stuck on a hard math homework problem? Upload a picture of your math problem or enter it and immediately get a step-by-step solution to your math problems.

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## Frequently Asked Questions

Can the math solver help me improve my grades (yes).

Now, we can't guarantee you'll get better grades, since the AI Math Solver is only half of the success equation, but the majority of students who use the application report full letter grade improvements in their grades. Most see improvements in their homework grades immediately.

## How long does it take to get an answer to my math problem?

Our application is available 24/7 and will start working on a solutions immediately after you send it. The time it takes to solve each problem is dependant on the complexity of the problem. The application will post a step by step solution.

## Can I really ask unlimited questions?

How is this app different from your tutoring service.

The AI Math Solver is FREE to try and powered by our proprietary mathematical computation engine and AI while our Tutoring service enables students to chat with professional (human) math tutors.

## Can it answer Physics questions?

Yes, the AI has been trainined on physics concepts and problems. However if it can't answer a question, then we recommend subscribing to our Tutoring service to connect with a physics tutor.

## Will it work on my phone?

Yes, the application is optimized for mobile and tablet, no need to download another app onto your phone. An internet connection is required.

## Can I submit a picture of my math problem?

Yes, simply tap or click the carmera icon next to the Solve button in the application then select the image or if you're on your phone open your camera to immediately take a picture of your math problem.

The application can interpret most handwritten or typed math problems.

## Is it free to use?

Yes, it's free to try! You can ask 3 questions for free before reaching the free question limit.

## Which math subjects are covered?

The AI LLM has been trained on a large array of mathematical subjects including, but not limited to Basic Algebra, Advanced Algebra, Geometry, Trigonometry, Calculus, Advanced Calculus, Physics and much more.

## Can it Solve Basic Math Problems?

Yep! The AI LLM has been trained on a large array of mathematical subjects including, but not limited to Basic Algebra, Advanced Algebra, Geometry, Trigonometry, Calculus, Advanced Calculus, Physics and much more.

## How do I cancel my subscription?

You can cancel your subscription very easily in several ways.

1) Login, go to the Manage Account tab, then click the Cancel Plan button.

2) Click the cancel plan link in your sign up email.

3) If you can't find it or no longer have it, just send us an email at [email protected] and we'd be happy to assist you.

## Can I change my subscription?

Yes you certainly can! You can change your subscription by accessing the Manage Account page within the application or using the link provided in your sign up email. If you can't find it or no longer have it, just send us an email at [email protected] or ask your tutor for assistance they will be happy to assist.

## How much does it cost?

You can view the price of our subscription packages here . We're also providing freebies and exclusive deals from our large network of high quality partners. We obsess over the details to ensure you get 10x more value than the price tag!

## Can it Solve Calculus Math Problems?

Can it solve geometry math problems.

P.S. We're currently working to enable in app graphing to accompany solutions.

## Can it solve Trigonometric Functions?

Can it solve simple equations math problems.

Yep! The AI LLM has been trained on a large array of mathematical problems and subjects including, but not limited to Basic Algebra, Advanced Algebra, Geometry, Trigonometry, Calculus, Advanced Calculus, Physics and much more.

## Can it solve any math problems and equations?

How do i get math solutions.

Simply upload an image of your math problem or enter it and click Solve. Our AI math problem solving calculator will provide a step by step solution to the problem with the answer.

## Can it solve word problems?

Yes! Our AI math word problem solver will provide a step by step solution and answer to any word problem.

## How do you find the answers to math word problems?

Step by step solutions and answers to any word problem or equations can be found in the chat window indicated in blue text bubbles.

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Khan Academy Blog

## Free Math Worksheets — Over 100k free practice problems on Khan Academy

Looking for free math worksheets.

You’ve found something even better!

That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!

## Just choose your grade level or topic to get access to 100% free practice questions:

Kindergarten, basic geometry, pre-algebra, algebra basics, high school geometry.

- Trigonometry

## Statistics and probability

High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.

- Addition and subtraction
- Place value (tens and hundreds)
- Addition and subtraction within 20
- Addition and subtraction within 100
- Addition and subtraction within 1000
- Measurement and data
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- Measurement and geometry
- Place value
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- Add and subtract within 20
- Add and subtract within 100
- Add and subtract within 1,000
- Money and time
- Measurement
- Intro to multiplication
- 1-digit multiplication
- Addition, subtraction, and estimation
- Intro to division
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- Equivalent fractions and comparing fractions
- More with multiplication and division
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- Quadrilaterals
- Represent and interpret data
- Multiply by 1-digit numbers
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- Factors, multiples and patterns
- Add and subtract fractions
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- Understand decimals
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- Measuring angles
- Area and perimeter
- Units of measurement
- Decimal place value
- Add decimals
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- Multi-digit multiplication and division
- Divide fractions
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- Powers of ten
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- Converting units of measure
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- Data and statistics
- Negative numbers: addition and subtraction
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- Transformations, congruence, and similarity
- Arithmetic properties
- Factors and multiples
- Reading and interpreting data
- Negative numbers and coordinate plane
- Ratios, rates, proportions
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- Exponents, radicals, and scientific notation
- Foundations
- Algebraic expressions
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- Expressions with exponents
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- Algebra foundations
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- Absolute value & piecewise functions
- Exponents & radicals
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- Performing transformations
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- Right triangles & trigonometry
- Non-right triangles & trigonometry (Advanced)
- Analytic geometry
- Conic sections
- Solid geometry
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- Polynomial factorization
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- Polynomial graphs
- Rational exponents and radicals
- Exponential models
- Transformations of functions
- Rational functions
- Trigonometric functions
- Non-right triangles & trigonometry
- Trigonometric equations and identities
- Analyzing categorical data
- Displaying and comparing quantitative data
- Summarizing quantitative data
- Modeling data distributions
- Exploring bivariate numerical data
- Study design
- Probability
- Counting, permutations, and combinations
- Random variables
- Sampling distributions
- Confidence intervals
- Significance tests (hypothesis testing)
- Two-sample inference for the difference between groups
- Inference for categorical data (chi-square tests)
- Advanced regression (inference and transforming)
- Analysis of variance (ANOVA)
- Scatterplots
- Data distributions
- Two-way tables
- Binomial probability
- Normal distributions
- Displaying and describing quantitative data
- Inference comparing two groups or populations
- Chi-square tests for categorical data
- More on regression
- Prepare for the 2020 AP®︎ Statistics Exam
- AP®︎ Statistics Standards mappings
- Polynomials
- Composite functions
- Probability and combinatorics
- Limits and continuity
- Derivatives: definition and basic rules
- Derivatives: chain rule and other advanced topics
- Applications of derivatives
- Analyzing functions
- Parametric equations, polar coordinates, and vector-valued functions
- Applications of integrals
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- Differentiation: composite, implicit, and inverse functions
- Contextual applications of differentiation
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- AP Calculus AB solved free response questions from past exams
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- Alternate coordinate systems (bases)

## Frequently Asked Questions about Khan Academy and Math Worksheets

Why is khan academy even better than traditional math worksheets.

Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

## What do Khan Academy’s interactive math worksheets look like?

Here’s an example:

## What are teachers saying about Khan Academy’s interactive math worksheets?

“My students love Khan Academy because they can immediately learn from their mistakes, unlike traditional worksheets.”

## Is Khan Academy free?

Khan Academy’s practice questions are 100% free—with no ads or subscriptions.

## What do Khan Academy’s interactive math worksheets cover?

Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.

## Is Khan Academy a company?

Khan Academy is a nonprofit with a mission to provide a free, world-class education to anyone, anywhere.

## Want to get even more out of Khan Academy?

Then be sure to check out our teacher tools . They’ll help you assign the perfect practice for each student from our full math curriculum and track your students’ progress across the year. Plus, they’re also 100% free — with no subscriptions and no ads.

## Get Khanmigo

The best way to learn and teach with AI is here. Ace the school year with our AI-powered guide, Khanmigo.

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Ask Questions

## Solver Title

## Generating PDF...

- Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics
- Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
- Pre Calculus Equations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
- Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
- Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
- Linear Algebra Matrices Vectors
- Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
- Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
- Physics Mechanics
- Chemistry Chemical Reactions Chemical Properties
- Finance Simple Interest Compound Interest Present Value Future Value
- Economics Point of Diminishing Return
- Conversions Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time
- Pre Algebra
- One-Step Addition
- One-Step Subtraction
- One-Step Multiplication
- One-Step Division
- One-Step Decimals
- Two-Step Integers
- Two-Step Add/Subtract
- Two-Step Multiply/Divide
- Two-Step Fractions
- Two-Step Decimals
- Multi-Step Integers
- Multi-Step with Parentheses
- Multi-Step Rational
- Multi-Step Fractions
- Multi-Step Decimals
- Solve by Factoring
- Completing the Square
- Quadratic Formula
- Biquadratic
- Logarithmic
- Exponential
- Rational Roots
- Floor/Ceiling
- Equation Given Roots
- Newton Raphson
- Substitution
- Elimination
- Cramer's Rule
- Gaussian Elimination
- System of Inequalities
- Perfect Squares
- Difference of Squares
- Difference of Cubes
- Sum of Cubes
- Polynomials
- Distributive Property
- FOIL method
- Perfect Cubes
- Binomial Expansion
- Logarithmic Form
- Absolute Value
- Rational Number
- Partial Fractions
- Is Polynomial
- Leading Coefficient
- Leading Term
- Standard Form
- Complete the Square
- Synthetic Division
- Linear Factors
- Rationalize Denominator
- Rationalize Numerator
- Identify Type
- Convergence
- Interval Notation
- Pi (Product) Notation
- Boolean Algebra
- Truth Table
- Mutual Exclusive
- Cardinality
- Caretesian Product
- Age Problems
- Distance Problems
- Cost Problems
- Investment Problems
- Number Problems
- Percent Problems
- Addition/Subtraction
- Multiplication/Division
- Dice Problems
- Coin Problems
- Card Problems
- Pre Calculus
- Linear Algebra
- Trigonometry
- Conversions

## Most Used Actions

Number line.

- \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
- \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
- \mathrm{Bob's\:age\:is\:twice\:that\:of\:Barry's.\:Five\:years\:ago,\:Bob\:was\:three\:times\:older\:than\:Barry.\:Find\:the\:age\:of\:both.}
- \mathrm{Two\:men\:who\:are\:traveling\:in\:opposite\:directions\:at\:the\:rate\:of\:18\:and\:22\:mph\:respectively\:started\:at\:the\:same\:time\:at\:the\:same\:place.\:In\:how\:many\:hours\:will\:they\:be\:250\:apart?}
- \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
- How do you solve word problems?
- To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
- How do you identify word problems in math?
- Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
- Is there a calculator that can solve word problems?
- Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
- What is an age problem?
- An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

word-problems-calculator

- High School Math Solutions – Inequalities Calculator, Exponential Inequalities Last post, we talked about how to solve logarithmic inequalities. This post, we will learn how to solve exponential... Read More

EDUCATIONISE

- Jan 31, 2021

## 8 Free Math Problem Solving Websites and Applications

Updated: Oct 23

Are you struggling with math problems and looking for a way to improve your math problem-solving skills? Look no further because these 8 free math problem-solving websites and applications will give you a detailed solution to any math problem! Whether you're a student, educator, or just someone who wants to sharpen their math skills, these resources offer a wealth of interactive tools and exercises to help you master everything from basic arithmetic to advanced calculus.

6 Websites Offering Free Math Worksheets for All Levels

Not only are these websites and applications easy to use, but they also provide a fun and engaging way to learn and practice math. With some of these tools you can even ask math questions and get answers for free. Whether you are a teacher or a student, now you can avail online math problem-solving websites and smartphone applications to get the step-by-step answer to a complex problem. Teachers can even use these tools to develop math quizzes. With interactive games, video tutorials, and real-world examples, you'll be able to put your math knowledge to the test and see real results in no time.

So what are you waiting for? Check out these 8 free math problem-solving websites and applications and start boosting your math skills today!

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In this article, we have compiled a list of 8 such resources that offer interactive tools and expert guidance to help you master math problem-solving and achieve success.

Mathway calculator is a smart math problem solver which gives you a step by step solution to a math problem. Just type your question and press enter to reveal a detailed answer to your math problem. This intelligent math problem solver, simplifies the process with step by step solutions. All it takes is a question input, and upon hitting enter, you unlock a detailed answer. This powerful tool is your key to conquering math challenges efficiently.

## 2. Photomath

It is a smartphone application which is also known as a camera calculator. All you have to do is take a picture of a math problem and upload it. This math app will scan the problem, solve it, and will display a detailed solution on your screen. Photomath, the renowned camera calculator app, makes math effortless. Snap a photo of your math problem, upload it, and watch as this math app scans, solves, and displays a comprehensive solution.

The application efficiently scans, computes, and presents you with a meticulous, step-by-step solution, answering the ever-persistent question: "What is the answer to this math problem?" It's a seamless way to navigate the world of mathematics, placing the solution at your fingertips.

## 3. Microsoft Math Solver

From algebra and trigonometry to statistics and calculus, Microsoft math solver provides you a free platform where you can not only get detailed solutions to your questions, but also other supporting materials such as interactive graphs, relevant practice problems, and online videos.

In addition to detailed answers, it equips you with valuable resources like interactive graphs, pertinent practice problems, and instructive online videos. It's your gateway to a richer mathematical learning experience, combining the power of answers with educational support.

Cymath is a free application that gives a step by step solution to any math problem. This app does not give you the final answer only, rather the whole solution is broken down into steps for your understanding.

This math problem solver with steps empowers you to tackle math problems with ease, no matter where you are. Simply input your math problem, and let Cymath work its magic, providing you with a detailed solution broken down into manageable steps. No more math conundrums – Cymath has got your back!

## 5. Snapcalc

This math application that allows you to take a picture of a math problem, solves it intuitively, and displays answer on the screen. This app provides solutions to many math problems ranging from algebra to calculus. The best thing about this app is that it can recognize handwritten math problems too. Isn’t that cool?

Unlock the magic of having your own on-the-go math tutor available at your fingertips! With this revolutionary solution, you'll never be left struggling with a math problem again. Simply snap a picture of the math problem you're facing, and voila! You'll receive a personalized step by step answer to a math problem along with a thorough explanation. It's like having a math genius in your pocket, ready to assist you at any moment.

## 6. QuickMath

Quick math provides quick solutions to students for all types of math problems, whether they are related to algebra, calculus, or matrices. Quick Math is your ultimate solution for rapid, hassle-free problem-solving in various mathematical domains. Whether you're grappling with algebra, calculus, or matrices, Quick Math delivers swift and precise answers, empowering students to excel in their studies.

Don't let complex math problems hold you back – unlock the power of Quick Math for seamless problem resolution and mathematical mastery.

## 7. Symbolab

Here is another amazing website that answers math problems. Symbolab is an online website that gives you detailed solutions to any math problem related to algebra, trigonometry, and calculus. It is an incredible online math solver that offers comprehensive solutions to a wide range of math problems.

Whether you're a student seeking math homework help or an individual looking for math assistance, Symbolab is your go-to resource. This math help platform provides step-by-step answers and thorough explanations, making it easier for you to grasp complex math concepts. Say goodbye to math-related stress and hello to seamless problem-solving with Symbolab!

## 8. Chegg Math Solver

It gives you full-time access to an online math calculator or math solver where you can type any math question and get a detailed explanation along with the final answer. Chegg Math Solver is an invaluable step-by-step math problem solver and calculator designed to enhance your comprehension of mathematical concepts.

With its instantaneous solutions, it empowers users to conquer problems in subjects like Pre-Calculus and beyond, making math learning more accessible and engaging.

Read our article: The Future of Education: 8 Predictions for the Next Decade

- Mathematics

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## Math Solver

Solves many common math problems found in school and everyday life. shows work and explains the steps for arriving at the answer., 3/22/2013 6:09:16 pm, math solver does not collect any personal information but is supported by microsoft advertising. learn more about microsoft’s privacy practices and your choices. learn more link: https://choice.microsoft.com/advertisementchoice/.

## 7 Best Math Solver Apps and Websites

We have already talked about math learning apps for Android and iOS before. These apps allow you to study and brush up on mathematical concepts regardless of where you are. But what do you do when you get stuck on a problem and there is no one to help you out? The answer is easy. There are tons of apps and websites that you can use to solve math problems in no time. So if you don’t want to depend on anybody, here are some of the best math solver apps and websites you can try. Let’s begin.

## How to Tackle Homework with Math Solver Apps

1. mathway: scan photos, solve problems.

Mathway is the most recommended app when it comes to math problem-solving apps. It covers a large area of mathematics such as basic math, algebra, trigonometry, calculus, etc. So whether you want to solve basic square roots or word out complicated limits and derivatives, this one is the only tool you may need.

Mathway also allows you to connect with experts. You can submit your question for a fee of $5/month (one pending question at a time) or $30/month (1st plan + 20 sessions live with experts).

To start solving problems, all you have to do is select a subject area and take a photo of the question. Moreover, if you want to type in the question, you can do that with the keyboard as well. The numbers on the keyboard keep changing according to the subject of your choice. The best part is that it shows you steps to solve each problem. However, it is behind the paywall and would cost you $9.99/month. This also removes ads.

- Cover multiple areas (algebra, trigonometry, calculus, etc.)
- Supports three types of input (keyboard, camera, voice)
- Stp by step problem solving
- No sign-in required
- Ask an expert might be costly for many

Get Mathway for ( iOS | Android | Web )

## 2. Slader Homework Answers

If you have a lot of math questions, taking a picture or typing each problem can be a big hassle. Since most math problems are extracted out of textbooks, why not simply scroll through the questions/answers from the book itself? This app does exactly that. You can scan the barcode of a book or browse from the category of the books already solved.

In addition to high school math (pre-algebra, geometry, trigonometry) and upper-level math (differential equations, statistics, etc.), it also covers other subjects such as English, management, accounting, etc. Although the app has a large database of books, there are chances that you won’t find the book you’re looking for. Moreover, most of the advanced math books are locked. So you can only view them by upgrading to a premium plan that comes at $3.99/monthly.

- Find math solutions book-wise
- Clearly shows chapter number, page, and exercise number
- Users can rate and comment on solutions
- Very slow to load
- Tons of banner ads
- Limited database of books
- No option to scan questions

Get Slader Homework Answers for ( iOS | Android )

## 3. Cymath – Math Problem Solver

Cymath is similar to Mathway, however, I like it more because of a few additional features. But before that, let’s first talk about the common features. Both math solver apps allow you to capture math problems and have keyboard input as well. However, Mathway has far more sub-fields of math when compared to Cymath. I tried a few algebra questions where both performed well. However, Cymath often showed errors when I ran trigonometry questions.

In conclusion, if you want to cover a large area of subjects and want extreme accuracy, Mathway is still better.

Cymath shines in a few other aspects, for example, the history section and the ability to bookmark solutions. This comes in handy whenever you are stuck and wish to refer to an old problem. In addition, it also has a learning tab that has common references, practice questions and also discusses one problem each week. The plus version comes at $4.99/month. It removes ads, shows the step-by-step solutions, and even answer why a certain step is used (in addition to how).

- Covers most topics (algebra, calculus, graphing)
- Clean interface (easy to browser)
- Supports image and keyboard input
- History and bookmark option
- Stumbles a bit on accuracy
- Not as comprehensive as Mathway

Get Cymath – Math Problem Solver for ( iOS | Android )

## 4. Geometry solver ² lite

Most math solver apps don’t deal with geometry, but here is an app that does it well. So the next time you struggle to find the area of a figure or you cannot recall a specific formula, you know where to look. You can easily toggle between 2D or 3D figures from the sidebar. Moreover, all the figures are given in a listicle form along with a line diagram for easy understanding.

The calculation is also extremely easy. All you have to do is add the variables and the app will show you all the results live as you change these variables in real-time. In case you do not want to rely on the auto-calculation feature, it shows all the formulae in the same tab for quick reference as well. While all the formulas are free, the calculator for several figures is locked. On the plus side, you can simply watch a 15 seconds video ad to unlock them. If you do not wish to see ads, you have the option to remove ads and unlock all figures by paying a $3.99/one-time fee.

- 2D ad 3D figure section
- Auto-calculator with variables
- Lists all the formulas (area, perimeter, centroid, etc.)
- Purely a geometry app

Get Geometry solver ² lite for ( iOS | Android )

## 5. Google Lens (Homework)

Did you know you can use the Google Search app to solve math problems? Very few people know about it and I’m sure even less actually use it. In order to use this feature, you must have the Google Search app installed. Simply tap on the camera icon and select the Homework option from the bottom. Now all you have to do is point the camera towards the question and adjust the frame accordingly.

If the app can scan the question successfully, you’ll get a preview for the same. If it’s not accurate you have the option to edit the question. You can also view the solution step-wise. Google also has another problem-solving app Socratic ( iOS , Android ) that covers all subjects. You can try that as well however it doesn’t allow you to upload questions from your gallery. Hence when your friends send you a problem on WhatsApp, using the Google Search app is a better solution.

- Shows step by step solution
- Allows you to edit the question
- See similar questions/concepts with Google search results
- Not a dedicated math solver app
- Might not work for advance math

Get Google Search App for ( iOS | Android )

## 6. QuickMath

If you prefer using a PC over the phone to study, you should check QuickMath’s website. The website isn’t fancy but easily solves basic math problems. Similar to the math solver apps we have discussed above, it solves math problems automatically. Whether you are in school or college, it covers a vast array of subjects. You can solve simple equations, algebra, calculus, percentage problems, etc.

The website is easy to browse and all the options are well laid out. You can click on the type of question from the side or top bar. Once you scroll down, you can also view a step-by-step solution for any given problem. In addition to that, it also provides a brief explanation for each step.

- Easy to switch between types of questions
- Solves both basic and advanced math problems
- Features help and tutorial section
- Step by step explanation
- No option to upload questions
- On-screen keyboard is a flimsy way to type (personal choice)

Get QuickMatch for ( iOS | Android | Web )

## 7. WolframAlpha

Wolfram is often called a search engine for solving problems. Unlike Google which heavily relies on search results, Wolfram uses deep computational power (extremely sourced and curated data) to solve mathematical equations and has a vast variety of areas it deals with. You can solve problems related to elementary math, algebra, calculus geometry, etc. To begin, type the question, upload a picture, even just paste a link containing the question.

Wolfram Alpha will likely solve all your problems. The only hiccup is that a lot of great features are exclusive to the pro version which comes at $5.59/monthly. This not only unlocks step-by-step solutions but also adds useful features like practice problems, guided calculators (finance, nutrition, etc), option to download results, etc. If you are a student, I highly recommend you try this. It’s a great factual resource not only for solving maths but other subjects such as chemistry, engineering, economics, stats, etc. too.

- Solutions based on factual data
- Covers most subject besides mathematics
- Useful features behind the paywall (step-by-step solution, download results, etc.)

Visit WolframAlpha

## Closing Remarks: Which Math Solver Apps Should You Choose

In my opinion, Mathway is the perfect app, to begin with. It deals with most of the problems in addition to being accurate. You can type, use voice command and even capture questions to find answers. If you’re on PC, try the QuickMath website which will work in most cases.

Also Read: 19 Best Math Game Apps for Android and iOS

Vaibhav is a broadcast journalist with a keen interest in tech. He doesn't believe in fanboying a specific product. He writes about things he believes are actually helpful in some way to the user.

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## Google can now solve trickier math problems for you with these new features

Math is a challenging subject because it requires an understanding of how to perform the operation to reach an answer, which makes it more difficult to Google an equation to find the answer difficult -- until now.

Google added new updates to Search and Lens that make it easier for users to get assistance when solving math problems. All users have to do now is type the equation or integral into the Search bar, or take a picture with Lens to get a step-by-step explanation or solution.

Also: Chrome on iOS unveils a much-anticipated feature. Here's how to access it

To test out the experience for yourself, on desktop, you can type in an equation or type the term "Math Solver" on Google Search where you will be prompted to enter a math problem or select from the examples to see how it works. The math solver experience will be coming to mobile soon.

Lens can also be leveraged by users to take a photo of geometry triangle problems, solving the challenge of trying to put primarily visual problems into words.

Advancements in Google's large language models also give Search the capability to solve word problems.

All you have to do is type the problem into Search, where you will be met with steps that tell you how to solve the problem by identifying the known and unknown values and providing correct formulas.

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Lastly, Google is also making it easier to explore STEM-related concepts on Search by including 3D models and interactive diagrams for almost 1,000 biology, chemistry, physics, astronomy, and related topics, according to Google.

For example, if you Google "mitochondrion" you will have the opportunity to click on and learn from an interactive diagram that provides an overview, as well as specific details about the individual parts.

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## Google Search can now help you solve geometry, physics and calculus problems

Google updated its search engine and Lens tool with new features to help you visualize and solve problems in more difficult subjects like geometry, physics, trigonometry and calculus.

The update allows you to type an equation into the Search bar or take a photo with Lens to get the correct answer and a step-by-step explanation. The new feature also provides solutions to word problems. For instance, the solver can explain high school physics concepts like finding the average acceleration using the equation “vf= vi + at.”

You can also access the math solver feature by typing “[math solver]” directly into the search bar. However, this function is only available on desktop. It will launch on mobile by the end of the year, the company told TechCrunch.

Another useful new feature is the geometry solver. Since solving geometry problems requires a lot of visualization, Lens can now explain both the visual and the text components of the problem.

However, Lens can only interpret “certain triangle problems,” the company wrote in its blog post, attributed to Google product lead Robert Wong.

We reached out to Wong to clarify, who told us that the geometry solver can currently do the following:

- Find the area of a triangle using A = 1/2 x height x base or Heron’s formula.
- Find the perimeter of a triangle.
- Apply the “Isosceles Triangle Theorem” to determine an unknown side length or angle.
- Apply the “Pythagorean Theorem” to figure out the side lengths in right triangles.

“For our geometry experience, we wanted to focus on a subset of problems that could have a large impact before eventually expanding to cover a more diverse range of geometry problems,” Wong added.

Image Credits: Google

For the physics and geometry solver, Google leveraged its Multitask Unified Model (MUM), which understands specific search queries across various formats, including text, images and videos.

“Language and query understanding are complex challenges that require sophisticated systems to ensure we’re producing the most helpful results — especially in cases where our systems are looking at information in multiple different formats,” Wong explained. “In this case, these features need to understand information across both text and images to correctly interpret a problem and provide accurate step-by-step responses that include both text and diagrams.”

When asked about the accuracy rate for the new experience, the company declined to share specific numbers.

“Our testing shows the accuracy rate is very high,” Wong said.

In addition to problem-solving, Google also launched new 3D models on Search, letting you examine interactive diagrams related to nearly 1,000 topics, such as biology, chemistry, physics, astronomy and more. Google introduced 3D models in 2021, rolling out diagrams for more than 200 chemistry, biology, physics and anatomy concepts.

Over the years, the tech giant has launched multiple features that help you learn, including its interactive feature, “practice problems,” that tests your knowledge of high school topics like math, chemistry and physics. Google Search recently rolled out an English tutoring tool that provides prompts and asks you to say the answers out loud using a provided vocabulary word.

Google takes aim at Duolingo with new English tutoring tool

Android Central

## Google Search gets advanced features to help you solve math and science problems

Posted: November 1, 2023 | Last updated: November 1, 2023

## What you need to know

- You can now throw a geometry or trigonometry query to Google to help solve it.
- Search offers 3D diagrams to help grasp certain concepts better, such as the structure of mitochondria.
- All these are now possible through Google Search and Lens — thanks to new updates.

Google is incorporating new features to Search and Lens for students and consumers to help them solve their math problems, the search giant announced.

Not just math problems but new updates will also help users in solving complicated physics problems next to geometry as well, Google explains in the announcement post. The new feature includes the ability to visualize STEM-related concepts and find relevant equations in a more "natural and intuitive way."

Users can look up various types of math problems on Google Search, and it involves subjects like trigonometry and calculus.

"Simply type your equation or integral into the Search bar, or take a picture with Lens, to see a step-by-step explanation and solution," Google writes in the blog. "You can also type 'math solver' to give the experience a try on desktop and coming soon, on mobile."

The search giant has also provided examples to give users an idea of how to ask Google about a math problem, from equations, integrals, and word problems — thanks to advanced LLMs, which help solve fundamental topics from high-school physics.

Another critical concept is geometry, which is less describable, unlike the others, and this is where the good old Google Lens comes in. Users can scan their geometry problem, like an area of a triangle, for instance, by just using Google Lens. It will then interpret both the visual and text components from the geometry diagram, further revealing step-by-step explanations helping in solving it.

Lastly, Search will help in understanding biology as well, providing 3D models with interactive diagrams that also provide definitions and overviews. Google says there are around 1,000 such examples with biology, chemistry, physics, and astronomy combined. The 1000 number of STEM-related 3D objects rose from 100 when Google first rolled out relevant tools to help students back in 2020.

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## 5 powerful websites that solve math problems for student

- 22 April 2022 14 July 2022

Today we will discuss some good math websites for mathematics students to solve complex mathematics problems.

The word “ Mathematics ↱ ” (ancient Greek máthēma) has different meanings like “knowledge, study, and learning”. Mathematics is not just a subject it is a vast field. It has different branches, the two main branches are pure mathematics and applied mathematics. Applied mathematics is widely used in our daily life.

Applied mathematics is being used in every field like physics, biology, business, computer science, etc. Whereas pure mathematics is a branch that is totally based on theorems and poofs of different rules of applied mathematics, it deals with abstract concepts.

When we go to school from the very first day of our learning life, the teacher tells us about the numbers (Number theory) 1, 2, 3, 4, etc. He/she teaches us numbers with the help of daily life examples. As we go into the upper standards the problems become tricky some students enjoy them and some get afraid of these tricky problems.

Recommended: Is Mathematics Harder Than Physics?

Mathematics is fun for some students but for some dull students, it is a very boring subject. They don’t take it seriously and ultimately they are not able to score well in this subject. If you need to get good grades in this subject you have to be focused and consistent, because consistency is the main key to solve mathematical problems.

The second main key to getting good mathematics grades is “practice” . More practice will result in more grades. Some students get afraid of the long calculation, they get bored and feel mentally uncomfortable. Hundreds of online mathematical websites are there that can help these kinds of students.

Recommended: 6 Practical ways to study Long hours without getting tired .

Just because of these online mathematical websites, calculations become easier. There are some simple steps you have to follow, input your problem and click on the calculate button you will get the step-by-step solution of your problem within seconds.

## Top 5 websites for Mathematics students to solve complex math problems

1. allmath.com ↱.

AllMath is a free online website that contains 350+ calculators for solving different problems of mathematics, physics, statistics, etc. The students who get afraid of long calculations can use this website to solve the problems.

This website provides different tools to solve the educational and daily life calculations and conversions.There is also a blog section where you can read the blogs and learn mathematical topics easily.

Almost every tool on this website contains tool content in which the procedure is completely described. By reading this tool content you’ll be able to solve the problems manually.

Some online tools offered by Allmath are given below:

- Slope intercept form
- Potential Energy Calculator
- L’hopital’s Rule Calculator
- Limit calculator
- Proportion calculator
- Multiplication table
- Fibonacci Sequence Calculator

Students who are weak in mathematics and physics can use these calculators to get the exact answer of the problems and to get rid of lengthy and time taking calculations.

Students can also solve their assignments by using this website because AllMath is offering a step-by-step solution. This site is free of cost. Students and teachers can use this site anytime without spending a single penny.

## 2. Meracalculator.com ↱

MeraCalculator is a site that provides various mathematical tools to help students who face difficulty in finding the solution of a mathematical problem. This website provides almost 300+ mathematical tools. It also provides many other tools related to education . It also provides non-educational tools.

MeraCalculator offers almost 13 different categories that help students to perform different educational and daily life conversions and calculations. Some important educational categories available on this website are Math, physics, chemistry, engineering, etc.

Here is the list of some top-ranked tools of MeraCalculator:

- Derivative calculator
- Integral calculator
- LCM calculator
- Half angle identity calculator
- GCF calculator
- Cross product calculator

The relevant topic of each tool is given on this website (Tool content). Students can easily learn all the basics and formulas to solve problems. This website also offers articles based on mathematics in the blog section. Just like AllMath this site is also free of cost. Students can use this site anytime, anywhere without thinking about the expense.

## 3. Calculators.tech ↱

Calculators.tech is a free website related to mathematics. It provides various categories of calculators like health, informative, finance, fitness, construction, real estate,etc.

It provides almost 300+ different tools related to different problems.With hundreds of free online tools, calculators.tech is helping thousands of students, teachers, businessmen, and nutritionists every month.

Some famous online calculators on this site are listed below:

- Macro Calculator
- BMI calculator
- TDEE calculator
- Standard form calculator
- FIFO LIFO calculator
- GPA calculator

This site also provides a blog section where you can read different mathematics and daily life topics. Don’t be afraid of spending money because this site is totally free.

## 4. Antiderivativecalculator.net ↱

AntiderivativeCalculator is an online source that gives a step-by-step calculation of integral problems. This site also contains some other mathematical tools related to calculus.

List of calculus related tools:

- Triple integral calculator
- Derivative Calculator
- Taylor series calculator
- Double integral calculator
- Laplace transform calculator
- Implicit differentiation calculator
- Maclaurin series calculator
- Partial derivative calculator

Every tool on this website has tool content in which the working of the tool is described briefly. This source is very useful for solving problems and assignments containing calculus problems. This site provides the step-by-step solutionfor both definite and indefinite integrals.

FAQs section is also present at the bottom of every tool, where you can read the frequently asked questions to improve your clarity about the topic. Antiderivativecalculator.net also has a mobile application you can download from the Google play store or Apple app store.

## 5. Limitcalculator.online ↱

Limitcalculator.online is a free website that gives the step-by-step solution for the limit problems. This site also offers other mathematical tools that are related to daily life calculus.

This online limit calculator is very easy to use and user-friendly. This website also contains an example section where you can get three different categories easy, medium, and hard.

Limitcalculator.online also offers some other tools related to calculus the list is given below:

- Implicit Differentiation Calculator
- Simpsons Rule Calculator
- Second Derivative Calculator
- Laplace Transform Calculator
- Improper Integral Calculator
- Directional Derivative Calculator
- Double Integral Calculator
- Triple Integral Calculator
- Integral Calculator
- Partial Derivative Calculator
- Taylor Series Calculator
- Maclaurin Series Calculator
- Inverse Laplace Transform Calculator

Students can also copy the result of their required problem from the site. Students who are not familiar with Limit or find this topic difficult can read the content about the limit to grab all the basics of this topic.

In this post, we have discussed the list of the five best math websites that are very beneficial for the students to solve any kind of mathematical problems in no time. Many students can reduce the difficulty of larger calculations by using the tools of these free websites. They can also prepare for exams by having a look at the content and examples given on these worthy websites.

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## Android Police

Google's ai can now solve word problems you paste into the search bar.

Lens and Search just got a major math makeover

- Google's new features in Search and Lens make it easier for users to visualize STEM concepts and solve complex equations.
- Search can now handle physics word problems, and Lens can interpret visual problems in geometry, providing step-by-step guides on how to solve them.
- Google's AI capabilities, powered by technology like PaLM, contribute to the development of these new tools, but they should be used as supplementary resources alongside traditional learning methods.

Both students and working professionals frequently rely on search engines to find solutions to intricate queries. Google, in its efforts to maintain its edge as the world's leading search engine, has recently upgraded its features to better serve those in STEM fields. As of recently, if you're grappling with a challenging math or physics problem, Google's Search and Lens might just be your new best friends.

Google has introduced new features in both Search and Lens to assist users in visualizing STEM-related concepts and determining the right equations for their problems. Whether you're trying to decipher a complicated physics concept or a perplexing geometry problem, these tools aim to make the process more intuitive.

For instance, if you're stuck on a calculus problem, you can now simply type your equation into the Search bar or snap a photo with Lens to receive a step-by-step explanation and solution. This feature is not limited to just equations; it extends to word problems , especially those from high-school physics topics.

The integration of Lens, in particular, addresses a unique challenge in geometry. Describing visual problems using words can be cumbersome. For example, if you're given a diagram of a triangle with measurements of two sides and need to find its area, Lens can now interpret both the visual and text components of the problem, offering a comprehensive step-by-step guide on how to solve it.

This advancement isn't just about problem-solving. Google has also introduced new interactive 3D models on Search, allowing users to visually explore almost 1,000 topics from biology, chemistry, physics, and astronomy — an example given by the company was a search for the term "mitochondria." This feature can be particularly useful for those who wish to gain a deeper visual understanding of complex STEM concepts.

The underlying technology that powers these features can be traced back to Google's efforts in enhancing its AI capabilities. A notable mention on this front is the integration of PaLM into Bard . Initially, Bard, based on Google’s Language Model for Dialogue Application (LaMDA), was more adept at holding conversations than logical reasoning. However, with the fusion of PaLM into its code base, Bard's capabilities expanded to include arithmetic, code completion, semantic parsing, logical inference, and more. We could be seeing a similar implementation of machine learning here with the new tools in Search and Lens.

While AI tools like the features Google is introducing today with Search and Lens are becoming increasingly sophisticated, it's essential for users to approach them as supplementary resources, complementing traditional learning and problem-solving methods. As technology continues to evolve, the line between human and machine capabilities might blur, but the essence of learning and understanding will always remain inherently human.

## The Math Problem That Took Nearly a Century to Solve

Uc san diego mathematicians unlock the secret to ramsey numbers.

- Michelle Franklin - [email protected]

## Published Date

Share this:, article content.

We’ve all been there: staring at a math test with a problem that seems impossible to solve. What if finding the solution to a problem took almost a century? For mathematicians who dabble in Ramsey theory, this is very much the case. In fact, little progress had been made in solving Ramsey problems since the 1930s.

Now, University of California San Diego researchers Jacques Verstraete and Sam Mattheus have found the answer to r(4,t), a longstanding Ramsey problem that has perplexed the math world for decades.

## What was Ramsey’s problem, anyway?

In mathematical parlance, a graph is a series of points and the lines in between those points. Ramsey theory suggests that if the graph is large enough, you’re guaranteed to find some kind of order within it — either a set of points with no lines between them or a set of points with all possible lines between them (these sets are called “cliques”). This is written as r(s,t) where s are the points with lines and t are the points without lines.

To those of us who don’t deal in graph theory, the most well-known Ramsey problem, r(3,3), is sometimes called “the theorem on friends and strangers” and is explained by way of a party: in a group of six people, you will find at least three people who all know each other or three people who all don’t know each other. The answer to r(3,3) is six.

“It’s a fact of nature, an absolute truth,” Verstraete states. “ It doesn't matter what the situation is or which six people you pick — you will find three people who all know each other or three people who all don't know each other. You may be able to find more, but you are guaranteed that there will be at least three in one clique or the other.”

{/exp:typographee}

Verstraete first saw r(4,t) in a book written by two UC San Diego professors.

What happened after mathematicians found that r(3,3) = 6? Naturally, they wanted to know r(4,4), r(5,5), and r(4,t) where the number of points that are not connected is variable. The solution to r(4,4) is 18 and is proved using a theorem created by Paul Erdös and George Szekeres in the 1930s.

Currently r(5,5) is still unknown.

## A good problem fights back

Why is something so simple to state so hard to solve? It turns out to be more complicated than it appears. Let’s say you knew the solution to r(5,5) was somewhere between 40-50. If you started with 45 points, there would be more than 10 234 graphs to consider!

“Because these numbers are so notoriously difficult to find, mathematicians look for estimations,” Verstraete explained. “ This is what Sam and I have achieved in our recent work. How do we find not the exact answer, but the best estimates for what these Ramsey numbers might be?”

The problem r(4,t) is a conjecture from Erdös, who offered $250 to the first person who could solve it.

Math students learn about Ramsey problems early on, so r(4,t) has been on Verstraete’s radar for most of his professional career. In fact, he first saw the problem in print in Erdös on Graphs: His Legacy of Unsolved Problems, written by two UC San Diego professors, Fan Chung and the late Ron Graham. The problem is a conjecture from Erdös, who offered $250 to the first person who could solve it.

“Many people have thought about r(4,t) — it’s been an open problem for over 90 years,” Verstraete said. “But it wasn’t something that was at the forefront of my research. Everybody knows it's hard and everyone’s tried to figure it out, so unless you have a new idea, you’re not likely to get anywhere.”

Then about four years ago, Verstraete was working on a different Ramsey problem with a mathematician at the University of Illinois-Chicago, Dhruv Mubayi. Together they discovered that pseudorandom graphs could advance the current knowledge on these old problems.

In 1937, Erdös discovered that using random graphs could give good lower bounds on Ramsey problems. What Verstraete and Mubayi discovered was that sampling from pseudo random graphs frequently gives better bounds on Ramsey numbers than random graphs. These bounds — upper and lower limits on the possible answer — tightened the range of estimations they could make. In other words, they were getting closer to the truth.

In 2019, to the delight of the math world, Verstraete and Mubayi used pseudorandom graphs to solve r(3,t). However, Verstraete struggled to build a pseudorandom graph that could help solve r(4,t).

It took a pseudorandom graph from finite geometry, called an O'Nan configuration, to solve a longstanding Ramsey problem.

He began pulling in different areas of math outside of combinatorics, including finite geometry, algebra and probability. Eventually he joined forces with Mattheus, a postdoctoral scholar in his group whose background was in finite geometry.

“It turned out that the pseudorandom graph we needed could be found in finite geometry,” Verstraete stated. “Sam was the perfect person to come along and help build what we needed.”

Once they had the pseudorandom graph in place, they still had to puzzle out several pieces of math. It took almost a year, but eventually they realized they had a solution: r(4,t) is close to a cubic function of t . If you want a party where there will always be four people who all know each other or t people who all don’t know each other, you will need roughly t 3 people present. There is a small asterisk (actually an o) because, remember, this is an estimate, not an exact answer. But t 3 is very close to the exact answer.

The findings are currently under review with the Annals of Mathematics . A preprint can be viewed on arXiv.

“It really did take us years to solve,” Verstraete stated. “And there were many times where we were stuck and wondered if we’d be able to solve it at all. But one should never give up, no matter how long it takes.”

Verstraete emphasizes the importance of perseverance — something he reminds his students of often. “If you find that the problem is hard and you're stuck, that means it's a good problem. Fan Chung said a good problem fights back. You can't expect it just to reveal itself.”

Verstraete knows such dogged determination is well-rewarded: “I got a call from Fan saying she owes me $250.”

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Ai might disrupt math and computer science classes — in a good way.

For as long as Jake Price has been a teacher, Wolfram Alpha – a website that solves algebraic problems online – has threatened to make algebra homework obsolete.

Teachers learned to work around and with it, said Price, assistant professor of mathematics and computer science at the University of Puget Sound. But now, they have a new homework helper to contend with: generative artificial intelligence tools, such as ChatGPT.

Price doesn’t see ChatGPT as a threat, and he’s not alone. Some math professors believe AI, when used correctly, could help strengthen math instruction. And it’s arriving on the scene at a time when math scores are at a national historic low and educators are questioning if math should be taught differently.

AI can serve as a tutor, giving a student who is floundering with a problem immediate feedback. It can help a teacher plan math lessons, or write a variety of math problems geared toward different levels of instruction. It can even show new computer programmers sample code, allowing them to skip over the boring chore of learning how to write basic code.

As schools across the country debate banning AI tools, some math and computer science teachers are embracing the change because of the nature of their discipline.

“Math has always been evolving as technology evolves,” said Price. Years ago, people were using slide rules and doing their multiplication with logarithmic tables. Then, along came calculators.

Price teaches with human-capable technologies in mind, making sure to give students the skills in class by hand. Then, he discusses with them the limitations of the technologies they might be tempted to use when they get home.

“Computers are really good at doing tedious things,” Price said. “We don’t have to do all the tedious stuff. We can let the computer do it. And then we can interpret the answer and think about what it tells us about the decisions we need to make.”

He wants his students to enjoy looking for patterns, seeing how different methods can give different or the same answers and how to translate those answers into decisions about the world.

“ChatGPT, just like the calculator and just like the slide rule and all the technology before, just helps us get at that core, real part of math,” Price said.

Conversely, ChatGPT has its limits. It can show the right steps to solving a math problem – and then give the wrong answer.

This is because it’s “not actually doing the math,” Price said. It’s just pulling together pieces of the sentences where other people have described how to solve similar problems.

Min Sun, a University of Washington education professor, thinks students should use ChatGPT like a personal tutor. If students get lost in class and don’t understand a mathematical operation, they can ask ChatGPT to explain it and give them a few examples.

The Khan Academy, an educational nonprofit that provides a collection of online learning tools and videos and has long been a go-to for math homework, has created exactly that.

The tutor is called Khanmigo. Students can open it while completing math problems and tell it that they are stuck.

They can have a conversation with the AI tutor, telling it what they don’t understand, and the AI tutor helps to explain, said Kristen DiCerbo, the chief learning officer at Khan Academy.

“Instead of saying, ‘Here’s the answer for you,’ it says things like, ‘What’s the next step?’ or ‘What do you think might be the next thing to do?’ ” DiCerbo said.

## For the math teacher

Sun, the UW education professor, wants teachers to use ChatGPT as their own assistant: to plan math lessons, give students good feedback and communicate with parents.

Teachers can ask AI, “What is the best way to teach this concept?” Or “What are the kinds of mistakes students tend to make when learning this math concept?” Or, “What kinds of questions will students have about this concept?”

Teachers can also ask ChatGPT to recommend different levels of math problems for students with different mastery of the concept, she said. This is particularly helpful for teachers who are new to the profession or have students with diverse needs – special education or English language learners, Sun said.

“I’m amazed by the details that sometimes ChatGPT can offer,” Sun said. “It gives you some initial ideas and possible problem areas for students so I can get myself more prepared before walking into the classroom.”

And, if a teacher already has a high-quality lesson plan, they could feed that to ChatGPT and ask it to create another lesson in a similar teaching style, but for a different concept.

Sun hopes ChatGPT can also help teachers write more culturally appropriate word-problem questions to make all their students feel included.

“The current technology is really a technical assistant to support them, empower them, amplify their creative abilities,” Sun said. “It is really not a substitute to their own agency, their own creativity, their own professionalism. They really need to keep that in mind.”

## For the computer science teacher

A year ago, if you asked Daniel Zingaro how he assesses his introductory computer science students, he would say: “We ask them to write code.”

But if you ask him today, the answer would be far more complex, said Zingaro, an associate professor at the University of Toronto.

Zingaro and Leo Porter, a computer science professor at the University of California, San Diego, authored the book Learn AI-Assisted Python Programming with GitHub Copilot and ChatGPT. They believe AI will allow introductory computer science classes to tackle big-picture concepts.

A lot of beginner students get stuck writing very simple code, Porter and Zingaro said. They never move on to more advanced questions – and many still can’t write simple code after they complete the course.

“It’s not just uninteresting, it is frustrating,” Porter added. “They are trying to build something and they forgot a semicolon and they’ll lose three hours trying to find that missing semicolon” or some other bit of syntax that prevents a code from running properly.

AI doesn’t make those mistakes, and allows computer science professors to spend more of their time teaching higher-level skills.

The professors now ask their students to take a big problem and break it down to smaller questions or tasks the code needs to do. They also ask students to test and debug code once it is already written.

“If we think bigger picture about what we want our students to do, we want them to write software that is meaningful to them,” Porter said. “And this process of writing software is taking this fairly big, often not-well-defined problem and figuring out, how do I break them into pieces?”

Magdalena Balazinska, director of the University of Washington’s Paul G. Allen School of Computer Science and Engineering, embraces the progress AI has made.

“With the support of AI, human software engineers get to focus on the most interesting part of computer science: answering big software design questions,” Balazinska said. “AI allows humans to focus on the creative work.”

Not all professors in the field think AI should be integrated into the curriculum. Some interviewed for a UC San Diego research paper and in an Education Week survey prefer blocking or negating the use of ChatGPT or similar tools like Photomath, at least in the short term.

Zingaro and Porter argue that reading a lot of code generated by AI doesn’t feel like cheating. Rather, it’s how a student is going to learn.

“I think a lot of programmers read a lot of code, just like how I believe the best writers read a lot of writing,” Zingaro said. “I think that is a very powerful way to learn.”

## Robotic heart surgery gives Donny Jones a rapid recovery, more energy

Donny Jones was born with a heart that was a little bit different.

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