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• 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.

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Geogebra math solver.

Get accurate solutions and step-by-step explanations for algebra and other math problems, while enhancing your problem-solving skills!

ScanMath - Algebra Solver

Discover the power of the TOP math solving tool , designed to make your math homework a breeze

Just scan your math problem, and get instant, accurate solutions with comprehensive step-by-step explanations. ScanMath's calculator is the reliable companion for learning math and study success.

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ScanMath provides instant solutions and detailed explanations to math problems including Trigonometry, Statistics, Algebra, Calculus, Arithmetic, and more.

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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):.

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Best 5 Websites For Solving Math Problems

Florencia basavilbaso.

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Find the top 5 websites to solve math problems in our video too!

Mathematics can be challenging for many, with complex equations and mind-bending concepts that require time, patience, and skill to master.

Fortunately, in the age of technology, we have plenty of websites to solve math problems and make the subject more accessible and exciting.

At Gradehacker, we dedicate ourselves to providing the best resources to non-traditional adult students and improving their college experience. 

Here are the best 5 websites to solve the math concepts you need to learn!

1. Symbolab

first on our list of websites to solve math is Symbolab. 

Whether you’re a beginner or an advanced student, this math skills resource has you covered with its detailed step-by-step solutions, interactive graphics, and helpful examples.

You can also put equations or problems and get math answers with detailed steps, graphics, and examples , making it a game-changer when it comes to finding solutions to math problems.

As a mathematical resource for students’ grades, it covers a wide range of topics, such as:

• Trigonometry

And in addition to it, the website offers a note-taking section, allowing users to write down key details for future reference.

Symbolab’s availability in both free and premium options ensures that students of all backgrounds can benefit from its remarkable features and unleash their full mathematical potential.

Symbolab Subscription and Cost

Symbolab has both price-free and premium options.

Free Plan: You have access immediately to practice problems, custom settings, and save notes. 

Pro Plan: Here, besides having the benefits of the free subscription, you’ll also be available to:

• Full access to solution steps
• Web & Mobile subscription
• Assessments
• Detailed progress report

The platform offers three different payment options:

• Monthly: $7.99
• Semi-Annual: $29.99
• Annual: $34.99

Symbolab is also available on Google Play and App Store

Mathway is another of the best websites to solve math problems that can help you with your class activities.

It stands as a reliable and accessible online tool for a range of math topics like:

• Trigonometric functions
• Descriptive statistics

One key feature that sets Mathway apart is its ability to provide step-by-step solutions to math problems.

It simplifies solving math problems by breaking down the solution process when entering an equation or problem, serving as a valuable companion for students , educators, and individuals seeking instant support.

With its step-by-step explanation and advanced graphing capabilities, this math solution app helps users obtain correct answers and understand each step, concept, and reasoning.

Mathway Subscription and Cost

Mathway subscription consists of its “Step-by-Step Access,” allowing users to see each step of the solution without advertisements.

This is the only current subscription plan that costs:

• $9.99 with a monthly subscription
• $39.99 with a yearly subscription

This smart calculator is available on Google Play and Apple Store

Cymath offers college students a powerful tool for solving math questions easily and precisely.

With its very simple interface and advanced capabilities, this website simplifies the process of tackling any complex math question you may have, making it a great resource for learners at all levels.

Unlike other math solver websites, it only covers algebra and calculus functions, but it’s a very intuitive tool that provides instant feedback and suggestions , ensuring users can correct errors or misconceptions along the way.

Cymath Subscription and Price

You can use this app for free, or you can pay $5 a month for:

• Shows how a step is done
• Shows why a step is taken
• Learn from reference material

Cymath has a mobile app available for iOS and Android .

4. QuickMath

QuickMath allows you to solve equations and simplify fractions by just typing your problem.  

After that, QuickMath will generate a step-by-step solution. It also includes a graphing tool that can be used to visualize solutions. 

One of the advantages of QuickMath is that it also provides instant feedback to students, allowing them to identify any mistakes they have made quickly . This can be especially useful for students struggling with math and needing extra support.

QuickMath is also accessible from anywhere with an internet connection , making it a useful tool for students studying remotely or outside the classroom. 

This math solver app will help you with:

• Solving complex math equations
• Factor polynomials
• Simplify expressions
• Graph equations and inequalities

And it also has features like:

• Advanced solvers: Partial fractions, matrices, factors, etc.
• All solvers: Arithmetics, fractions, etc.

QuickMath Subscription Plan and Costs

To see what steps to take, they offer a subscription plan that costs:

• $9.99 a month
• $19.99 every six months
• $29.99 a year

You can find it available on Google Play and Apple Store .

5. Microsoft Math Solver

Microsoft Math Solver is a powerful and versatile mobile application that serves as your personal math assistant on the go.

This app combines the convenience of a calculator with advanced problem-solving capabilities to help users easily tackle a wide range of mathematical equations and problems.

One of the standout features of Microsoft Math Solver is its ability to solve math problems using various methods and approaches. Users can simply snap a photo of a handwritten or printed math problem, and the app will analyze and provide step-by-step solutions.

This feature saves time and promotes a deeper understanding of the problem-solving process.

 This math problem solver covers:

• Pre-algebra
• Algebra calculator
• Trigonometric equations

This app is absolutely free, and you can find it on Google Play and Apple Store .

Tips For Solving Math Problems

Having websites to solve math problems can be an effective solution when you are taking care of math homework, but there are other practices you can adopt that will help you improve your math skills without the internet needed.

We know that this subject can be challenging for many students, but it can also be enjoyable and rewarding with the right approach. Here are six tips for solving math problems:

1. Understand The Problem:

Before attempting to solve a math problem, take the time to read it carefully and make sure you understand what you are being asked to do. 

Look for important keywords, such as “find,” “calculate,” or “solve,” and make note of any important information or data that is provided.

2. Draw a diagram:

Sometimes, it can be helpful to draw a diagram or graph to visualize the problem and make it easier to understand . 

This can be especially useful for geometry problems or problems involving complex data sets.

3. Work from left to right:

When performing calculations, always work from left to right and be sure to follow the order of operations Parentheses, Exponents, Multiplication and Division (PEMDAS). 

This will help you avoid errors and ensure that you arrive at the correct answer.

4. Show your work:

When solving a math problem, be sure to show your work step-by-step. 

This not only helps you keep track of your progress, but it also allows you to identify any mistakes you may have made and correct them before moving on.

5. Check your answer:

After solving a math problem, double-check your answer to ensure it is correct .

If possible, try using a different method to arrive at the same answer to confirm that your solution is accurate.

This step helps you catch any potential errors or miscalculations that may have occurred during the problem-solving process , especially when dealing with complex equations like quadratic equations.

6. Practice, practice, practice:

The more you practice solving math problems, the easier it will become. 

Set aside time each day to work on these problems, and don’t be afraid to ask for help if you need it. Remember, with perseverance and dedication, anyone can become proficient in math problem-solving!

Solving Math Problems Like a Pro

The world of mathematics is now more accessible and exciting thanks to effective websites to solve math calculations.

Whether you’re a student struggling with homework, a professional needing quick solutions or improving your abilities, these websites provide the necessary tools and resources.

From the comprehensive step-by-step solutions offered by Symbolab to the fast and efficient calculations of Mathway and the versatile capabilities of Microsoft Math Office, each website brings its unique features to the table.

But if you are looking for one-on-one guidance with your complex math problems, here at Gradehacker, we have years of experience helping students like you with their homework assignments and even entire STEM classes .

You can also check more tips to enhance your learning experience:

7 Best Websites to Find Free College Textbooks in 2023

Best iPads For College Students

How to Become a Minimalist Student: A Lifestyle That Improves The Study

Best AI to Write Essays

How to Take Notes Like a Pro 

Best Sites For Scholarly Sources | Websites To Find The Best Academic Sources

Florencia Basavilbaso is a content creator passioned for writing, music, films, and the arts. At Gradehacker, she helps to improve non-traditional students life’s by finding and providing the most useful information, so they can always progress. You can find her on LinkedIn .

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Need help? Chat with a tutor anytime, 24/7.

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.

Sign up for free 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

Looking for the old Mathway Calculator? We've moved it to here .

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

Solver Title

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• Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Mean, Median & Mode
• 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 Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales 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 Roman Numerals 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 Volume
• 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
• Negative Rule
• Product Rule
• Quotient Rule
• Expand Power Rule
• Fraction Exponent
• Exponent Rules
• Exponential Form
• Logarithmic Form
• Absolute Value
• Rational Number
• Powers of i
• 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{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
• \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
• \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
• 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?
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How do you solve word problems in math?

Master word problems with eight simple steps from a math tutor!

Author Amber Watkins

Published April 2024

• Key takeaways
• Students who struggle with reading, tend to struggle with understanding and solving word problems. So the best way to solve word problems in math is to become a better reader!
• Mastery of word problems relies on your child’s knowledge of keywords for word problems in math and knowing what to do with them.
• There are 8 simple steps each child can use to solve word problems- let’s go over these together.

Table of contents

• How to solve word problems

Lesson credits

As a tutor who has seen countless math worksheets in almost every grade – I’ll tell you this: every child is going to encounter word problems in math. The key to mastery lies in how you solve them! So then, how do you solve word problems in math?

In this guide, I’ll share eight steps to solving word problems in math.

How to solve word problems in math in 8 steps

Step 1: read the word problem aloud.

For a child to understand a word problem, it needs to be read with accuracy and fluency! That is why, when I tutor children with word problems, I always emphasize the importance of reading properly.

Mastering step 1 looks like this:

• Allow your child to read the word problem aloud to you. 
• Don’t let your child skip over or mispronounce any words. 
• If necessary, model how to read the word problem, then allow your child to read it again. Only after the word problem is read accurately, should you move on to step 2.

Step 2: Highlight the keywords in the word problem

The keywords for word problems in math indicate what math action should be taken. Teach your child to highlight or underline the keywords in every word problem. 

Here are some of the most common keywords in math word problems: 

• Subtraction words – less than, minus, take away
• Addition words – more than, altogether, plus, perimeter
• Multiplication words – Each, per person, per item, times, area 
• Division words – divided by, into
• Total words – in all, total, altogether

Let’s practice. Read the following word problem with your child and help them highlight or underline the main keyword, then decide which math action should be taken.

Michael has ten baseball cards. James has four baseball cards less than Michael. How many total baseball cards does James have? 

The words “less than” are the keywords and they tell us to use subtraction .

Step 3: Make math symbols above keywords to decode the word problem

As I help students with word problems, I write math symbols and numbers above the keywords. This helps them to understand what the word problem is asking.

Let’s practice. Observe what I write over the keywords in the following word problem and think about how you would create a math sentence using them:

Step 4: Create a math sentence to represent the word problem

Using the previous example, let’s write a math sentence. Looking at the math symbols and numbers written above the word problem, our math sentence should be: 10 – 5 = 5 ! 

Each time you practice a word problem with your child, highlight keywords and write the math symbols above them. Then have your child create a math sentence to solve. 

Step 5: Draw a picture to help illustrate the word problem

Pictures can be very helpful for problems that are more difficult to understand. They also are extremely helpful when the word problem involves calculating time , comparing fractions , or measurements . 

Step 6: Always show your work

Help your child get into the habit of always showing their work. As a tutor, I’ve found many reasons why having students show their work is helpful:

• By showing their work, they are writing the math steps repeatedly, which aids in memory
• If they make any mistakes they can track where they happened
• Their teacher can assess how much they understand by reviewing their work
• They can participate in class discussions about their work

Step 7: When solving word problems, make sure there is always a word in your answer!

If the word problem asks: How many peaches did Lisa buy? Your child’s answer should be: Lisa bought 10 peaches .

If the word problem asks: How far did Kyle run? Your child’s answer should be: Kyle ran 20 miles .

So how do you solve a word problem in math?

Together we reviewed the eight simple steps to solve word problems. These steps included identifying keywords for word problems in math, drawing pictures, and learning to explain our answers. 

Is your child ready to put these new skills to the test? Check out the best math app for some fun math word problem practice.

Parents, sign up for a DoodleMath subscription and see your child become a math wizard!

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring elementary through college level math. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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The math problem that took nearly a century to solve: Secret to Ramsey numbers

Mathematicians unlock the secret to ramsey numbers.

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."

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?"

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).

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 .

"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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Story Source:

Materials provided by University of California - San Diego . Original written by Michelle Franklin. Note: Content may be edited for style and length.

Journal Reference :

• Sam Mattheus, Jacques Verstraete. The asymptotics of r(4,t) . Annals of Mathematics , 2024; 199 (2) DOI: 10.4007/annals.2024.199.2.8

Cite This Page :

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The Sunday Read: ‘What Deathbed Visions Teach Us About Living’

Researchers are documenting a phenomenon that seems to help the dying, as well as those they leave behind..

By Phoebe Zerwick

Read by Samantha Desz

Produced by Jack D’Isidoro and Aaron Esposito

Narration produced by Anna Diamond and Emma Kehlbeck

Original music by Aaron Esposito

Engineered by Sophia Lanman and Sharon Kearney

Listen and follow The Daily Apple Podcasts | Spotify

Chris Kerr was 12 when he first observed a deathbed vision. His memory of that summer in 1974 is blurred, but not the sense of mystery he felt at the bedside of his dying father. Throughout Kerr’s childhood in Toronto, his father, a surgeon, was too busy to spend much time with his son, except for an annual fishing trip they took, just the two of them, to the Canadian wilderness. Gaunt and weakened by cancer at 42, his father reached for the buttons on Kerr’s shirt, fiddled with them and said something about getting ready to catch the plane to their cabin in the woods. “I knew intuitively, I knew wherever he was, must be a good place because we were going fishing,” Kerr told me.

Kerr now calls what he witnessed an end-of-life vision. His father wasn’t delusional, he believes. His mind was taking him to a time and place where he and his son could be together, in the wilds of northern Canada.

Kerr followed his father into medicine, and in the last 10 years he has hired a permanent research team that expanded studies on deathbed visions to include interviews with patients receiving hospice care at home and with their families, deepening researchers’ understanding of the variety and profundity of these visions.

There are a lot of ways to listen to ‘The Daily.’ Here’s how.

We want to hear from you. Tune in, and tell us what you think. Email us at [email protected] . Follow Michael Barbaro on X: @mikiebarb . And if you’re interested in advertising with The Daily, write to us at [email protected] .

Additional production for The Sunday Read was contributed by Isabella Anderson, Anna Diamond, Sarah Diamond, Elena Hecht, Emma Kehlbeck, Tanya Pérez and Krish Seenivasan.

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