How to Solve Word Problems

Most students find math word problems difficult.   Word problems are found on must High School Proficiency Exams and a few Nursing Entrance exams like the PAX.  Tackling word problems is much easier if you have a systematic approach which we outline below.

See Also:

Types of Word Problems

Word Problem Practice

Common Word Problem Mistakes on a Test

Practice regularly and systematically.   Sounds simple and easy right?   Yes it is, and yes it really does work.

Word problems are a way of thinking and require you to translate a real word problem into mathematical terms.

Some math instructors go so far as to say that learning how to think mathematically is the main reason for teaching word problems.

Studying word problems and math in general requires a logical and mathematical frame of mind. The only way you can get this is by practicing regularly, which means every day.

It is critical that you practice word problems every day for the 5 days before the exam as the absolute minimum.

If you practice and miss a day, you have lost the mathematical frame of mind and the benefit of your previous practice is gone.  You must start all over again.

All the information given in the prob­lem has some purpose. There is no unnecessary informa­tion! Word problems are typically around 50 words in 2 or 3 sentences.

Often, the relationships are complicated.  To explain everything, every word counts.

Make sure that you use every piece of information.

Step 1 – Read through the problem at least three times. The first reading should be a quick scan, and the next two read­ings should be done slowly to find answers to these ques­tions:

What does the problem ask? (Usually located at the end)

Mark all information and underline all important words or phrases.

Step 2 – Draw a picture.  Use arrows, circles, lines, whatever works for you.   This makes the problem real.

A favorite word problem is something like, 1 train leaves Station A travelling at 100 km/hr and another train leaves Station B travelling at 60 km/hr. …

Draw a line, the two stations, and the two trains at either end.

Depending on the question, make a table with a blank portion to show information you don’t know.

Step 3 – Assign a single letter to represent each unknown.

You may want to note the unknown that each letter represents so you don’t get confused.

Step 4 – Translate the information into an equation.

Remember that the main problem with word problems is that they are not expressed in regular math equations. Your ability to identify correctly the variables and translate the information into an equation determines your ability to solve the problem.

Step 5 – Check the equation to see if it looks like regular equations that you are used to seeing and whether it looks sensible.

Does the equation appear to represent the informa­tion in the question? Take note that you may need to rewrite some formulas needed to solve the word problem equation.

Step 6 – Use algebra rules to solve the equation.

Simplify each side of the equation by removing parentheses and combining like terms.

Use addition or subtraction to isolate the variable term on one side of the equation.  If a number crosses to the other side of the equation, the sign changes to the opposite — for example positive to negative.

Use multiplication or division to solve for the variable.  What you to once side of the equation you must do for the other.

Where there are multiple unknowns you will need to use elimination or substitution methods to resolve all the equations.

Step 7 – Check your final answers to see if they make sense with the information given in the problem.

For example, if the word problem involves a discount, the final price should be less or if a product was taxed then the final answer has to cost more.

 Extensive Word Problem Resources here

Word Problem Practice Problems

Most Common Word Problem Mistakes on a Test

1. Not reading the problem carefully and thoroughly, so that you either misunderstand or solve the problem incorrectly.
2. Not identifying the important information in the problem, such as the quantities, units, and the operation to be performed.
3. Not translating the information in the problem into mathematical language and equations.
4. Not checking the units of measure and making sure they match your final answer.
5. Not double-checking the answer to ensure it makes sense.
6. Not understanding the underlying mathematical concept or operation the problem is asking for.
7. Not using estimation or approximations as a tool to check the reasonableness of your answer.