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
- Sum—as in the sum of 2, 3, and 6 …
- Total—as in the total of the first six payments …
- Addition—as in a recipe calls for the addition of five pints …
- Plus—as in three liters plus two liters …
- Increase—as in her pay was increased by $15 …
- More than—as in this week the enrollment was eight more than last week …
- Added to—as in if you added $3 to the cost …
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Subtract
- Difference—as in what is the difference between …
- Fewer—as in there were fifteen fewer men than women …
- Remainder—as in how many are left or what quantity remains …
- Less than—as in a number is five less than another number …
- Reduced—as in the budget was reduced by $5,000 …
- Decreased—as in if he decreased the speed of his car by ten miles per hour …
- Minus—as in some number minus 9 is …
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Multiply
- Product—as in the product of 8 and 5 is …
- Of—as in one‐half of the group …
- Times—as in five times as many girls as boys …
- At—as in the cost of ten yards of material at 70¢ a yard is …
- Total—as in if you spend $15 a week on gas, what is the total for a three‐week period …
- Twice—as in twice the value of some number …
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Divide
- Quotient—as in the final quotient is …
- Divided by—as in some number divided by 12 is …
- Divided into—as in the group was divided into …
- Ratio—as in what is the ratio of …
- 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?