In working with word problems, there are some words or phrases that give clues as to how the problem should be solved. The most common words or phrases are as follows.
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Add
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Sum—as in the sum of 2, 3, and 6 …
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Total—as in the total of the first six payments …
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Addition—as in a recipe calls for the addition of five pints …
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Plus—as in three liters plus two liters …
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Increase—as in her pay was increased by $15 …
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More than—as in this week the enrollment was eight more than last week …
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Added to—as in if you added $3 to the cost …
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Subtract
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Difference—as in what is the difference between …
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Fewer—as in there were fifteen fewer men than women …
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Remainder—as in how many are left or what quantity remains …
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Less than—as in a number is five less than another number …
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Reduced—as in the budget was reduced by $5,000 …
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Decreased—as in if he decreased the speed of his car by ten miles per hour …
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Minus—as in some number minus 9 is …
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Multiply
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Product—as in the product of 8 and 5 is …
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Of—as in one‐half of the group …
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Times—as in five times as many girls as boys …
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At—as in the cost of ten yards of material at 70¢ a yard is …
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Total—as in if you spend $15 a week on gas, what is the total for a three‐week period …
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Twice—as in twice the value of some number …
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Divide
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Quotient—as in the final quotient is …
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Divided by—as in some number divided by 12 is …
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Divided into—as in the group was divided into …
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Ratio—as in what is the ratio of …
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Half—as in half the profits are … (dividing by 2)
As you work a variety of word problem types, you will discover more “clue” words.
A final reminder: Be sensitive to what each of these questions is asking. What time? How many? How much? How far? How old? What length? What is the ratio?