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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.

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Examples: 1+2 , 1/3+1/4 , 2^3 * 2^2   (x+1)(x+2) (Simplify Example), 2x^2+2y @ x=5, y=3 (Evaluate Example)   y=x^2+1 (Graph Example), 4x+2=2(x+6) (Solve Example)

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Type your algebra problem into the text box.

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Online Equation Solver

Solve linear, quadratic and polynomial systems of equations with wolfram|alpha.

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More than just an online equation solver

Wolfram|Alpha is a great tool for finding polynomial roots and solving systems of equations. It also factors polynomials, plots polynomial solution sets and inequalities and more.

Learn more about:

• Equation solving

Tips for entering queries

Enter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to formulate queries.

• find roots to quadratic x^2-7x+12
• plot inequality x^2-7x+12<=0
• solve {3x-5y==2,x+2y==-1}
• plot inequality 3x-5y>=2 and x+2y<=-1
• solve 3x^2-y^2==2 and x+2y^2==5
• plot 3x^2-y^2>=2 and x+2y^2<=5
• View more examples

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Get immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator

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About solving equations

A value is said to be a root of a polynomial if ..

The largest exponent of appearing in is called the degree of . If has degree , then it is well known that there are roots, once one takes into account multiplicity. To understand what is meant by multiplicity, take, for example, . This polynomial is considered to have two roots, both equal to 3.

One learns about the "factor theorem," typically in a second course on algebra, as a way to find all roots that are rational numbers. One also learns how to find roots of all quadratic polynomials, using square roots (arising from the discriminant) when necessary. There are more advanced formulas for expressing roots of cubic and quartic polynomials, and also a number of numeric methods for approximating roots of arbitrary polynomials. These use methods from complex analysis as well as sophisticated numerical algorithms, and indeed, this is an area of ongoing research and development.

Systems of linear equations are often solved using Gaussian elimination or related methods. This too is typically encountered in secondary or college math curricula. More advanced methods are needed to find roots of simultaneous systems of nonlinear equations. Similar remarks hold for working with systems of inequalities: the linear case can be handled using methods covered in linear algebra courses, whereas higher-degree polynomial systems typically require more sophisticated computational tools.

How Wolfram|Alpha solves equations

For equation solving, Wolfram|Alpha calls the Wolfram Language's Solve and Reduce functions, which contain a broad range of methods for all kinds of algebra, from basic linear and quadratic equations to multivariate nonlinear systems. In some cases, linear algebra methods such as Gaussian elimination are used, with optimizations to increase speed and reliability. Other operations rely on theorems and algorithms from number theory, abstract algebra and other advanced fields to compute results. These methods are carefully designed and chosen to enable Wolfram|Alpha to solve the greatest variety of problems while also minimizing computation time.

Although such methods are useful for direct solutions, it is also important for the system to understand how a human would solve the same problem. As a result, Wolfram|Alpha also has separate algorithms to show algebraic operations step by step using classic techniques that are easy for humans to recognize and follow. This includes elimination, substitution, the quadratic formula, Cramer's rule and many more.

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🤖 Math Solver & Calculator

This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of artificial intelligence large language models to parse and generate natural language answers. This creates a math problem solver that's more accurate than ChatGPT, more flexible than a math calculator, and provides answers faster than a human tutor.

Learn more here .

Problem Solver Subjects

Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.

• Math Word Problems
• Pre-Algebra
• Geometry Graphing
• Trigonometry
• Precalculus
• Finite Math
• Linear Algebra

Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

Basic Math Solutions

Below are examples of basic math problems that can be solved.

• Long Arithmetic
• Rational Numbers
• Operations with Fractions
• Ratios, Proportions, Percents
• Measurement, Area, and Volume
• Factors, Fractions, and Exponents
• Unit Conversions
• Data Measurement and Statistics
• Points and Line Segments

Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

Below are examples of Pre-Algebra math problems that can be solved.

• Variables, Expressions, and Integers
• Simplifying and Evaluating Expressions
• Solving Equations
• Multi-Step Equations and Inequalities
• Ratios, Proportions, and Percents
• Linear Equations and Inequalities

Algebra Solutions

Below are examples of Algebra math problems that can be solved.

• Algebra Concepts and Expressions
• Points, Lines, and Line Segments
• Simplifying Polynomials
• Factoring Polynomials
• Linear Equations
• Absolute Value Expressions and Equations
• Radical Expressions and Equations
• Systems of Equations
• Quadratic Equations
• Inequalities
• Complex Numbers and Vector Analysis
• Logarithmic Expressions and Equations
• Exponential Expressions and Equations
• Conic Sections
• Vector Spaces
• 3d Coordinate System
• Eigenvalues and Eigenvectors
• Linear Transformations
• Number Sets
• Analytic Geometry

Trigonometry Solutions

Below are examples of Trigonometry math problems that can be solved.

• Algebra Concepts and Expressions Review
• Right Triangle Trigonometry
• Radian Measure and Circular Functions
• Graphing Trigonometric Functions
• Simplifying Trigonometric Expressions
• Verifying Trigonometric Identities
• Solving Trigonometric Equations
• Complex Numbers
• Analytic Geometry in Polar Coordinates
• Exponential and Logarithmic Functions
• Vector Arithmetic

Precalculus Solutions

Below are examples of Precalculus math problems that can be solved.

• Operations on Functions
• Rational Expressions and Equations
• Polynomial and Rational Functions
• Analytic Trigonometry
• Sequences and Series
• Analytic Geometry in Rectangular Coordinates
• Limits and an Introduction to Calculus

Calculus Solutions

Below are examples of Calculus math problems that can be solved.

• Evaluating Limits
• Derivatives
• Applications of Differentiation
• Applications of Integration
• Techniques of Integration
• Parametric Equations and Polar Coordinates
• Differential Equations

Statistics Solutions

Below are examples of Statistics problems that can be solved.

• Algebra Review
• Average Descriptive Statistics
• Dispersion Statistics
• Probability
• Probability Distributions
• Frequency Distribution
• Normal Distributions
• t-Distributions
• Hypothesis Testing
• Estimation and Sample Size
• Correlation and Regression

Finite Math Solutions

Below are examples of Finite Math problems that can be solved.

• Polynomials and Expressions
• Equations and Inequalities
• Linear Functions and Points
• Systems of Linear Equations
• Mathematics of Finance
• Statistical Distributions

Linear Algebra Solutions

Below are examples of Linear Algebra math problems that can be solved.

• Introduction to Matrices
• Linear Independence and Combinations

Chemistry Solutions

Below are examples of Chemistry problems that can be solved.

• Unit Conversion
• Atomic Structure
• Molecules and Compounds
• Chemical Equations and Reactions
• Behavior of Gases
• Solutions and Concentrations

Physics Solutions

Below are examples of Physics math problems that can be solved.

• Static Equilibrium
• Dynamic Equilibrium
• Kinematics Equations
• Electricity
• Thermodymanics

Geometry Graphing Solutions

Below are examples of Geometry and graphing math problems that can be solved.

• Step By Step Graphing
• Linear Equations and Functions
• Polar Equations

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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.

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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
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• Addition and subtraction within 20
• Addition and subtraction within 100
• Addition and subtraction within 1000
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• Measurement and geometry
• Place value
• Measurement, data, and geometry
• 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
• Understand fractions
• Equivalent fractions and comparing fractions
• More with multiplication and division
• Arithmetic patterns and problem solving
• Quadrilaterals
• Represent and interpret data
• Multiply by 1-digit numbers
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• Factors, multiples and patterns
• Add and subtract fractions
• Multiply fractions
• Understand decimals
• Plane figures
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• 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
• Coordinate plane
• Algebraic thinking
• Converting units of measure
• Properties of shapes
• Ratios, rates, & percentages
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• Properties of numbers
• Variables & expressions
• Equations & inequalities introduction
• Data and statistics
• Negative numbers: addition and subtraction
• Negative numbers: multiplication and division
• Fractions, decimals, & percentages
• Rates & proportional relationships
• Expressions, equations, & inequalities
• Numbers and operations
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• Linear equations and functions
• Systems of equations
• Geometric transformations
• Data and modeling
• Volume and surface area
• Pythagorean theorem
• Transformations, congruence, and similarity
• Arithmetic properties
• Factors and multiples
• Reading and interpreting data
• Negative numbers and coordinate plane
• Ratios, rates, proportions
• Equations, expressions, and inequalities
• Exponents, radicals, and scientific notation
• Foundations
• Algebraic expressions
• Linear equations and inequalities
• Graphing lines and slope
• Expressions with exponents
• Quadratics and polynomials
• Equations and geometry
• Algebra foundations
• Solving equations & inequalities
• Working with units
• Linear equations & graphs
• Forms of linear equations
• Inequalities (systems & graphs)
• Absolute value & piecewise functions
• Exponents & radicals
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• Quadratics: Multiplying & factoring
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• Irrational numbers
• Performing transformations
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• Right triangles & trigonometry
• Non-right triangles & trigonometry (Advanced)
• Analytic geometry
• Conic sections
• Solid geometry
• Polynomial arithmetic
• Complex numbers
• Polynomial factorization
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• Polynomial graphs
• Rational exponents and radicals
• Exponential models
• Transformations of functions
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• 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
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• Random variables
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• Scatterplots
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• Two-way tables
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• 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
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• 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
• Differentiation: definition and basic derivative rules
• Differentiation: composite, implicit, and inverse functions
• Contextual applications of differentiation
• Applying derivatives to analyze functions
• Integration and accumulation of change
• Applications of integration
• AP Calculus AB solved free response questions from past exams
• AP®︎ Calculus AB Standards mappings
• Infinite sequences and series
• AP Calculus BC solved exams
• AP®︎ Calculus BC Standards mappings
• Integrals review
• Integration techniques
• Thinking about multivariable functions
• Derivatives of multivariable functions
• Applications of multivariable derivatives
• Integrating multivariable functions
• Green’s, Stokes’, and the divergence theorems
• First order differential equations
• Second order linear equations
• Laplace transform
• Vectors and spaces
• Matrix transformations
• 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.

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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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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. 

Also: The AI I want to see in the world: 5 ways it could manage my Gmail inbox for me

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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These two past Pixel phone problems are popping up again on Google's new flagship

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

2023 Election Center: See the latest headlines from the 2023 general election here

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.”

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