Understand what the word problem is asking.
How many days will it take Raymond to read the entire book?
Organize the information that is important.
Amount = 250 pages total
Rate = plans to read 25 pages per day
Time = unknown
Identify which math operation you will need to solve the problem. The clue to
look for is:
How many would each one have? In this case, each one would be the same
as each day.
Answer this question by using the following formula.
It will take Raymond 10 days to read the entire book, if he reads 25 pages per
day.
Plug the answer back into the equation to see if it is correct.
The answer is correct.
Some Helpful Tools
Math: Word Problem Solving - Tutorial
Steps to Follow
Below are some steps that should help make solving word problems a breeze.
Operations Chart
The following chart will help you decide what operation is needed when solving
your word problem.
Subtraction
The order that the numbers are added together makes no difference.
For example: 3 + 4 = 7 and 4 + 3 = 7
Clues to look for:
- What is the combined amount?
- How many is in all?
- How many is there altogether?
The order that the numbers are subtracted is important.
For example: 5 - 2 = 3 but 2 - 5 = -3
Clues to look for:
- How many are left over?
- How many remain?
- How much more is needed?
Multiplication
Division
The order that the numbers are
multiplied is not important.
For example: 8 x 9 = 72 and 9 x 8 = 72
Clues to look for:
- If a unit equals this, how many does this many units equal?
- What is the percent or fraction of something?
The order that the numbers are divided are important.
For example:
Clues to look for:
- What is the average?
- Based on a total amount, how many would each one have or receive?
Addition
Two Formulas
To find the distance of how far someone is traveling, how fast they are going, and
how long will it take for them to get there, use the distance formula: D = R x T
D = distance
R = rate of speed
T = time
To find the amount of something, the cost, or the speed, and the time it takes to complete the task, use the following formula: A = R x T
A = amount
R = rate or speed (either, or)
T = time
Understand what the word problem is asking.
How many miles per hour was Sam driving?
To find the answer to this question, let's use the following formula.
D = R x T
In this case, rate will be expressed in miles per hour. Since miles per hour is
unknown, we will use R to solve for rate (miles per hour).
Distance = 219 miles
Rate = unknown
Time = 3 hours
Rewrite the formula using the information that you already know.
To solve for R, divide both sides by 3 hours. Remember, when you are given the
amount for several equal items and are asked to find the amount for one item use division.
Divide 219 miles by 3 hours in order to find the rate. Since the question originally asked how many miles per hour was Sam driving, the answer will be expressed in
miles per hour. So the answer is 73 mph (miles per hour).
Plug the answer back into the equation to see if it is correct. Since our rate is 73, replace R with 73 in the equation. Then multiply.
The answer is correct.
Keep in mind, when solving word problems, the steps to follow are only guidelines. Shortcuts may be taken. However, try to stay with the main concept to make sure
that the problem is worked correctly. Let's try one more example.
Measurement Chart
in. = inch
ft = feet
yd = yard
mi = mile
Abbreviations:
73 = R
oz = ounce
lb pound
T = ton
pt = pint
gal = gallon
pk = peck
bu = bushel
c = cup
Solving Word Problems
Understand what the word problem is asking.
How much more yarn does Madeline need to complete her project?
Organize the information that is important.
project requires: 3 feet of yarn.
already has: 24 inches of yarn.
amount needed: unknown
Identify which math operation you will need to solve the problem.
The clue to look for is: How much more is needed?
This tells us that we will need to subtract.
First, we will use N to represent "the missing number". Next, we will set up our equation to look like this:
N + 24 inches = 3 feet
Since inches are smaller than feet, we will change feet to inches to make the units the same.
1 foot = 12 inches. (Refer to the Measurement Chart if needed.)
If you have one unit and you need to find out the amount for several units, which operation will you need to use? If you chose multiply, you are correct!
If 1 foot = 12 inches; then
3 feet = 12 + 12 + 12 or 3 x 12 = 36 inches
Rewrite the problem. N + 24 inches = 36 inches
How much more is needed means to subtract. Therefore, let's subtract 24 inches from 36 inches to find our answer.
Madeline will need 12 inches more of yarn.
Check to see if your answer is reasonable.
Plug the answer back into the equation to see if it is correct. Since our missing number N = 12 inches, replace N with 12 inches in the equation. Then add.
If the numbers are equal, the answer is correct.
12 inches + 24 inches = 36 inches
36 inches = 36 inches
The answer is correct.
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Example 1:
Madeline's art project requires 3 feet of yarn. She has 24 inches already. How much more yarn does Madeline need to complete her project?
To solve this problem, follow the steps below:
Example 2:
Sam traveled a distance of 219 miles in 3 hours. How many miles per hour was Sam driving?
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Example 3:
Raymond is reading a 250-page book. He plans to read 25 pages each day. How many days will it take Raymond to read the entire book?
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To solve for time, divide both sides by the rate, which is 25.
Understand what the word problem is asking.
Remove the added information that is not needed to solve the problem.
Organize the information that is important.
Decide which operation to use:
1.
This section will cover some basic steps that will help make solving word problems easier.
Hint: Move 24 inches to the
right of the equal sign to
subtract 24 from 36.
- Addition
- Subtraction
- Multiplication
- Division
Decide if any formulas are needed.
Check to see if your answer is reasonable.
An Equation
An equation is a statement where the values of two mathematical expressions are equal. Below is an example of an equation.
5 + 7 = 12
The equation may contain a letter that can represent any number depending on how it is used. These letters are called variables. Commonly used variables are x, y, and z.
Sometimes, the missing number in an equation will be represented by (N).
N + 7 = 12
You will need to find the missing value to make the statement true.
In our example above, the value of N is 5. Since 5 + 7 = 12, the statement is true.
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