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## How to Solve Math Problems

Last Updated: May 16, 2023 Approved

## Understanding the Problem

- Draw a Venn diagram. A Venn diagram shows the relationships among the numbers in your problem. Venn diagrams can be especially helpful with word problems.
- Draw a graph or chart.
- Arrange the components of the problem on a line.
- Draw simple shapes to represent more complex features of the problem.

## Developing a Plan

## Solving the Problem

## Expert Q&A Did you know you can get expert answers for this article? Unlock expert answers by supporting wikiHow

Support wikiHow by unlocking this expert answer.

- Seek help from your teacher or a math tutor if you get stuck or if you have tried multiple strategies without success. Your teacher or a math tutor may be able to easily identify what is wrong and help you to understand how to correct it. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
- Keep practicing sums and diagrams. Go through the concept your class notes regularly. Write down your understanding of the methods and utilize it. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0

## You Might Also Like

- ↑ Daron Cam. Math Tutor. Expert Interview. 29 May 2020.
- ↑ http://www.interventioncentral.org/academic-interventions/math/math-problem-solving-combining-cognitive-metacognitive-strategies
- ↑ http://tutorial.math.lamar.edu/Extras/StudyMath/ProblemSolving.aspx
- ↑ https://math.berkeley.edu/~gmelvin/polya.pdf

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- \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.

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## Course: Algebra 1 > Unit 2

Number of solutions to equations.

- Worked example: number of solutions to equations
- Creating an equation with no solutions
- Creating an equation with infinitely many solutions

## Want to join the conversation?

## Video transcript

## Top 3 Tips on How to Solve Math Problems

## What is Math?

## Types of Math

There are two types of math. We discuss below:

## Some common reasons: Why is math so important?

- Learning mathematics is always good for the brain.
- Math helps individuals to tell time.
- It supports you with finance management.
- Math supports you to become a better cook.
- It is useful to improve problem-solving skills.
- Math uses in practical life in each career in some or another way.
- Math applications exist all around us that help each person understand the world in a better way.

## How to solve math problems: Different techniques for different type of problem

How to solve math problems related to common factors.

Common factors are the number(s) that divide the specific number exactly.

- Write down the numbers that include the problem question number in its table.
- You can check it from the table of 2 to 9 if it is included in these number tables; then it will definitely include in other number tables also.
- If you have two or more numbers, you check the common factor(s) or number(s) that divides each question number.

Calculate the common factor of 5 and 10.

- The factor of 5 is 1 and 5 (as 5 include in the table of 1 and 5 only).
- The factor of 10 is 1, 2, 5, and 10 (10 includes in the table of 1 (at 1×5=5), 2 (at 2 x5 = 10), 5 (at 5×2 = 10), and 10 (at 10×1 =10)).
- Now, find out the common factor of both numbers; that will give: 1 and 5.

## How to solve geometry math problems?

To solve the geometry math problems, you need to follow the following steps:

- Check all the facts about the given problem, like height, length, and diameter. If it is possible to draw a picture of the shape, then draw it that helps you understand the question more easily.
- Check the assigned problem, such as whether you need to calculate surface area, volume, and perimeter.
- Identify the formula that can be applied to the problem, like you can use the length * width formula to calculate the area of the rectangle.
- Put the value to the formula and solve it step by step.
- Finally, remember to check the solution’s SI unit (like cm). If you do not write the SI unit, then you may lose the marks.

Calculate the area of the rectangle of length 10 cm and width 5 cm.

- The formula for the area of rectangle = length x width.
- Put the value in the rectangle formula that is 10 x 5 = 50.

## How to solve trigonometric equations

- First of all, understand the trigonometric identities and reference angles.
- Grasp all necessary ratios that lie between the 0 degrees to 360 degrees of a graph.
- Proceed by using the substitution formula.
- Solve the math problems to get the answer in degrees or radiations.

## Solve sin(x) + 2 = 3 in interval 0° ≤ x < 360°.

## A real-life example: How to use mathematics to solve urban problems?

The basic math concepts that we use to solve the urban problems are:

- We have given the angle of elevation from the ground as 42 degrees.
- The tree is located in a vertical direction that is perpendicular to the ground level.
- Therefore, this problem will deal with the “ hypotenuse ” and “ opposite ” that results in sine function.

Hence, sin (42 degrees) = x/8 (feet)

Here we will give you some tricks and tips which can be very useful in solving the math problems.

## 1. Knowing the Problem

## Read it carefully

## Summarize the difficulty

## Outline the problem

## Study the examples

## 2. Outline the answers

Write the things you need to get the answer.

## Easier to harder

## Using a graphical calculator

- Make sure you can solve for y before you try to construct a graph.
- Consider all available shortcut menus and use as many calculator functions as you can.
- Type an expression exactly as it looks, and the calculator will do the work and simplify the expression.

## 3. The last step is problem-solving

There are three simple steps, which are followed for problem-solving. Steps are given below:

## Go with your plan

## Another method implement

## See the problem again

## FAQs Related With How to Solve Math Problems

There are two types of math. We discuss below: 1.Pure Mathematics 2.Applied Mathematics

## How to solve math problems?

## How do you solve math problems?

## What are the 7 hardest math problems?

## Why do I struggle with math so much?

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## How to Solve Math Problems Faster: 15 Techniques to Show Students

Here are 15 techniques to show students, helping them solve math problems faster:

## Addition and Subtraction

The first step is to add what’s easy. The second step is to add the rest.

With this fast technique, big numbers won’t look as scary now.

## 2. Two-Step Subtraction

There’s a similar method for subtraction.

Remove what’s easy. Then remove what’s left.

Instead of two complex numbers, students will only have to tackle one.

## 3. Subtracting from 1,000

You can give students confidence to handle four-digit integers with this fast technique.

Let’s say students must solve 1,000 – 438. Here are the steps:

This also applies to 10,000, 100,000 and other integers that follow this pattern.

## Multiplication and Division

Using 33 x 48 as an example, here’s the process:

The only prerequisite is understanding the 2 times table.

## 5. Multiplying by Powers of 2

This tactic is a speedy variation of doubling and halving.

Here’s what to do: For each power of 2 that makes up that number, double the other number.

## 6. Multiplying by 9

But there’s an easy tactic to solve this issue, and it has two parts.

Despite more steps, altering the equation this way is usually faster.

## 7. Multiplying by 11

There’s an easier way for multiplying two-digit integers by 11.

Let’s say students must find the product of 11 x 34.

It’s multiplication without having to multiply.

## 8. Multiplying Even Numbers by 5

This technique only requires basic division skills.

The result is 30, which is the correct answer.

It’s an ideal, easy technique for students mastering the 5 times table.

## 9. Multiplying Odd Numbers by 5

This is another time-saving tactic that works well when teaching students the 5 times table.

This one has three steps, which 5 x 7 exemplifies.

## 10. Squaring a Two-Digit Number that Ends with 1

Squaring a high two-digit number can be tedious, but there’s a shortcut if 1 is the second digit.

There are four steps to this shortcut, which 812 exemplifies:

- Subtract 1 from the integer: 81 – 1 = 80
- Square the integer, which is now an easier number: 80 x 80 = 6,400
- Add the integer with the resulting square twice: 6,400 + 80 + 80 = 6,560
- Add 1: 6,560 + 1 = 6,561

## 11. Squaring a Two-Digit Numbers that Ends with 5

Squaring numbers ending in 5 is easier, as there are only two parts of the process.

First, students will always make 25 the product’s last digits.

Just like that, a hard problem becomes easy multiplication for many students.

## 12. Calculating Percentages

The result is 113.75, which is indeed the correct answer.

This shortcut is a useful timesaver on tests and quizzes.

## 13. Balancing Averages

With practice, this method may not even require pencil and paper. That’s how easy it is.

## Word Problems

This isn’t a trick. It’s a tactic.

Teach students to look for these buzzwords, and what skill they align with in most contexts:

As a result, they should have an easier time processing word problems .

## 15. Creating Sub-Questions

Each student should ask him or herself:

- What am I looking for? — Students should read the question over and over, looking for buzzwords and identifying important details.
- What information do I need? — Students should determine which facts, figures and variables they need to solve the question. For example, if they determine the question is rooted in subtraction, they need the minuend and subtrahend.
- What information do I have? — Students should be able to create the core equation using the information in the word problem, after determining which details are important.

These sub-questions help students avoid overload.

## Final Thoughts About these Ways to Solve Math Problems Faster

Showing these 15 techniques to students can give them the confidence to tackle tough questions .

A rewarding class equals an engaging class . That’s an easy equation to remember.

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Simplified Equation: 17 - x = 8

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

## Pre-Algebra Solutions

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- 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.

## 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
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## Physics Solutions

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

## Geometry Graphing Solutions

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

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Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app. ... Try Math Solver. Type a math problem. Type a math problem. Solve. Quadratic equation { x } ^ { 2 } - 4 x - 5 = 0. Trigonometry. 4 \sin \theta \cos \theta = 2 \sin \theta. Linear equation. y = 3x + 4 ...

Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app. ... Type a math problem. Type a math problem. Solve. Get step-by-step explanations. See how to solve problems and show your work—plus get definitions for mathematical concepts ...

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 ...

Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app. ... Type a math problem. Type a math problem. Solve. Examples. Quadratic equation { x } ^ { 2 } - 4 x - 5 = 0. Trigonometry. 4 \sin \theta \cos \theta = 2 \sin \theta ...

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To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem.

Draw a graph or chart. Arrange the components of the problem on a line. Draw simple shapes to represent more complex features of the problem. 5. Look for patterns. Sometimes you can identify a pattern or patterns in a math problem simply by reading the problem carefully.

You can solve multiplication and division during the same step in the math problem: after solving for parentheses, exponents and radicals and before adding and subtracting. Proceed from left to right for multiplication and division. Solve addition and subtraction last after parentheses, exponents, roots and multiplying/dividing.

Algebra. Equation Solver. Step 1: Enter the Equation you want to solve into the editor. The equation calculator allows you to take a simple or complex equation and solve by best method possible. Step 2: Click the blue arrow to submit and see the result!

3. Operations with Integers: Add, Subtract, Multiply & Divide. Learn about mathematical operations with integers using the operations of addition, subtraction, multiplication, and division ...

To solve your equation using the Equation Solver, type in your equation like x+4=5. The solver will then show you the steps to help you learn how to solve it on your own. Solving Equations Video Lessons

Solving algebraic word problems requires us to combine our ability to create equations and solve them. To solve an algebraic word problem: Define a variable. Write an equation using the variable. Solve the equation. If the variable is not the answer to the word problem, use the variable to calculate the answer.

Free math problem solver with steps from GeoGebra: solve equations, algebra, trigonometry, calculus, and get step-by-step answers to your homework questions!

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. Show more; word-problems-calculator. en

For a system of two linear equations and two variables, there can be no solution, exactly one solution, or infinitely many solutions (just like for one linear equation in one variable). 1) lf the ratio of the coefficients on the x's is unequal to the ratio of the coefficients on the y's (in the same order), then there is exactly one solution.

Four steps help you solve any math problems quickly: Read the problem carefully, understand it, and recognize the type of problem. Try to draw and review the math problem. Create a plan to solve it. Use the relevant formulas to solve the problem.

Square the integer, which is now an easier number: 80 x 80 = 6,400. Add the integer with the resulting square twice: 6,400 + 80 + 80 = 6,560. Add 1: 6,560 + 1 = 6,561. This work-around eliminates the difficulty surrounding the second digit, allowing students to work with multiples of 10.

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.

I'm too dumb for this😭😭 Here's a sample problem: A survey was conducted among 200 citizens to determine their preferences for two animals, cats and dogs. 100 liked cats and 35 disliked them. Meanwhile, 70 liked dogs and 60 hated them.