Tricks to Solving Percentage Word Problems

Doing the work in your head is often faster than relying on a calculator.
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Word problems test both your math skills and your reading comprehension skills. In order to answer them correctly, you'll need to examine the questions carefully. Always make sure you know what is being asked, what operations are necessary and what units, if any, you need to include in your answer.

Eliminate Extraneous Data

Sometimes, word problems include extraneous data that is not necessary to solve the problem. For example:

Kim won 80 percent of her games in June and 90 percent of her games in July. If she won 4 games in June and played 10 games in July, how many games did Kim win in July?

The simplest way to eliminate extraneous data is to identify the question; in this case, "How many games did Kim win in July?" In the example above, any information that doesn't deal with the month of July is unnecessary to answer the question. You are left with 90 percent of 10 games, allowing you to do a simple calculation:

0.9*10=9 games

Calculate Additional Data

Read the question portion twice to make sure you know what data you need to answer the question:

On a test with 80 questions, Abel got 4 answers wrong. What percentage of questions did he get right?

The word problem only gives you two numbers, so it would be easy to assume that the questions involves those two numbers. However, in this case, the question requires that you calculate another answer first: the number of questions Abel got right. You'll need to subtract 4 from 80, then calculate the percentage of the difference:

80-4=78, and 78/80*100=97.5 percent

Rephrase Difficult Problems

Remember that you can often rearrange problems to make them simpler. This is especially useful if you don't have a calculator available:

Gina needs to score at least 92 percent on her final exam to get an A for the semester. If there are 200 questions on the exam, how many questions does Gina need to get right in order to earn an A?

The standard approach would be to multiply 200 by 0.92: 200*.92=184. While this is a simple process, you can make the process even simpler. Instead of finding 92 percent of 200, find 200 percent of 92 by doubling it:


This method is particularly useful when you are dealing with numbers with known ratios. If, for example, the word problem asked you to find 77 percent of 50, you could simply find 50 percent of 77:

50*.77=38.5, or 77/2=38.5

Account for Units

Convert your answers into appropriate units:

Cassie works from 7 a.m. to 4 p.m. each weekday. If Cassie worked 82 percent of her shift on Wednesday and worked 100 percent of her other shifts, what percent of the week did she miss? How much time did she work in total?

First, calculate how many hours Cassie works per day, taking noon into account, then per week:

4+(12-7)=9 9*5=45

Next, calculate 82 percent of 9 hours:


Subtract the product from 9 for the total hours missed:


Calculate what percentage of the week she missed:

1.62/45*100=3.6 percent

The second question asks for an amount of time, which means you'll need to convert the decimal into time increments. Add the product to the other four work days:


Convert the decimal into minutes:


Convert the remaining decimal into seconds:


So Cassie missed 3.6 percent of her week, and worked 43 hours, 22 minutes and 48 seconds total.

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