The Keywords of Word Problems Study Guide
Find practice problems and solutions for these concepts at: The Keywords of Word Problems Practice Problems.
Now that you've completed the pretest, we're ready to start breaking down some word problems. Often, the hardest part of a word problem isn't the computation—it's figuring out what operation to use. In this chapter, we'll look at the keywords that signal addition, subtraction, multiplication, and division.
In math problems, a keyword is a word that signals what operation to use. A problem may contain more than one keyword, especially if the word problem requires more than one operation to solve.
Fuel for Thought
An operation is a procedure that is applied to one or more numbers or variables. Addition, subtraction, multiplication, and division are all operations. The symbol for each operation is called an operator. The symbols +, –, ×, and ÷ are all operators. Most operations involve two or more operands. An operand is a number or variable used in an operation. In the number sentence 4 + 5 = 9, 4 and 5 are operands, + is the operator, and the operation is addition.
What kinds of words signal addition? How would you describe addition to someone who had never heard of it? In order for a word problem to be about addition, the author of the word problem needs to describe addition in words, so that we'll know to use that operation. If you can think of how to describe addition in words, you'll likely use some of the same words a test maker may use to write a word problem.
An addition problem is made up of two or more addends and a sum. The addends are the numbers that are being added, and the sum is the result of adding the addends together, or the answer. In the number sentence 3 + 1 = 4, 3 and 1 are the addends, and 4 is the sum.
You could say, "Addition is combining two or more numbers together to form a total." Or you may say, "Addition is the sum of a few numbers." You may also say, "Addition is putting one quantity and another together," or "Addition is one number plus another number." Each of these sentences contains one or more keywords.
Here are those sentences again, with the keywords highlighted:
Addition is combining two or more numbers together to form a total.
Addition is the sum of a few numbers.
Addition is putting one quantity and another together.
Addition is one number plus another number.
The words combine, together, total, sum, and, and plus are all keywords that represent addition. When you thought about how to describe addition, you may have used these words or words like altogether, increase, both, or more.
Heather's cat weighs 8 pounds, and Serge's cat weighs 11 pounds.
How much do the two cats weigh in total?
This word problem asks us to find how much the cats weigh in total. Total is a keyword that signals addition, so we must add the weights of the two cats. 8 + 11 = 19 pounds. The two cats weigh 19 pounds in total.
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