Hey, guys! Welcome to this video on word problems.
The hardest thing about doing word problems is the part where you need to take the English words and translate them into mathematics. Usually, once you get the math equation, you’re fine. The actual math involved is often very simple. But figuring out the actual equation can seem nearly impossible.
What I’m going to talk about in this video is a list of hints and helps. Be advised, however, to really learn how to do word problems, you will need to practice, practice, practice!
Steps for Solving Word Problems
Reading the Problem
The first step to effectively translating and solving word problems is to read the problem entirely. Don’t try solving anything when you’ve only read half a sentence! Try first to get a feel for the whole problem, then see what information you have and figure out what you still need.
Working Orderly
The second step is to work in an orderly fashion. Figure out what you need but don’t have, and begin to name things. Always pick variables to stand for the unknowns, clearly labeling the variables with exactly what they stand for. Draw and label pictures neatly. Explain your reasoning as you go along. And make sure you know just exactly what the problem is asking for.
Working clearly will help you to think clearly, and figuring out what you will need will help you translate your final answer back into English.
It can be really frustrating, and kind of embarrassing, to spend 15 minutes solving a word problem on a test only realize that, in the end, you no longer have any idea what \(x\) stands for, so you have to do the whole problem over again.
Key Words for Mathematical Operations
The third step is to look for key words. Certain words indicate certain mathematical operations.
Addition
Here’s a list of words to be aware of when dealing with addition:
- Increased by
- More than
- Combined
- Together
- Total of
- Sum
- Plus
- Added to
- Comparatives (like “greater than”)
Subtraction
Here is a list of terms to look out for when dealing with subtraction:
- Decreased by
- Minus
- Less
- Difference between
- Difference of
- Less than
- Fewer than
- Left
- Left over
- After
- Save (more of an old-fashioned term)
- Comparatives (like “smaller than”)
Multiplication
Here are terms to be aware of when dealing with multiplication:
- Of
- Times
- Multiplied by
- Product of
- Increased/decreased by a factor of
- Twice, triple, etc.
- Each
Division
Next are terms to be aware of when dealing with division:
- Per
- A
- Out of
- Ratio
- Quotient of
- Percent (divided by 100)
- Equal pieces
- Split
- Average
Equality
Lastly, here are terms to be aware of when dealing with things that are equal:
- Is
- Are
- Was
- Were
- Will be
- Gives
- Yields
- Sold for
- Cost
As you work through word problems, be aware of these words and use them to help you identify what type of math is taking place.
I hope that this video was helpful! See you guys next time!
Word Problem Practice Questions
Which of the following is NOT a helpful strategy for solving word problems?
Word problems generally have the question as the last sentence, but this is not always the case. It can be helpful to underline the question in a word problem so that it is clearly identified within the text.
Which list provides key words that all indicate addition?
Terms that were listed that do not indicate addition are “quotient” (division), “product” (multiplication), and “less than” (subtraction). Paying close attention to key words can help you determine which operation to use when solving word problems.
Which list provides key words that all indicate multiplication?
There are many terms that refer to multiplication. The terms “of,” “times,” and “product” all indicate multiplication. When solving word problems, it is helpful to look for key words such as these in order to determine which operation the problem requires.
Which operations do the words “is” and “of” indicate in the following problem?
In this example, the term “is” can be interpreted as “equals,” and the term “of” can be interpreted as “multiplication.”
In this scenario, “40 is what percent of 200” can be re-written as an equation:
\(40=x\times200\)
This can be manipulated in order to solve for \(x\). When both sides of the equation are divided by 200, the equation shows that \(x=0.2\), which is the same as 20%.
George wants to purchase a computer that costs $1,000. George plans to use $455 from his savings account, $200 from his checking account, and his uncle says he can loan George the remaining cost. What is the leftover amount that George’s uncle will need to contribute?
The key word “leftover” indicates subtraction in this scenario. George is able to contribute a total of $655 to the computer, so subtracting this from the total of $1,000 will provide the “leftover” amount that George’s uncle will provide.
\(\$1{,}000 \: – \: \$655 = \$345\)
