WORD PROBLEMS

MIXED

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 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

Addition 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. One day, after drinking three Diet Colas, Lindsey Lohan drove miles to the market, miles to the hardware store, miles to the laundry, and miles back home. She stopped for gas once. Before the trip was over, the car overheated. How far did she drive?
| Determine what the word problem is asking you to find out. How far did she drive?
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 four distances given.
| What information is not needed to solve the problem? The facts that she drank three Diet Colas, that she stopped for gas once, and that the car overheated, are all facts that are 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 far Lindsey drove. We know that she drove miles, miles, miles, and miles. We must combine these four amounts. The math operation used to combine two numbers is addition.
| (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. + + + =
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. We have been asked how far Lindsey drove. We have combined (added) the four distances she drove. Our solution makes sense, and answers the question that was asked.

Subtraction 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. Before leaving on a weekend trip, Brittney withdrew $200 from the bank. As she pulled out of her driveway, sliding on the ice, she noticed that her mileage gauge registered miles. She stayed in the Holiday Inn for the weekend. When she returned home, the gauge registered miles. How many miles did Brittney drive?
| Determine what the word problem is asking you to find out. How many miles did Brittney drive that weekend?
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 mileage gauge reading before and after the trip.
| What information is not needed to solve the problem? The facts that she withdrew $200 from the bank, that she slid on the ice, and that she stayed in the Holiday Inn are facts that are 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 many miles Brittney drove that weekend. We know that the mileage gauge read when she returned home, and that it was when she left home. The difference between and will tell us how many miles Brittney drove. The math operation used to find the difference between two numbers is subtraction.
| (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. – =
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. We have been asked how many miles Brittney drove.. We have subtracted the beginning mileage reading from the ending mileage reading. The difference is our solution. Our solution makes sense, and answers the question that was asked.

Multiplication 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. A restaurant had 125 customers during the lunch rush hour on Monday. The same restaurant served 310 customers for dinner. Two-fifths of the lunch customers ordered the lunch special. How many customers ordered the lunch special?
| Determine what the word problem is asking you to find out. How many customers ordered the lunch special?
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 that there were 125 lunch customers, and that two-fifths of the lunch customers ordered the lunch special.
| What information is not needed to solve the problem? The fact that the same restaurant served 310 customers for dinner 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 many customers ordered the lunch special. We know that there were 125 lunch customers. We know that two-fifths of those customers ordered the special. We will use multiplication to determine what two-fifths of 125 is.
| (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. x 125 = 50
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. We have been asked how many customers ordered the lunch special. We have multiplied the fraction of the customers who ordered the lunch special by the total number of lunch customers to determine how many customers ordered the lunch special. Our solution makes sense, and answers the question that was asked.

Division 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. A housing subdivision has 24 acres of land available for sale. Half of this acreage is in Michigan and half is in Indiana. If this land is divided into home lots that are of an acre each, how many lots are in the housing subdivision?
| Determine what the word problem is asking you to find out. How many of an acre lots are in the 24 acre housing subdivision?
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 that there are 24 acres of land, and each lot is of an acre
| What information is not needed to solve the problem? The fact that half the acreage is in Michigan and half is in Indiana 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 many of an acre lots are in the 24 acre housing subdivision? The math operation needed to solve this problem 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. 24 ÷ = 32
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. We have been asked how many of an acre lots are in the 24 acre housing subdivision? We have divided the total acreage of the subdivision by the size of each individual lot to determine how many individual lots are in the subdivision. Our solution makes sense, and answers the question that was asked.