Arithmetic Word Problems Study Guide for McGraw-Hill's ASVAB
Practice questions for this study guide can be found at:
What is a word problem? Basically it is a description of a real-life situation that requires a mathematical solution. To solve a word problem, you need to translate the situation into mathematical terms and then calculate the answer.
All of the questions on the ASVAB Arithmetic Reasoning test are word problems. To do well, you need to learn good word problem–solving skills. The following article will show you many different kinds of arithmetic word problems. For each kind, you'll learn how to translate the facts of the problem into mathematical terms. Then you'll see how to use those terms to set up an equation. Finally, you'll see how to solve that equation for the missing piece of information that you're looking for. To start your study program, look at the following word problem-solving tips.
Key words Many word problems contain key words that tell you what mathematical operation you need to use to solve the problem. It pays to know these key words, so be sure you study the following list.
These key words tell you to add.
These key words tell you to subtract.
These key words tell you to multiply.
These key words tell you to divide.
These key words tell you to use an equal sign.
Setting Up an Equation and Solving For an Unknown
Before you start tackling word problems, you need to know how to set up an equation and solve for an unknown. For each problem, you will be given certain pieces of information ("what you know"). You first need to translate this information into mathematical terms. Then you can use those terms to set up an equation. An equation is nothing more than a mathematical expression that indicates that one mathematical term is equal to another. The terms in an equation are shown on opposite sides of an equal sign. The missing piece of information that you are looking for ("what you need to find") is called the unknown. In your equation, you can represent an unknown by a letter such as x or a.
In the pages that follow, you will see how to set up equations for many different kinds of word problems. The process of solving an equation for an unknown is pretty simple. Work through these examples until you get perfectly comfortable with the process.
Solve for x.
- 25x = 200
This equation is read, "25 times some unknown number x equals 200." Your task is to determine what number x is. Here is how to solve this equation.
- Divide both sides of the equation by 25:
Solve for x:
To solve this type of problem, cross-multiply (45 times x and 3 times 5).
Solve for x:
To solve this problem, cross-multiply (10 times 350 and 50 times x).
- 50x = 3,500
- x = 70
To check your answer, merely substitute 70 back into the equation and see if it works. Reduce the fractions to or cross-multiply (10 times 350 and 70 times 50), making 3,500 = 3,500. Either way, you are correct.
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