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.

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 …

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 …

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 …

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?