WORD PROBLEMS - DIVISION

Concept: Word problems use stories and sentences that contain numbers, and ask you to find the answer to a question. You can usually solve word problems by using 5 basic steps.

Steps for Solving Word Problems

Step 1 | Read the word problem carefully and completely. Determine what the word problem is asking you to find out.
Step 2 | Determine what information given in the word problem is needed to solve the problem, and what information is not needed to solve the problem.
Step 3 | Determine which math operation to use in solving the word problem.
Step 4 | Set up the math operation, and solve it.
Step 5 | Re-read the word problem to make sure that the solution makes sense, and that you answered the question that was asked.

Key Words

There are many key words that are used in word problems. You must decide what they are and which type of math operation (addition, subtraction, multiplication, or division) they are asking you to use.

A short list of key words is given here. There are many more key words than are listed here. Remember that sometimes the key words are hard to find, but you can usually figure out what math operation you need to use by thinking about how the question is stated. Remember, also, that key words can be misleading, and are only to be used as guides.

ADDITION | SUBTRACTION | MULTIPLICATION | DIVISION
Increase Sum Total And More than Plus Add Raise Both Combined In all Altogether Additional | Decrease Difference Less than Reduced Minus More than Lost Leftover Remain Fell Dropped Changed How many left | Multiplied Times Total Of Per As much Twice By Area Volume | Divided evenly Split Each Cut Equal pieces Average Every Out of Ratio Shared Part of

Example

Step 1 | Read the word problem carefully and completely. Determine what the word problem is asking you to find out.
| Read the word problem carefully and completely. John purchased 3 CDs for $29.97. All 3 CDs cost the same. The CD was priced $4.95 less at Wal-Mart. How much did John pay for each CD?
| Determine what the word problem is asking you to find out. How much did John pay for each CD?
Step 2 | Determine what information given in the word problem is needed to solve the problem, and what information is not needed to solve the problem.
| Determine what information given in the word problem is needed to solve the problem. The needed information is the $29.97 total cost, the fact that there are 3 CDs, and the fact that all 3 CDs cost exactly the same.
| What information is not needed to solve the problem? The fact that the CD was priced $4.95 less at Wal-Mart is information that is not needed to solve the problem.
Step 3 | Determine which math operation to use in solving the word problem.
| Determine which math operation to use in solving the word problem. We have been asked how much John paid for each CD. We know that he paid a total of $29.97 for all 3 CDs. We know that each CD costs exactly the same. We must divide the total into 3 equal amounts. The math operation used is division.
| (See the Key Words Table for help with determining which math operations to use in solving word problems.)
Step 4 | Set up the math operation, and solve it.
| Set up the math operation, and solve it. $29.97 ÷ 3 = $9.99
Step 5 | Re-read the word problem to make sure that the solution makes sense, and that you answered the question that was asked.
| Re-read the word problem to make sure that the solution makes sense, and that you answered the question that was asked. John purchased 3 CDs for $29.97. All 3 CDs cost the same. The CD was priced $4.95 less at Wal-Mart. How much did John pay for each CD? We have been asked how much John paid for each CD. We have divided the total cost of the CDs ($29.97) by the number of CDs (3). Our answer is $9.99. Our solution makes sense, and answers the question that was asked.