Cracking the Word Problem, Part 3: Keywords in Action

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One of the best-kept secrets to mastering math word problems can be summed up in three words: do the opposite.

Consider the following:

"The Bunbury Community Center has 480 flyers for an upcoming job fair to deliver. The after-school program director distributes one-half of them. The office interns give out one-third of the total. How many remaining flyers are left for the three administrative staff members to distribute themselves?" (See answer at bottom of page)

Too often, students attempt to solve a problem like the example above by only paying attention to the numbers, sometimes barely looking at the words. This method depends a little too much on luck for comfort. Words are important in a word problem!

A more productive approach is to do the opposite. Focus on the sentences. Be alert for keywords. Understand the logic of the problem (see Part 2 of this series).

Solving the problem above obviously requires working with fractions. However, note that the phrase “what fraction of” does not appear in the last sentence. Thus, you need to show how many papers are left rather than find the fraction of the total remaining (answer choices should give a clue to this as well). The word “of”—often indicating multiplication—appears twice. The word “remaining” appears once. Remaining is a subtraction keyword. To get the correct answer, it is necessary to multiply twice and subtract the products from the total.

Reading the words first also helps us to realize the number of administrative staff does not, in this case, impact how many flyers are left to deliver. This means that the number three is unnecessary.

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Let’s try this system with another problem.

"Gwendolyn and Cecily are exercise buddies. In two weeks, Gwendolyn increased her daily walking distance from three-fourths of a mile to one mile. Cecily increased her walking distance from one mile to 1½ miles. At the end of two weeks, how much more did Cecily increase her distance than Gwendolyn did?" (See answer at bottom of page)

Like the flyer crisis at the Bunbury Community Center, this problem requires multiple steps. It also has multiple keywords. We know “of” means multiply. Multiplying three-fourths times one mile, though, is not too much of a challenge. The more important phrase in the last sentence is “how much more.” “How much” with a comparative (how much longer, how much older, how much smaller) almost always indicates subtraction. But what are we subtracting from what?

There are three operations to perform. Subtract each girl’s old distance from her new distance. Once we find out how each has increased, our final step is to subtract the smaller increase from the larger one.

Here are a few common keywords and the operations they normally indicate:

  • And, increase, sum, total – addition
  • Decrease, difference, left, remaining – subtraction
  • Of, product, times – multiplication
  • Each, quotient, per, share—division


This is not a complete list. However, the first step to mastering word problems is simply being aware of the words rather than jumping over them to get to the numbers. The second step? Practice, practice, practice! 

At A+ Test Prep and Tutoring, we have an excellent team of tutors who can help you with word problems, math in general, or any other school subject. Our Client Service Directors, Anne Stanley and Susan Ware, are available to answer your questions and provide solutions. You may reach either of them by calling A+ Test Prep and Tutoring at 215-886-9188.

Answer to A: There are 80 flyers left for the job fair organizers to distribute.

Answer to B: Gwendolyn increased her distance by one-fourth. Cecily increased her distance by one-half. One-half is one-fourth more than one-fourth.

Photo credit: Hades2k

 

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