## Math Solver

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Starting at $5 .00 /month ## Step-by-Step Solutions Features Not just answers—step-by-step solutions buttons expand answers and explain how that answer was found. ## Show Intermediate Steps Break steps down even further with intermediate steps. These optional additional explanations for individual pieces of step-by-step solutions help guide you. ## Choose a Method Explore different ways of finding a solution. Use your classroom's teaching method to guide you through the answer. Your own tutor—hints are also frequently provided to not just provide answers, but also to guide you towards finding the solution yourself. ## Examples of Step-by-Step Solutions Explore some of the content areas covered by step-by-step solutions, including math, chemistry and physics, or view more examples » ## Equation Solving ## More Math Topics ## Algebra Calculator What do you want to calculate. • Solve for Variable • Practice Mode • Step-By-Step 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) Algebra Calculator is a calculator that gives step-by-step help on algebra problems. See More Examples » Disclaimer: This calculator is not perfect. Please use at your own risk, and please alert us if something isn't working. Thank you. ## How to Use the Calculator Type your algebra problem into the text box. For example, enter 3x+2=14 into the text box to get a step-by-step explanation of how to solve 3x+2=14. ## More Examples Calculator Examples » ## Math Symbols If you would like to create your own math expressions, here are some symbols that the calculator understands: Calculator Tutorial » Get the MathPapa mobile app! It works offline! ## Feedback (For students 13+) Please use this feedback form to send your feedback. Thanks! Need more practice problems? Try MathPapa Math Practice More Examples » Back to Algebra Calculator » ## Share this page ## How to Solve Algebra Problems Step-By-Step • Pre Algebra & Algebra • Math Tutorials • Exponential Decay • Worksheets By Grade • B.B.A., Finance and Economics, University of Oklahoma Solving Algebra word problems is useful in helping you to solve earthly problems. While the 5 steps of Algebra problem solving are listed below, the following will help you learn how to first identify the problem. • Identify the problem. • Identify what you know. • Make a plan. • Carry out the plan. • Verify that the answer makes sense. ## Identify the Problem Back away from the calculator ; use your brain first. Your mind analyzes, plans, and guides in the labyrinthine quest for the solution. Think of the calculator as merely a tool that makes the journey easier. After all, you wouldn’t want a surgeon to crack your ribs and perform a heart transplant without first identifying the source of your chest pains. The steps of identifying the problem are: • Express the problem question or statement. • Identify the unit of the final answer. ## Express the Problem Question or Statement In Algebra word problems, the problem is expressed as either a question or a statement. • How many trees will John have to plant? • How many televisions will Sara have to sell to earn$50,000?
• Find the number of trees John will have to plant.
• Solve for the number of televisions Sara will have to sell to earn $50,000. ## Identify the Unit of the Final Answer What will the answer look like? Now that you understand the word problem’s purpose, determine the answer’s unit. For example, will the answer be in miles, feet, ounces, pesos, dollars, the number of trees, or a number of televisions? ## Algebra Word Problem Javier is making brownies to serve at the family picnic. If the recipe calls for 2 ½ cups of cocoa to serve 4 people, how many cups will he need if 60 people attend the picnic? • Identify the problem: How many cups will Javier need if 60 people attend the picnic? • Identify the unit of the final answer: Cups In the market for computer batteries, the intersection of the supply and demand functions determines the price, p dollars , and the quantity, q , of goods sold. Supply function: 80 q - p = 0 Demand function: 4 q + p = 300 Determine the price and quantity of computer batteries sold when these functions intersect. • Identify the problem: How much will the batteries cost and how much will be sold when supply and demand functions meet? • Identify the unit of the final answer: The quantity, or q , will be given in batteries. The price, or p , will be given in dollars. • Proportions Word Problems Worksheet 1 • Proportions Word Problems Worksheet: Answers and Explanations • How to Do Algebra Word Problems • How to Solve Proportions to Adjust a Recipe • Algebra Age-Related Word Problem Worksheets • Lesson Plan: Addition and Subtraction with Pictures • The Quantity Theory of Money • Stoichiometry Definition in Chemistry • 2nd Grade Math Word Problems • Math Glossary: Mathematics Terms and Definitions • Ideas for Thanksgiving Math Word Problems • Sixth Grade Word Problems • Quiz 8th-Graders With These Math Word Problems • Learn to Calculate Percent Change • How to Cancel Units - Chemistry Metric Conversions • Simple Interest Worksheets With Answers ## Math Calculator Enter the expression you want to evaluate. Please ensure that your password is at least 8 characters and contains each of the following: • a special character: @$#!%*?&

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## Solving equations

Here you will learn about solving equations, including linear and quadratic algebraic equations, and how to solve them.

Students will first learn about solving equations in grade 8 as a part of expressions and equations, and again in high school as a part of reasoning with equations and inequalities.

## What is solving an equation?

Solving equations is a step-by-step process to find the value of the variable. A variable is the unknown part of an equation, either on the left or right side of the equals sign. Sometimes, you need to solve multi-step equations which contain algebraic expressions.

To do this, you must use the order of operations, which is a systematic approach to equation solving. When you use the order of operations, you first solve any part of an equation located within parentheses. An equation is a mathematical expression that contains an equals sign.

For example,

\begin{aligned}y+6&=11\\\\ 3(x-3)&=12\\\\ \cfrac{2x+2}{4}&=\cfrac{x-3}{3}\\\\ 2x^{2}+3&x-2=0\end{aligned}

There are two sides to an equation, with the left side being equal to the right side. Equations will often involve algebra and contain unknowns, or variables, which you often represent with letters such as x or y.

You can solve simple equations and more complicated equations to work out the value of these unknowns. They could involve fractions, decimals or integers.

## Common Core State Standards

How does this relate to 8 th grade and high school math?

• Grade 8 – Expressions and Equations (8.EE.C.7) Solve linear equations in one variable.
• High school – Reasoning with Equations and Inequalities (HSA.REI.B.3) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

## [FREE] Math Equations Check for Understanding Quiz (Grade 6 to 8)

Use this quiz to check your grade 6 to 8 students’ understanding of math equations. 10+ questions with answers covering a range of 6th, 7th and 8th grade math equations topics to identify areas of strength and support!

## How to solve equations

In order to solve equations, you need to work out the value of the unknown variable by adding, subtracting, multiplying or dividing both sides of the equation by the same value.

• Combine like terms .
• Simplify the equation by using the opposite operation to both sides.
• Isolate the variable on one side of the equation.

## Solving equations examples

Example 1: solve equations involving like terms.

Solve for x.

Combine like terms.

Combine the q terms on the left side of the equation. To do this, subtract 4q from both sides.

The goal is to simplify the equation by combining like terms. Subtracting 4q from both sides helps achieve this.

After you combine like terms, you are left with q=9-4q.

2 Simplify the equation by using the opposite operation on both sides.

Add 4q to both sides to isolate q to one side of the equation.

The objective is to have all the q terms on one side. Adding 4q to both sides accomplishes this.

After you move the variable to one side of the equation, you are left with 5q=9.

3 Isolate the variable on one side of the equation.

Divide both sides of the equation by 5 to solve for q.

Dividing by 5 allows you to isolate q to one side of the equation in order to find the solution. After dividing both sides of the equation by 5, you are left with q=1 \cfrac{4}{5} \, .

## Example 2: solve equations with variables on both sides

Combine the v terms on the same side of the equation. To do this, add 8v to both sides.

7v+8v=8-8v+8v

After combining like terms, you are left with the equation 15v=8.

Simplify the equation by using the opposite operation on both sides and isolate the variable to one side.

Divide both sides of the equation by 15 to solve for v. This step will isolate v to one side of the equation and allow you to solve.

15v \div 15=8 \div 15

The final solution to the equation 7v=8-8v is \cfrac{8}{15} \, .

## Example 3: solve equations with the distributive property

Combine like terms by using the distributive property.

The 3 outside the parentheses needs to be multiplied by both terms inside the parentheses. This is called the distributive property.

\begin{aligned}& 3 \times c=3 c \\\\ & 3 \times(-5)=-15 \\\\ &3 c-15-4=2\end{aligned}

Once the 3 is distributed on the left side, rewrite the equation and combine like terms. In this case, the like terms are the constants on the left, –15 and –4. Subtract –4 from –15 to get –19.

Simplify the equation by using the opposite operation on both sides.

The goal is to isolate the variable, c, on one side of the equation. By adding 19 to both sides, you move the constant term to the other side.

\begin{aligned}& 3 c-19+19=2+19 \\\\ & 3 c=21\end{aligned}

Isolate the variable to one side of the equation.

To solve for c, you want to get c by itself.

Dividing both sides by 3 accomplishes this.

On the left side, \cfrac{3c}{3} simplifies to c, and on the right, \cfrac{21}{3} simplifies to 7.

The final solution is c=7.

As an additional step, you can plug 7 back into the original equation to check your work.

## Example 4: solve linear equations

Combine like terms by simplifying.

Using steps to solve, you know that the goal is to isolate x to one side of the equation. In order to do this, you must begin by subtracting from both sides of the equation.

\begin{aligned} & 2x+5=15 \\\\ & 2x+5-5=15-5 \\\\ & 2x=10 \end{aligned}

Continue to simplify the equation by using the opposite operation on both sides.

Continuing with steps to solve, you must divide both sides of the equation by 2 to isolate x to one side.

\begin{aligned} & 2x \div 2=10 \div 2 \\\\ & x= 5 \end{aligned}

Isolate the variable to one side of the equation and check your work.

Plugging in 5 for x in the original equation and making sure both sides are equal is an easy way to check your work. If the equation is not equal, you must check your steps.

\begin{aligned}& 2(5)+5=15 \\\\ & 10+5=15 \\\\ & 15=15\end{aligned}

## Example 5: solve equations by factoring

Solve the following equation by factoring.

Combine like terms by factoring the equation by grouping.

Multiply the coefficient of the quadratic term by the constant term.

2 x (-20) = -40

Look for two numbers that multiply to give you –40 and add up to the coefficient of 3. In this case, the numbers are 8 and –5 because 8 x -5=–40, and 8+–5=3.

Split the middle term using those two numbers, 8 and –5. Rewrite the middle term using the numbers 8 and –5.

2x^2+8x-5x-20=0

Group the terms in pairs and factor out the common factors.

2x^2+8x-5x-20=2x(x + 4)-5(x+4)=0

Now, you’ve factored the equation and are left with the following simpler equations 2x-5 and x+4.

This step relies on understanding the zero product property, which states that if two numbers multiply to give zero, then at least one of those numbers must equal zero.

Let’s relate this back to the factored equation (2x-5)(x+4)=0

Because of this property, either (2x-5)=0 or (x+4)=0

Isolate the variable for each equation and solve.

When solving these simpler equations, remember that you must apply each step to both sides of the equation to maintain balance.

\begin{aligned}& 2 x-5=0 \\\\ & 2 x-5+5=0+5 \\\\ & 2 x=5 \\\\ & 2 x \div 2=5 \div 2 \\\\ & x=\cfrac{5}{2} \end{aligned}

\begin{aligned}& x+4=0 \\\\ & x+4-4=0-4 \\\\ & x=-4\end{aligned}

The solution to this equation is x=\cfrac{5}{2} and x=-4.

## Example 6: solve quadratic equations

Combine like terms by factoring the quadratic equation when terms are isolated to one side.

To factorize a quadratic expression like this, you need to find two numbers that multiply to give -5 (the constant term) and add to give +2 (the coefficient of the x term).

The two numbers that satisfy this are -1 and +5.

So you can split the middle term 2x into -1x+5x: x^2-1x+5x-5-1x+5x

Now you can take out common factors x(x-1)+5(x-1).

And since you have a common factor of (x-1), you can simplify to (x+5)(x-1).

The numbers -1 and 5 allow you to split the middle term into two terms that give you common factors, allowing you to simplify into the form (x+5)(x-1).

Let’s relate this back to the factored equation (x+5)(x-1)=0.

Because of this property, either (x+5)=0 or (x-1)=0.

Now, you can solve the simple equations resulting from the zero product property.

\begin{aligned}& x+5=0 \\\\ & x+5-5=0-5 \\\\ & x=-5 \\\\\\ & x-1=0 \\\\ & x-1+1=0+1 \\\\ & x=1\end{aligned}

The solutions to this quadratic equation are x=1 and x=-5.

## Teaching tips for solving equations

• Use physical manipulatives like balance scales as a visual aid. Show how you need to keep both sides of the equation balanced, like a scale. Add or subtract the same thing from both sides to keep it balanced when solving. Use this method to practice various types of equations.
• Emphasize the importance of undoing steps to isolate the variable. If you are solving for x and 3 is added to x, subtracting 3 undoes that step and isolates the variable x.
• Relate equations to real-world, relevant examples for students. For example, word problems about tickets for sports games, cell phone plans, pizza parties, etc. can make the concepts click better.
• Allow time for peer teaching and collaborative problem solving. Having students explain concepts to each other, work through examples on whiteboards, etc. reinforces the process and allows peers to ask clarifying questions. This type of scaffolding would be beneficial for all students, especially English-Language Learners. Provide supervision and feedback during the peer interactions.

## Easy mistakes to make

• Forgetting to distribute or combine like terms One common mistake is neglecting to distribute a number across parentheses or combine like terms before isolating the variable. This error can lead to an incorrect simplified form of the equation.
• Misapplying the distributive property Incorrectly distributing a number across terms inside parentheses can result in errors. Students may forget to multiply each term within the parentheses by the distributing number, leading to an inaccurate equation.
• Failing to perform the same operation on both sides It’s crucial to perform the same operation on both sides of the equation to maintain balance. Forgetting this can result in an imbalanced equation and incorrect solutions.
• Making calculation errors Simple arithmetic mistakes, such as addition, subtraction, multiplication, or division errors, can occur during the solution process. Checking calculations is essential to avoid errors that may propagate through the steps.
• Ignoring fractions or misapplying operations When fractions are involved, students may forget to multiply or divide by the common denominator to eliminate them. Misapplying operations on fractions can lead to incorrect solutions or complications in the final answer.

## Related math equations lessons

• Math equations
• Rearranging equations
• How to find the equation of a line
• Solve equations with fractions
• Linear equations
• Writing linear equations
• Substitution
• Identity math
• One step equation

## Practice solving equations questions

1. Solve 4x-2=14.

Divide both sides by 4.

2. Solve 3x-8=x+6.

Subtract x from both sides.

Divide both sides by 2.

3. Solve 3(x+3)=2(x-2).

Expanding the parentheses.

Subtract 9 from both sides.

Subtract 2x from both sides.

4. Solve \cfrac{2 x+2}{3}=\cfrac{x-3}{2}.

Multiply by 6 (the lowest common denominator) and simplify.

Expand the parentheses.

Subtract 4 from both sides.

Subtract 3x from both sides.

5. Solve \cfrac{3 x^{2}}{2}=24.

Multiply both sides by 2.

Divide both sides by 3.

Square root both sides.

6. Solve by factoring:

Use factoring to find simpler equations.

Set each set of parentheses equal to zero and solve.

x=3 or x=10

## Solving equations FAQs

The first step in solving a simple linear equation is to simplify both sides by combining like terms. This involves adding or subtracting terms to isolate the variable on one side of the equation.

Performing the same operation on both sides of the equation maintains the equality. This ensures that any change made to one side is also made to the other, keeping the equation balanced and preserving the solutions.

To handle variables on both sides of the equation, start by combining like terms on each side. Then, move all terms involving the variable to one side by adding or subtracting, and simplify to isolate the variable. Finally, perform any necessary operations to solve for the variable.

To deal with fractions in an equation, aim to eliminate them by multiplying both sides of the equation by the least common denominator. This helps simplify the equation and make it easier to isolate the variable. Afterward, proceed with the regular steps of solving the equation.

## The next lessons are

• Inequalities
• Types of graph
• Coordinate plane

## Still stuck?

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Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.

## [FREE] Common Core Practice Tests (Grades 3 to 6)

Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.

40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!

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## How to Ace Math Problem Solving

When your kids struggle with their math, it’s time to take a step back and take a deep breath. They need to slow down and take their time. Here’s a step by step guide that will help your kids get through those tough math problems.

We’ll use a grade 3 addition word problem as an example to clarify:

Pinky the Pig bought 36 apples while Danny the Duck bought 73 apples and 14 bananas. How many apples do they have altogether?

Carefully read through the problem to make sure you understand what is being asked.

Pinky the pig and Danny the duck bought apples and bananas. The question is how many apples they have together.

Read through the problem again and as you read through it, make notes.

Pinky the pig –36 apples. Danny the duck –73 apples and 14 bananas. How many apples together?

## What is the problem asking

In your own words, say or write down exactly what the question is asking you to solve.

The question is asking how many apples the pig and the duck bought together.

## Write it down in detail

Go through the problem and write out the information in an organized fashion. A diagram or table might help.

## Turn it into math

Figure out what math operation(s) or formula(s) you need to use in order to solve this problem.

The problem wants us to add the number of apples Pinky the Pig and Danny the Duck have together. That means we need to make use of addition to add the apples.

## Find an example

Are you still struggling? Sometimes it’s hard to work out the solution, especially if the math problem involves several steps. It’s time to present the problem in an easier way. As teachers and parents we can often help our kids simplify the problem from our own math knowledge. If the problem is a bit harder, there are lots of resources online that you can look up for similar problems that have been worked out on paper or a video tutorial to watch.

In our example, let’s say the double-digit numbers are intimidating our student, so we’re going to simplify the equation for the sake of helping our student understand the operation needed.

Let’s say Pinky the Pig bought 3 apples and Danny the Duck 7 apples and 1 banana. Now, how many apples have they bought together? With 3 apples and 7 apples bought, the total number of apples is 10.

## Work out the problem

Now that we have got to the bottom of what is being asked and know what operation to use, it’s time to work out the problem.

Pinky the Pig bought 36 apples. Danny the Duck bought 73 apples. (The 14 bananas do not matter) We need to add up the apples. 36 + 73 = 109

Let’s round the numbers: 30 + 70 = 100. That is close to the exact number so it’s in the correct range.

The beauty of the basic operations is that addition and subtraction can be used to check answers too.

If we use the sum and take away one of the numbers, it should equal the other number.

109 – 73 = 36 109 – 36 = 73

If our student did not work out the sum correctly, we would not come to these sums.

(By the way, the same can be done with multiplication and division.)

Finally, go back and review the problem one last time. By going over the concepts, operations and formulas, it will help your kids to internalize the process and help them tackle harder math problems in the future.

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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. ## Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class. Email Address Sign Up ## Game Central • Solve equations and inequalities • Simplify expressions • Factor polynomials • Graph equations and inequalities • Advanced solvers • All solvers • Arithmetics • Determinant • Percentages • Scientific Notation • Inequalities ## Welcome to QuickMath main tutorials page. This is work in progress, so please keep checking. Linear equations are the easiest ones to solve. Don't try any other equations before you master these with our tutorials and interactive linear equation solvers. Graphing functions is very similar graphing equations. Here you will learn proper functional notation as well as graphing functions that are more complex that the ones found in Graphing equations tutorials. Are absolute values absolutely incomprehensible? Take a quick look at our step-by-step tutorials with interactive absolute value problem solvers. Math roots worse than root canals? Not with our tutorials and interactive solvers. You will learn how to add, subtract multiply and divide roots as well as rationalize denominators. Are you unsure about exponent rules, polynomial operations and similar topics? These tutorials will teach you the basic rules and operations, and our polynomial solvers will generate infintely many step-by-step solutions to a variety of problems Quadratic equations are a little bit trickier than linear ones. If you are unsure about linear equations go over linear equations tutorials first. If you think you can handle them, use our quadratic equations tutorials and interactive solvers to learn about quadratic formula and other ways of solving second order equations. Are complex numbers too complex to learn? No, they are not if you use our complex number solvers and interactive tutorials. You will learn about why we need them, what an imaginary unit is, and a lot of other interesting things. Have problems with factoring? Which rule to apply when? Take a look at these handy interactive tutorials on different factoring methods. Are fractions giving you a headache? Learn how to reduce fractions and simplify a variety of rational expressions using our tutorials that include interactive fraction solvers. Need a bit of a brush up on arithmetics? Review the basics of arithmetics calculations and learn about representation of integers and real numbers using our interactive solvers. Graphing equations with our interactive graphers is easy! Not only do they let you graph equations, but with our tutorials you also learn about characteristic shapes and points of of common equations. Is exponential function exponentially harder to learn than other functions? Not so with our interactive solvers, graphers and tutorials! If you already know how to graph equations, inequalities are easy-peasy. Lots of shading involved! Use our interactive graphers and tutorials to learn this important topic This set of tutorials will explain how to solve and graph a system of two linear equations in a variety of ways There is nothing very radical about radical equations! That is, if you know what a radical is. If not, go through our Roots and Radicals tutorial first. Then come back and use our interactive radical equations solvers and tutorials to learn how to solve this type of equations. This set of tutorials explains how to simplify a variety of expressions, such as fractions and radicals. Good news: Solving linear inequalities inequalities is very similar to solving linear equations. Bad news: there is this pesky little inequality sign (< or >) that can change directions based on what you do with your inequality. Read our tutorials and use the absolute value solver to learn more. ## Math Topics More solvers. • Add Fractions • Simplify Fractions Advertisement ## How to Do Long Division: Step-by-Step Instructions • Share Content on Facebook • Share Content on LinkedIn • Share Content on Flipboard • Share Content on Reddit • Share Content via Email In math, few skills are as practical as knowing how to do long division . It's the art of breaking down complex problems into manageable steps, making it an essential tool for students and adults alike. This operation has many practical uses in our daily lives. For instance, imagine you have a bag of 2,436 candies and want to share them equally among 4 friends. Long division helps you determine that each friend gets 609 candies, ensuring everyone gets their fair share. Let's dive into the fundamentals of long division and learn about other everyday situations where we can put it to use. ## What Is Long Division? How to do long division in simple steps, long division method: an apple example, using long division in everyday life, how to divide a decimal point by a whole number, practice problems and answers. Long division is a handy way to divide big numbers by smaller ones, helping us figure out how many times one number fits into another. It turns a tricky math problem into easier steps. When we do long division, we work with four main parts: • the big number we want to divide (called the " dividend ") • the smaller number we're dividing by (the " divisor ") • the answer to our division (the " quotient ") • sometimes a little bit left over (the " remainder ") ## Long Division vs. Short Division Short and long division are both methods to divide numbers, but they differ in complexity. The short-division method is a quick way to find the answer when dividing simple numbers. For example, say you want to divide 36 by 6. You write it as 36 ÷ 6, using a division sign, and quickly get the answer, which is 6. Long division is used for bigger, more complicated numbers, typically two or more digits. This method involves several steps, like writing out the numbers neatly and carefully. Let's dive into long division with a clear example. We'll use 845 ÷ 3 to walk through this step-by-step process: • Set up the problem. Write the dividend (845) under the division bar and the divisor (3) outside the bar. • Divide. Look at the first digit of the dividend (8). How many times does 3 go into 8? Twice, because 3 x 2 = 6, and that's the closest we can get without going over. Write the 2 above the division bar, over the 8. • Multiply. Multiply the quotient (2) by the divisor (3). (2 x 3 = 6). Write 6 under the 8. • Subtract. Subtract 6 from 8 to get 2. Draw a line under the 6, subtract, and write 2 below the line. • Bring down the next digit. Now, bring down the next digit of the dividend, which is 4, to sit next to the 2, making 24. • Repeat the steps. 3 goes into 24 eight times (3 x 8 = 24), so write 8 above the bar next to the 2. Subtract 24 from 24 to get 0. Now, follow the same process you used in steps 1 through 5 and bring down the last digit, which is 5, to form 05. The number 3 goes into 5 once (3 x 1 = 3), leaving a remainder of 2. Write the 1 above the bar and the remainder 2 below after subtracting 3 from 5. • The final answer with a remainder. You've divided 845 by 3 to get a final answer of 281 with a remainder of 2. • Convert the remainder to decimal form. Depending on how far along you are in learning long division, this may be your final answer. If you've progressed to decimals, you will add .0 to 845 and put a decimal point above the division bar, right after the 1. Bring 0 down to form 20. The number 3 goes into 20 six times (3 x 6 = 18). Write 6 after the decimal point above the division bar. Normally, you would continue adding another 0 after 845. until there is no remainder, but since 20 – 18 = 2, you would be repeating this process infinitely because 3 does not divide evenly into 845. Instead, you will draw a horizontal line over the 6 in 281.6 to indicate that it is a repeating decimal. A calculator would show the answer as 281.666667 to indicate that the repeating decimal rounds up. Now let's use a practical example to work through the long division process. Imagine you just went apple picking and came home with a massive haul of delicious fruit. In your kitchen, you have 456 apples, and you want to share them equally among 3 baskets to give to your friends, so you're dividing 3 by 456 (456 ÷ 3). To figure out how many apples go into each basket, you'd tackle the division problem step by step. • 3 goes into the first digit (4) once, so you write 1 above the division bar, above the 4 in 456. Then you show the subtraction: 4 – 3 = 1. • Bring down the next digit (5) to form 15. 3 goes into 15 five times (3 x 5 = 15), so you write 5 above the division bar, above the 5 in 456. Then you show the subtraction: 15 – 15 = 0. • Bring down the final digit (6) to form 06. 3 goes into 6 twice (3 x 2 = 6), so you write 2 above the division bar, above the 2 in 456. Then you show the subtraction: 6 – 6 = 0. • Since there is no remainder left to divide, you quotient is now written atop the division bar: 152. You will need to place 152 apples in each of the 3 baskets to evenly distribute the 456 apples. Long division also pops up in real-life situations . Think about when you need to divide something, like pizza or cake, into equal parts. Want to cut a large recipe in half or figure out how many days are left till summer vacation? Long division can help with that. It's a great way to help us figure out those splits and manage resources better. And, of course, practicing long division sharpens our problem-solving skills . It teaches us to tackle big problems step by step, breaking them down into smaller, more manageable pieces. This approach is super helpful in math and figuring out all sorts of challenges we might face. So, long division is more than just a bunch of steps we follow. It's a key that unlocks a lot of doors in the world of math and beyond, helping us understand and connect different concepts and apply them in all sorts of ways. Dividing decimals by whole numbers is useful in our everyday lives. For instance, if you're splitting a sum of money equally among a certain number of people, you'll need to divide the total (a decimal) by the number of people (a whole number) to determine how much each person gets. Dividing a decimal point (decimal number) by a whole number is similar to regular division, but you must be mindful of the placement of the decimal point. Here's how to do it: Example : Divide 0.5 by 5. • Set up the problem. Begin by setting up the division, with 0.5 as the dividend (the number you're dividing, which will be under the division bar) and 5 as the divisor (the number you're dividing by, which will be to the left of the division bar). • Begin dividing. 5 goes into the first digit of the dividend 0 times, so you'll write 0 above the division bar, above the 0 in 0.5, and place a decimal point after the 0 you just wrote. It should be directly above the decimal point in the dividend. • Bring down the next digit. Bring down the 5 to form 05 (you do not bring the decimal down). 5 goes into 5 once (5 x 1 = 5), so you'll write 1 above the division bar, above the 5 in 0.5. • Show the final answer. When you show the subtraction (5 – 5 = 0), you'll have no remainder. This means the number above the division bar is your final answer: 0.1. Let's put our long division skills to the test with some word problems. Tackle these problems one step at a time, and don't rush. If you get stuck, pause and review the steps. Remember, practice makes perfect, and every problem is an opportunity to improve your long-division skills. ## 1. Emma has 672 pieces of candy to share equally among her 4 friends. How many pieces of candy does each friend get? Solution : To find out, divide 672 by 4. Start with the first part of 672, which is 6, and see how many times 4 can fit into it. It fits 1 time, leaving us with 2. Bringing down the 7 turns it into 27, which 4 fits into 6 times, leaving us with 3. Finally, bringing down the 2 to join the remaining 3 makes 32, which 4 divides into 8 times. So, each friend gets 168 pieces of candy. ## 2. A teacher has 945 stickers to distribute equally in 5 of her classes. How many stickers does each class get? Solution : We'll divide 945 by 5. Looking at 9 first, 5 goes into it 1 time. With 4 leftover, we bring down the 4 from 945 to get 44, which 5 divides into 8 times with another 4 leftover. Lastly, bringing down the 5 to the remaining 4 makes 45, which 5 divides into 9 times. Therefore, each class receives 189 stickers. ## Solver Title ## Generating PDF... • 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. 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Conic Sections Transformation • Linear Algebra Matrices Vectors • Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify • Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution • Physics Mechanics • Chemistry Chemical Reactions Chemical Properties • Finance Simple Interest Compound Interest Present Value Future Value • Economics Point of Diminishing Return • Conversions Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time • Pre Algebra • One-Step Addition • One-Step Subtraction • One-Step Multiplication • One-Step Division • One-Step Decimals • Two-Step Integers • Two-Step Add/Subtract • Two-Step Multiply/Divide • Two-Step Fractions • Two-Step Decimals • Multi-Step Integers • Multi-Step with Parentheses • Multi-Step Rational • Multi-Step Fractions • Multi-Step Decimals • Solve by Factoring • Completing the Square • Quadratic Formula • Biquadratic • Logarithmic • Exponential • Rational Roots • Floor/Ceiling • Equation Given Roots • Newton Raphson • Substitution • Elimination • Cramer's Rule • Gaussian Elimination • System of Inequalities • Perfect Squares • Difference of Squares • Difference of Cubes • Sum of Cubes • Polynomials • Distributive Property • FOIL method • Perfect Cubes • Binomial Expansion • 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? • An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age. word-problems-calculator • Middle School Math Solutions – Simultaneous Equations Calculator Solving simultaneous equations is one small algebra step further on from simple equations. Symbolab math solutions... Read More Please add a message. Message received. Thanks for the feedback. We explain and teach technology, solve tech problems and help you make gadget buying decisions. ## How to View Multiple Worksheets Side-by-Side in Excel Having multiple workbooks or worksheets open side-by-side can eliminate the need to switch between different tabs or windows, making it more convenient to work on multiple tasks at once. Note that the process is a lot easier if you have multiple display screens or monitors tethered to your PC. However, you don’t need to get a dual-screen setup if you want to do a side-by-side comparison. Using the View tab on the Microsoft Excel Ribbon, you can view multiple worksheets on one screen at a go. Here’s how to do so: ## How to View Two Worksheets in the Same Excel Workbook Side-by-Side Here’s how to view two worksheets in the same workbook side-by-side without switching between sheet tabs: Step 1: From your PC’s Start menu or Taskbar, click the Microsoft Excel app or workbook to open it. Step 2: On the Excel Ribbon, click the View tab. Step 3: In the Window group of the View tab, click New Window. This will create a duplicate of your open workbook. Step 4: Click the View tab again and within the Window group, click View Side by Side. This will place both workbooks side by side. Step 5: In each workbook window, click the sheet that you want to compare. ## How to View Two Worksheets in Different Excel Workbooks Side-by-Side Here are the steps you should take to place worksheets from different workbooks side-by-side: Step 1: Open the workbooks with the worksheets that you want to place side-by-side. Step 3: Click the View tab and click View Side by Side within the Window group. Step 4: If you have more than two workbooks open, Excel will launch the Compare Side by Side dialog box. Select the workbook you want to compare and click OK. This will place both workbooks side by side. Step 5: Once done, simply click the sheet that you want to compare in each workbook window. ## How to Enable Synchronous Scrolling to Scroll Through Two Excel Worksheets When you have two worksheets open, you may want to scroll through both at the same time without having to navigate their respective bars. The Synchronous Scrolling feature on Microsoft Excel makes this possible. However, it only works when two workbooks are open and the View Side by Side option is enabled. Here’s how to enable synchronous scrolling in your Excel. Step 1: On the Excel Ribbon, click the View tab. Step 2: Click the View tab and click View Side by Side within the Window group. This will place both workbooks side by side. Step 3: Click the View tab of one of the opened workbooks, and within the Window group, click Synchronous Scrolling. ## How to Arrange the View of The Excel Workbooks When you enable the View Side by Side option, Excel, by default, will place both worksheets in a Tiled view. However, you can change the view of your worksheets using the steps below: Step 2: Click the View tab, and within the Window group, click Arrange All. This will launch the Arrange Window dialog box. Step 3: From the following options, select how you want your Excel workbooks stacked: • Tiled: the windows are arranged as equally sized squares in the order you open them. • Horizontal: the windows are stacked one below another. • Vertical: the windows are placed next to each other. • Cascade: the windows overlap one another. Step 4: If you have multiple worksheets in a workbook that you want to work with, tick the box beside ‘Windows of active workbook.’ Step 5: Click OK to save your changes. ## Using Microsoft Spreadsheet Compare to Analyze Excel Versions Placing Excel worksheets side by side for comparison requires a lot of manual tracking. It is also best used when the data changes being compared are minute. When comparing a large data set, you can use Microsoft Spreadsheet Compare to save some time and ensure accuracy. Last updated on 01 February, 2024 The above article may contain affiliate links which help support Guiding Tech. However, it does not affect our editorial integrity. The content remains unbiased and authentic. ## DID YOU KNOW ## Maria Victoria Maria is a Content Writer with a keen interest in Technology and Productivity Tools. Her articles can be found on sites such as Onlinetivity and Delesign. Outside of work, you can find her mini-blogging about her life on social media. ## More in Smart Home ## Top 9 Ways to Fix YouTube Not Working on Google TV ## How to Browse the Web on Google Nest Hub (2nd Gen) Join the newsletter. Get Guiding Tech articles delivered to your inbox. #### IMAGES 1. Classroom Poster: 4 Steps to Solve Any Math Problem 2. 3 Ways to Solve Two Step Algebraic Equations 3. How to solve recursive sequences in Math, practice problems explained 4. Solving multi-step equations (solutions, examples, videos) 5. Ways to Solve a Math Problem Poster by Carolyn's Classroom 6. 3 Ways To Solve a Math Problem by elementary math consultant #### VIDEO 1. How to solve this Math Olympiad question 2. how to solve maths problems quickly 3. How To Solve Math Problems 4. How To Solve math problem 5. How To Solve math problem 6. How To Solve math problem #### COMMENTS 1. Step-by-Step Math Problem Solver LCM New Example Help Tutorial Solve an equation, inequality or a system. Example: 2x-1=y,2y+3=x What can QuickMath do? QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. 2. Step-by-Step Calculator How to solve math problems step-by-step? 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. Show more Related Symbolab blog posts My Notebook, the Symbolab way 3. Microsoft Math Solver Get step-by-step solutions to your math problems Try Math Solver Type a math problem Solve Quadratic equation x2 − 4x − 5 = 0 Trigonometry 4sinθcosθ = 2sinθ Linear equation y = 3x +4 Arithmetic 699 ∗533 Matrix [ 2 5 3 4][ 2 −1 0 1 3 5] Simultaneous equation { 8x + 2y = 46 7x + 3y = 47 Differentiation dxd (x −5)(3x2 −2) Integration ∫ 01 xe−x2dx 4. Mathway Free math problem solver answers your algebra homework questions with step-by-step explanations. 5. Solve Integration. ∫ 01 xe−x2dx. Limits. x→−3lim x2 + 2x − 3x2 − 9. 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. 6. Cymath Cymath | Math Problem Solver with Steps | Math Solving App Join millions of users in problem solving! Choose Topic Examples " (x+1)/2+4=7" "factor x^2+5x+6" "integrate cos (x)^3" More » \"Solve 7. GeoGebra Math Solver Get accurate solutions and step-by-step explanations for algebra and other math problems with the free GeoGebra Math Solver. Enhance your problem-solving skills while learning how to solve equations on your own. Try it now! 8. Step-by-Step Solutions Starting at$5/month Get step-by-step answers and hints for your math homework problems. Learn the basics, check your work, gain insight on different ways to solve problems. For chemistry, calculus, algebra, trigonometry, equation solving, basic math and more.

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Step 1: Multiply the denominators (x/3) Step 2: Cross multiply the numerators and denominators (2x1 and 3x1) Step 3: Add the two products together (2x1=2, 3x1=3 therefore, add 2+3). WITHOUT touching the denominator! Step 4: 5/3b + 5 = 20. Subtract 5 from both sides of the equation to cancel out 5.

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Quadratic equations. Quadratic equations are a little bit trickier than linear ones. If you are unsure about linear equations go over linear equations tutorials first. If you think you can handle them, use our quadratic equations tutorials and interactive solvers to learn about quadratic formula and other ways of solving second order equations.

24. How to Do Long Division: Step-by-Step Instructions

Draw a line under the 6, subtract, and write 2 below the line. Bring down the next digit. Now, bring down the next digit of the dividend, which is 4, to sit next to the 2, making 24. Repeat the steps. 3 goes into 24 eight times (3 x 8 = 24), so write 8 above the bar next to the 2. Subtract 24 from 24 to get 0.

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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

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27. How to View Multiple Worksheets Side-by-Side in Excel

Here's how to enable synchronous scrolling in your Excel. Step 1: On the Excel Ribbon, click the View tab. Step 2: Click the View tab and click View Side by Side within the Window group. This ...

28. How To Become A CPA: A Step-By-Step Guide

Below we list the typical requirements to become a CPA. We'll go into these in more detail in the next section of this article. Hold a bachelor's degree. Complete 150 credits of college ...