When Math Gives You Word Problems – Make Sense of Them!
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!
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.
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.
The third step is to look for key words. Certain words indicate certain mathematical operations.
Here’s a list of words to be aware of when dealing with addition:
More than
Combined
Together
Total of
Sum
Plus
Added to
Comparatives (like “greater than”)
Here is a list of terms to look out for when dealing with subtraction:
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”)
Here are terms to be aware of when dealing with multiplication:
Times
Multiplied by
Product of
Increased/decreased by a factor of
(and this can involve both addition or subtraction and multiplication!)
Twice, triple, etc.
Each (e.g. “They got 3 each.”)
Next are terms to be aware of when dealing with division:
Now lastly, here are terms to be aware of when dealing with things that are equal:
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.
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See you guys next time!
Word Problem Practice Questions
The items below, except for one, are all helpful things to remember when solving word problems in math. Which item is not a helpful strategy for solving word problems?
Read the problem thoroughly, all the way to the end. Consider re-reading the problem a few times so that you are familiar with what the question is about.
Draw pictures or models that represent what is happening in the story.
Identify what you need to know, and label unknown values with variables.
Locate the last sentence in the word problem because this is always where the question is located.
All items are helpful strategies except the item that states that the last sentence in a word problem is where the question is located. 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?
Total of, quotient, more than
Combined, more than, together
Plus, product, sum
More than, sum, less than
Terms that were listed that do not indicate addition are “quotient” (division), “product” (multiplication), and “less than” (subtraction). All items in list B: Combined, more than, and together indicate addition. Paying close attention to keywords can help you determine which operation to use when solving word problems.
Which list provides key words that all indicate multiplication?
Of, times, product of
Times, difference, sum
Groups of, product, quotient
Total, is, sum
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 keywords such as these in order to determine which operation the problem requires.
Which operations do the bold words indicate?
40 is what percent of 200?
Is represents “equals”. Of represents “multiply”.
Is represents “equals”. Of represents “divide”.
Is represents “addition”. Of represents “multiply”.
Is represents “subtraction”. Of represents “division”.
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. The text “40 is what percent of 200” can be written as \(40=x\times200\) which can be manipulated in order to solve for x. When both sides of the equation are divided by 200, the equation shows that \(x=0.2\) or 20%.
George wants to purchase a computer that costs $1,000. George plans to use $455 dollars from his savings account, $200 from his checking account, and his uncle says he can loan George the remaining cost. What is the left over amount that George’s uncle will need to contribute?
$433
$223
$345
$200
The keywords “left over” indicate 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 “left over” amount that George’s uncle will provide. $1,000 take away $655 equals $345, so George’s uncle will loan him $345.
