How to Solve Word Problems

Most students find math word problems difficult.   Word problems are found on must High School Proficiency Exams, College 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.

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 everyday.

It is critical that you practice word problems everyday for the 5 days before the exam as a bare minimum.

If you practice and miss a day, you have lot lost the mathematical frame of mind and the benefit of your previous practice is pretty much gone.   Anyone who has done any amount of math will agree – you have to practice everyday.

The other critical point about word problems is that all of the information given in the problem is has some purpose.  There is no unnecessary information! Word problems are typically around 50 words in 1 to 3 sentences.  If the sometimes complicated relationships are to be explained in that short an explanation, every word has to count.   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 reading should be done slowly with a view to finding answers to these important questions:

1. What does the problem ask of me? (Usually located towards the end of the problem)
2. What does the problem imply? (This is usually a point you were asked to remember).
3. Mark all information, and underline all important words or phrases.Also – try to pick out Key Words – see Purple Math for more information 

Step 2 – Try to make a pictorial representation of the problem such as a circle and an arrow to indicate travel. This makes the problem a bit more real and sensible to you.

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

Draw a line and the two stations and the two trains at either end.  This will help solidify the situation in your mind.

More on Modelling Word Problems  

Step 3 – Use the information you have to make a table with a blank portion to indicate information you do not know.

Step 4 – Assign a single letter to represent each unknown data in your table. You can write down the unknown that each letter represents so that you do not make the error of assigning answers to the wrong unknown, because a word problem may have multiple unknowns and you will need to create equations for each unknown.

Step 5 – Translate the English terms in the word problem into a mathematical algebraic equation. Remember that the main problem with word problems is that they are not expressed in regular math equations. You ability to correctly identify the variables and translate the word problem into an equation determines your ability to solve the problem.

Step 6 – 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. For example, word distance problems may need you rewriting the distance formula, which is Distance = Time x Rate. If the word problem requires that you solve for time you will need to use Distance/Rate and Distance/Time to solve for Rate. If you understand the distance word problem you should be able to identify the variable you need to solve for.

Step 7 – Use algebra rules to solve the derived equation. Take note that the laws of equation demands that what is done on this side of the equation has to also be done on the other side. You have to solve the equation so that the unknown ends up alone on one side. Where there are multiple unknowns you will need to use elimination or substitution methods to resolve all the equations.

Step 8 – 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.

Step 9 – Cross check your answers by placing the answer or answers in the first equation to replace the unknown or unknowns. If your answer is correct then both side of the equation must equate or equal. If your answer is not correct then you may have derived a wrong equation or solved the equation wrongly. Repeat the necessary steps to correct.

 Extensive Word Problem Resources here

Word Problem Practice Problems