Solving Word Problems in Mathematics
Steps of solving a word problem.
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How to Solve Word Problems
A proven step-by-step method for solving word problems is actually quite simple.
- Read the problem out loud to yourself
Draw a Picture
- Think “What do I need to find?”
- List what is given
- Find the key words
- Check your work
Let’s put these steps into practice. Consider the word problem below.
Example: Kevin loves to read. He likes many different types of books. He has 3 large bookcases that each have 9 shelves on it all filled with his books. If each shelf can hold 16 books, how many books does Kevin have?
Read the Problem Out Loud
Kids have a tendency to rush through every problem. This is due to time limits on classwork and tests. If your child does not know what the problem is asking, then they cannot solve the problem. When your child reads the problem aloud, they are saying and hearing the problem. They can form a clearer picture in their head of the problem and they are more prepared to solve it.
Students need to visualize a problem to understand it, especially younger students. As they get older, they can start to visualize in their head but at a young age they should be drawing out a picture that explains to them what the problem is about. The picture should take into account all of the aspects of the problem.
Ask “What Do I Need to Find?”
Some word problems are straight forward with their questions. It can be as simple as “Molly has two dogs, Jason has three. How many dogs do Molly and Jason have together?” This one, however, we have to think about. There is more than one step for this problem. We first have to find how many shelves he has and then find out how many books are on all of the shelves to know how many books he has altogether.
List What is Given
It is always good to start with listing the things you know. If you try to solve the problem without knowing what tools you are given to solve it, you will not get the right answer. Think about the last time you tried to fill in the blanks or assume an answer without knowing all the facts. Your outcome probably did not turn out well. It is for this reason that we need to list what is given before any problem. The student should write it down at the top or side of the scrap paper so they always have it as a reference when doing the problem. For this problem, my list of what is given would be:
- Kevin has 3 book cases
- Each book case has 9 shelves
- Each shelve holds 16 books
Find the Key Words
Every word problem has key words to look out for that tell you what operation to do. As your child gets more practice with word problems, finding the key words will get easier. Here are some of the most popular key words for word problems:
*this can be a key word for addition and multiplication
According to the chart above, we should use multiplication. First, we should multiply the number of shelves per case by the number of cases. 9 shelves per case x 3 book cases = 27 shelves. Next, we must multiply the number of books per shelf by the number of shelves. 27 shelves x 16 books per shelf = 432 books.
Check your answer
The last step of course is to check your work by seeing if the answer fits the question asked. Mathematically, we can check our work by doing the opposite of whatever operation we used. So for this problem, we can divide 432 by 16 and we will get 27, then divide 27 by 3 and get 9.
As challenging as word problems can be for children, having them follow these simple 7 steps will help them better understand word problems and see beyond the complicated words. Soon enough, world problems will not be so troubling for them after all and they will grow to become more confident, eager learners.
Topics: Math , Child Education , Math Skills , Parenting Tips , Child Anxiety , Math Anxiety , Word Problems
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5 Easy Steps to Solve Any Word Problem in Math
- February 27, 2021
Picture this my teacher besties. You are solving word problems in your math class and every student, yes every student knows how to solve word problems without immediately entering a state of confusion! They know how to attack the problem head-on and have a method to solve every single problem that is presented to them.
How Do You Solve Word Problems in Math?
Ask yourself this, what do you think is the #1 phrase a student says as soon as they see a word problem?
You guessed it, my teacher friend, I don’t know how to do this! I think the most common question I get when I’m teaching my math classes, is how do I solve this?
Students see word problems and immediately enter freak-out mode! Let’s take solving word problems in the classroom and make it easier for students to SOLVE the problem!
How to Solve Word Problems Step by Step
There are so many methods that students can choose from when learning how to solve word problems. The 4 step method is the foundation for all of the methods that you will see, but what about a variation of the 4 step method that every student can do just because they get it.
Students are most likely confused about how to solve word problems because they have never used a consistent method over the years. I’m all about consistency in my classroom. Fortunately, in my school district, I get to teach most of the students year after year because of how small our class sizes are. So I’m going to give you a method based on the 4 step method, that allows all students to be successful at solving word problems.
Even the most unmotivated math student will learn how to solve word problems and not skip them!
Tips, Tricks, and Teaching Strategies to Solving Word Problems in Math
Going back to the 4 step method just in case you need a refresher. If you know me at all a little reminder of “oh yeah I remember that now” always helps me!
4 steps in solving word problems in math:
- Understand the Problem
- Plan the solution
- Solve the Problem
- Check the solution
This 4 step method is the basis of the method I’m going to tell you all about. The problem isn’t with the method itself, it is the fact that most students see word problems and just start panicking!
Why can they do an entire assignment and then see a word problem and then suddenly stop? Is there a reason why books are designed with word problems at the end?
These are questions that I constantly have asked myself over the last several years. I finally got to the point where my students needed a consistent approach to solving word problems that worked every single time.
The first thing I knew I needed to start doing was introducing students to word problems at the beginning of each lesson.
Once students first see the word problems at the beginning of the lesson, they are less likely to be scared of them when it comes time to do it by themselves!
This also will increase their confidence in the classroom. In case you missed it, I shared all about how I increase my students’ confidence in the classroom.
Wonder how increasing their confidence will help keep them motivated in the classroom?
So confident motivated students will see word problems that could be on their homework, any standardized test, and say I GOT THIS!
Steps to Solving Word Problems in Mathematics
We are ready to SOLVE any word problem our students are going to encounter in math class.
Here are my 5 easy steps to SOLVE any word problem in math:
- S – State the objective
- O – Outline your plan
- L – Look for Key Details – Information
- V – Verify and Solve
- E – Explain and check your solution
Do you want to learn how to implement this 5 steps problem-solving strategy into your classroom? I’m hosting a FREE workshop all about how to implement this strategy in your classroom!
I am so excited to be offering a workshop to increase students’ confidence in solving word problems. The workshop is held in my Facebook Group The Round Robin Math Community. It also will be sent straight to your inbox and you can watch it right now!
If you’re interested, join today and all the details will be sent to you ASAP!
I will see you there!
PS. Need the SOLVE method for your bulletin board for your students’ math journals/notebooks? Check out this bulletin board resource here:
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How to Solve Word Problems in 3 Simple Steps
July 23, 2018 by Evan-Moor | 0 comments
1. Read: Read the problem and decide what the question is asking.
- Read the problem 2 times or more.
- Underline or circle key words, phrases, and numbers. Draw a line through irrelevant information.
2. Plan: Think about what the story is asking you to do. What information are you given, and what do you need to find out?
- Draw a picture.
- Circle or underline key words. (Use highlighters or crayons to color-code key numbers and phrases.)
- Write out the question in your own words.
3. Solve: What strategy could you use to find the missing information: addition, subtraction, multiplication, or division?
- Write a number sentence and solve.
- Use counters.
- Create charts.
Different Strategies to Solve Word Problems
Everyone learns in a different way. What makes sense to one individual often isn’t the easiest option for another. Incorporating different strategies to solve word problems can help your child discover what strategy works best for him or her. A few tips to use are:
1. Circle numbers in a story and underline key phrases.
Color coding is a fun method to incorporate to help children decide what operation the question is asking for. Assign a color to each operation and highlight the phrase that identifies it. For example, red links to addition and blue links to subtraction.
2. Incorporate a key word list.
Key word lists are best used for teaching younger children how to solve word problems. As math curriculum advances, children should not be dependent on a key word list to solve a problem. The questions get trickier.
Addition In all Together Total Altogether Combine Sum Join
Subtraction Difference Fewer How many more How much more Left Remain Less
If your child is a visual learner, drawing a picture or using counters can help him or her understand what the problem is asking. Use number lines, charts, or counters or draw a picture.
4. Write your own word problem. Knowing what is needed to write a word problem is the first step in identifying key words to solve a story. Take turns writing your own word problems with your child and exchange them to solve.
5. Stay organized.
It is important to write clearly and keep work space neat so children can read and follow their own computations. Many children need a separate piece of paper to allow them enough space to solve and understand their answer. Graphing paper is a great option to help students record neat work.
How to solve a two-step word problem
In a two-step word problem children are being asking to solve two related equations. These can get tricky for children to understand when they transition from one-step to two-step problems. Help your child understand his or her relationships within two-step word problems with these strategies:
1. Circle important information.
Circle numbers and important phrases that ask questions. The number sentences needed to solve these equations are hidden in those asking questions. Identify the first and second questions needed to solve.
2. Distinguish the two parts of the problem.
First identify the first step of the first part of the word problem. Write a number sentence and solve.
3. Use the answer from the first-step solution to the whole problem.
Use the answer from the first question to help you solve the next equation. What operation does the second question require?
Check your work by explaining your reasoning. What was the question answered? Is the answer reasonable for the question being asked?
Evan-Moor’s Math Fundamentals is a great resource for training students how to solve word problems in 3 simple steps. It provides step-by-step directions for solving questions and guides children with helpful visuals and key phrases.
Check out Daily Word Problems for consistent practice solving word problems.
For more fun math tips and strategies check out our Math- Ideas, Activities and Lessons Pinterest Board .
Save these tips and Pin It now!
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5 Easy Steps to Solving Word Problems
Word problems strike fear into the hearts of many students, and the trauma can even carry into adulthood. This is why word problems are the topic of many education jokes.
“If two trains start at the same station and travel in opposite directions at the same speed, when will the bacon be ready for breakfast?”
This is obviously a silly scenario, but it shows how word problems are regarded by many: a mangle of confusion that doesn’t make sense and can’t be solved!
Why Are Word Problems Difficult for Children?
Why can word problems be so confusing and scary? There are a few possible reasons.
- Word problems are often introduced to us at an age before our skills of abstract thinking are fully developed. However, a student’s imagination is a great asset to use in understanding word problems!
- Word problems are sometimes simply included as the “harder problems” at the end of homework assignments and the student is never really taught how to approach them.
- It is sometimes ignored that a student’s math and reading ability come into play when word problems are assigned. But if the second grade math student is still only reading on a first-grade level, he will have difficulty solving word problems even if he is otherwise good at math! It can thus be helpful to assess both a student’s math and reading ability to set him up for success. The tutoring service provided by masterygenius.com is a great option since both math and reading skills can be addressed.
A quick tip before we get started…
Explain to students that the word “problem” really means “question.” A word problem is just asking a question to which the students must find an answer. Show them that you need to identify the question before you even worry about which math operations are going to be used. Word problems can be treated like mysteries: the students are the detectives that are going to use the clues in the question to find the answer!
So what are the five easy steps to solving word problems? Let’s take a look!
Five Easy Steps to Solving Word Problems (WASSP)
- Write (or draw) what you know.
- Ask the question.
- Set up a math problem that could answer the question.
- Solve the math problem to get an answer.
- Put the answer in a sentence to see if the answer makes sense!
Let’s look at an example word problem to demonstrate these steps.
Matt has twelve cookies he can give to his friends during lunchtime. If Matt has three friends sitting at his table, how many cookies can Matt give to each of his friends?
1. Write (or draw) what you know.
It is important to convince students that they do not have to immediately know what math operation is required to solve the problem. They first need only understand the scenario itself. In this example, the student could simply write down “12 cookies” and “3 friends,” or draw Matt with 12 cookies sitting at a table with three other children.
2. Ask the question.
Again, we don’t need to know what the math operation is yet! We just need to identify what is actually being asked. What do we NOT know?
The student could write, “How many cookies can each of Matt’s friends have?”
Alternatively, the student could draw a question mark over each friend’s head, maybe with a thought bubble of a cookie!
3. Set up a math problem that could answer the question.
- It can be a good idea to teach students “clue” words or phrases in problems which can identify what math operation may be needed. However, this should not be the student’s only skill for deciding what math operation to use, because these “clue” words can sometimes be confusing. For example, the phrases “how many in all” and “how many more” seem very similar to a student, but the first phrase indicates addition and the second phrase indicates subtraction!
- It is good for a student to also be able to reason what math operation is needed based on understanding the scenario itself (which is a better builder of true critical thinking skills). This is why the first two steps (write what you know and ask the question) are so important. The student that has a true understanding of the scenario will be better equipped to reason what math operation is needed.
In this example, the “clue” word (if you are using that method of reasoning) would be “each,” which indicates division. Or, the student could understand that Matt has to split, or divide, the cookies among his friends. Thus a division problem is needed!
Dividing 12 cookies among 3 friends means 12 is divided by 3.
4. Solve the problem.
It is important to note that using units can be a good idea . Otherwise, the answer could be misunderstood. Is it 4 cookies, or 4 friends, or something else?
12 cookies ÷ 3 friends = 4 cookies per friend
5. Put the answer in a sentence to see if the answer makes sense.
“Each of Matt’s friends can have four cookies.”
Does this answer make sense? It seems reasonable. How could this step help identify an incorrect answer?
What if the student had decided this was a multiplication problem?
12 cookies × 3 friends = 36 cookies per friend
If the student then writes a sentence using the answer, he may realize the answer can’t be right.
“Each of Matt’s friends can have 36 cookies.”
How would that be possible if Matt only had 12 cookies to start with? This must not be a multiplication problem. Let’s try again!
Practice the Five Easy Steps for Word-Problem Success!
Steps 1 and 2 ( Write what you know and Ask the question) help the student gain an understanding of the scenario.
Steps 3 and 4 ( Set up the math problem and Solve the problem) can be more easily navigated with critical thinking once the scenario is understood.
Step 5 ( Put the answer in a sentence) can help the student decide whether the answer makes sense.
Now your student is ready for word-problem success!
Make sure to start at the student’s level of understanding so he can experience success and build confidence, moving on to more challenging problems as appropriate. Customized curriculum is always best, which again makes masterygenius.com a great option if tutoring is needed. Students are assessed and then matched with a curriculum that strikes balance between building confidence and tackling challenges, leading to topic mastery.
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Strategies for Solving Word Problems
It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.
The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!
How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.
Here are the seven strategies I use to help students solve word problems.
1. read the entire word problem.
Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.
2. Think About the Word Problem
Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.
Here are the questions:
A. what exactly is the question.
What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.
B. What do I need in order to find the answer?
Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.
This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined ), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better
Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.
One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.
If you’d like to download this FREE Key Words handout, click here:
C. What information do I already have?
This is where students will focus in on the numbers which will be used to solve the problem.
3. Write on the Word Problem
This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:
- Circle any numbers you’ll use.
- Lightly cross out any information you don’t need.
- Underline the phrase or sentence which tells exactly what you’ll need to find.
4. Draw a Simple Picture and Label It
Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.
For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!
5. Estimate the Answer Before Solving
Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.
6. Check Your Work When Done
This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable ? I want students to do more than to be number crunchers but to really think about what those numbers mean.
Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.
7. Practice Word Problems Often
Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.
When students practice word problems, often several things happen. Word problems become less scary (no, really).
They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.
If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.
This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..
There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.
CLICK HERE to take a look at 3rd grade:
This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.
CLICK HERE to see 4th grade:
This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.
CLICK HERE to take a look at 5th grade:
Want to try a FREE set of math task cards to see what you think?
3rd Grade: Rounding Whole Numbers Task Cards
4th Grade: Convert Fractions and Decimals Task Cards
5th Grade: Read, Write, and Compare Decimals Task Cards
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5 Steps to Word Problem Solving
How to Learn Math Multiplication and Show Your Work
Word problems often confuse students simply because the question does not present itself in a ready-to-solve mathematical equation. You can answer even the most complex word problems, provided you understand the mathematical concepts addressed. While the degree of difficulty may change, the way to solve word problems involves a planned approach that requires identifying the problem, gathering the relevant information, creating the equation, solving and checking your work.
Identify the Problem
Begin by determining the scenario the problem wants you to solve. This might come as a question or a statement. Either way, the word problem provides you with all the information you need to solve it. Once you identify the problem, you can determine the unit of measurement for the final answer. In the following example, the question asks you to determine the total number of socks between the two sisters. The unit of measurement for this problem is pairs of socks.
"Suzy has eight pairs of red socks and six pairs of blue socks. Suzy's brother Mark owns eight socks. If her little sister owns nine pairs of purple socks and loses two of Suzy's pairs, how many pairs of socks do the sisters have left?"
Create a table, list, graph or chart that outlines the information you know, and leave blanks for any information you don't yet know. Each word problem may require a different format, but a visual representation of the necessary information makes it easier to work with.
In the example, the question asks how many socks the sisters own together, so you can disregard the information about Mark. Also, the color of the socks doesn't matter. This eliminates much of the information and leaves you with only the total number of socks that the sisters started with and how many the little sister lost.
Create an Equation
Translate any of the math terms into math symbols. For example, the words and phrases "sum," "more than," "increased" and "in addition to" all mean to add, so write in the "+" symbol over these words. Use a letter for the unknown variable, and create an algebraic equation that represents the problem.
In the example, take the total number of pairs of socks Suzy owns -- eight plus six. Take the total number of pairs that her sister owns -- nine. The total pairs of socks owned by both sisters is 8 + 6 + 9. Subtract the two missing pairs for a final equation of (8 + 6 + 9) - 2 = n, where n is the number of pairs of socks the sisters have left.
Solve the Problem
Using the equation, solve the problem by plugging in the values and solving for the unknown variable. Double-check your calculations along the way to prevent any mistakes. Multiply, divide and subtract in the correct order using the order of operations. Exponents and roots come first, then multiplication and division, and finally addition and subtraction.
In the example, after adding the numbers together and subtracting, you get an answer of n = 21 pairs of socks.
Verify the Answer
Check if your answer makes sense with what you know. Using common sense, estimate an answer and see if you come close to what you expected. If the answer seems absurdly large or too small, search through the problem to find where you went wrong.
In the example, you know by adding up all the numbers for the sisters that you have a maximum of 23 socks. Since the problem mentions that the little sister lost two pairs, the final answer must be less than 23. If you get a higher number, you did something wrong. Apply this logic to any word problem, regardless of the difficulty.
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- Mt. San Antonio College: Five-Step Strategy to Solving Word Problems
About the Author
Avery Martin holds a Bachelor of Music in opera performance and a Bachelor of Arts in East Asian studies. As a professional writer, she has written for Education.com, Samsung and IBM. Martin contributed English translations for a collection of Japanese poems by Misuzu Kaneko. She has worked as an educator in Japan, and she runs a private voice studio out of her home. She writes about education, music and travel.
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How to Solve Word Problems in Algebra
Last Updated: December 19, 2022 References
This article was co-authored by Daron Cam . Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary's College. This article has been viewed 53,768 times.
You can solve many real world problems with the help of math. In order to familiarize students with these kinds of problems, teachers include word problems in their math curriculum. However, word problems can present a real challenge if you don't know how to break them down and find the numbers underneath the story. Solving word problems is an art of transforming the words and sentences into mathematical expressions and then applying conventional algebraic techniques to solve the problem.
Assessing the Problem
- For example, you might have the following problem: Jane went to a book shop and bought a book. While at the store Jane found a second interesting book and bought it for $80. The price of the second book was $10 less than three times the price of he first book. What was the price of the first book?
- In this problem, you are asked to find the price of the first book Jane purchased.
- For example, you know that Jane bought two books. You know that the second book was $80. You also know that the second book cost $10 less than 3 times the price of the first book. You don't know the price of the first book.
- Multiplication keywords include times, of, and f actor.  X Research source
- Division keywords include per, out of, and percent.  X Research source
- Addition keywords include some, more, and together.  X Research source
- Subtraction keywords include difference, fewer, and decreased.  X Research source
Finding the Solution
Completing a Sample Problem
- Robyn and Billy run a lemonade stand. They are giving all the money that they make to a cat shelter. They will combine their profits from selling lemonade with their tips. They sell cups of lemonade for 75 cents. Their mom and dad have agreed to double whatever amount they receive in tips. Write an equation that describes the amount of money Robyn and Billy will give to the shelter.
- Since you are combining their profits and tips, you will be adding two terms. So, x = __ + __.
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- Word problems can have more than one unknown and more the one variable. ⧼thumbs_response⧽ Helpful 2 Not Helpful 1
- The number of variables is always equal to the number of unknowns. ⧼thumbs_response⧽ Helpful 1 Not Helpful 0
- While solving word problems you should always read every sentence carefully and try to extract all the numerical information. ⧼thumbs_response⧽ Helpful 1 Not Helpful 0
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- ↑ Daron Cam. Academic Tutor. Expert Interview. 29 May 2020.
- ↑ http://www.purplemath.com/modules/translat.htm
- ↑ https://www.mathsisfun.com/algebra/word-questions-solving.html
- ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut8_probsol.htm
- ↑ http://www.virtualnerd.com/algebra-1/algebra-foundations/word-problem-equation-writing.php
- ↑ https://www.khanacademy.org/test-prep/praxis-math/praxis-math-lessons/praxis-math-algebra/a/gtp--praxis-math--article--algebraic-word-problems--lesson
About This Article
To solve word problems in algebra, start by reading the problem carefully and determining what you’re being asked to find. Next, summarize what information you know and what you need to know. Then, assign variables to the unknown quantities. For example, if you know that Jane bought 2 books, and the second book cost $80, which was $10 less than 3 times the price of the first book, assign x to the price of the 1st book. Use this information to write your equation, which is 80 = 3x - 10. To learn how to solve an equation with multiple variables, keep reading! Did this summary help you? Yes No
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