Is math a problem that keeps you from acing the Arithmetic Reasoning ASVAB test? You are not alone. Of all the test takers, this subtest seems to be the most challenging however, getting an appropriate preparation will boost your confidence and increase your score. Our comprehensive ASVAB Arithmetic Reasoning study guide is designed to help you master the main math concepts, solve word problems, and develop effective strategies to ace the test. Be it fractions, percentages, or equations, we will help you through the process step by step so that you will go into the test cool, clear-eyed, and confident. Ready? Let’s dive in!

## What is on the ASVAB Arithmetic Reasoning Test?

ASVAB Arithmetic Reasoning tests your ability to solve arithmetic word problems. The questions test the basic concepts in mathematics and how well you have learned to apply them in real life. In this subtest, there are 15 questions on the CAT ASVAB with a time limit of 55 minutes, while the P&P ASVAB requires 30 questions answered in 36 minutes. The calculators are not allowed during the AR ASVAB test. You will have to depend on your mental math capabilities and the ability to work problems out on paper. Here’s a breakdown of the key topics you need to focus on:

### Fraction

You will want to have a good working knowledge of fractions, as they are going to play an important part in the ASVAB Arithmetic Reasoning section. You will be solving problems with adding, subtracting, multiplying, and dividing fractions among other operations, such as converting mixed numbers to and from an improper fraction. Otherwise, you will be able to simplify your work by reducing a fraction to the lowest terms.

An example is as follows:

You will also get word problems with fractions set in more realistic situations such as a quantity that is to be divided into parts or proportions. You will learn the comparison of fractions, acquisition of common denominators, as well as conversion to decimals. You will gain a significant advantage during your test once you learn fraction problem-solving.

### Statistics

Statistics questions on the ASVAB Arithmetic Reasoning test usually consist of interpreting data and a general understanding of statistical measures that are seen frequently like mean, median, and mode. You may be asked to compute the values based on a given set of numbers, or you may be required to interpret data contained in charts, tables, or graphs.

- Mean is defined as the average of a series of numbers that is determined by summing all the numbers and later dividing by the total number of values.
- Median is the middle value when a set of data is organized from largest to smallest, or vice versa. If there is an even number of values, then the median is the average of the two middle numbers.
- Mode is the number that occurs most frequently in data. Of course, there may be more than one mode, or there may be no mode if each value occurs the same number of times.

Besides these general concepts, you might be asked to solve some problems involving event probabilities. In general, the probability of an event is the likelihood of its occurrence, usually described as a fraction or percentage.

An example is as follows:

### Distance, Rate, Time

Distance, rate, and time problems abound in the ASVAB Arithmetic Reasoning subtest. Each of these problems involves the relationship between how far something travels, how fast it is going, and how long it takes to cover a specific distance. These are usually word problems, where you apply the key formula:

Distance = Rate × Time

- Distance is the total quantity that an object is moved.
- Rate is related to the speed at which the object is moving, usually expressed in units like miles per hour (mph) or kilometers per hour (km/h).
- Time is the approximate measure of how long the object was in motion, usually rounded up or down in whole hours or minutes.

Depending on the problem, you may be solving for distance, rate, or time by re-arranging the formula:

An example is as follows:

These problems often involve unit conversions as well. For example, if the time is given in minutes and the rate is in miles per hour, you would need to convert the time to hours before applying the formula.

### Math Operations

Math operations form the very foundation of the ASVAB Arithmetic Reasoning section. You would be needed to carry out basic arithmetic operations such as addition, subtraction, multiplication, and division, sometimes even in word problems. You have to master these operations because they are building blocks on which more difficult mathematical problems get solved.

An example is as follows:

In addition to these simple operations, you’ll also have exercises that include putting more than one operation into one expression. You need to remember the proper order of operation, commonly called PEMDAS: Parentheses, Exponents, Multiplication, and Division from left to right, Addition and Subtraction from left to right. That will give you the exact solution to the problems.

### Percentage

Percentages are important in the ASVAB Arithmetic Reasoning test since you’ll be engaged in solving for percentages, percentage increases, or percentage decreases and then applying them in the real world. Note that percentage means a fraction of one hundred. One essential formula that you will be working with is:

Many problems in percent arise from applications involving sales, discounts, tax, and interest rates. A typical question might look like this:

### Ratio & Proportion

One of the most crucial things to know when trying to solve many kinds of word problems on the ASVAB Arithmetic Reasoning test is how to deal with ratios and proportions. A ratio is a comparison between two quantities. It tells you how many times one value contains or is contained within the other. You may write ratios as two numbers separated by a colon, such as 3:2, or as fractions, such as 3/2.

Proportions are especially helpful when trying to solve problems that involve scaling or measurement conversion. Suppose that a certain area requires a certain amount of paint. You want to find out how many gallons it would take for an area larger than this. Ratio and proportion problems also show up in questions about map scales, recipes, and population density.

An example is as follows:

### Geometry

Geometry refers to properties, measures, and relationships involving figures and shapes. You will be working on problems that require the use of basic principles related to geometric shapes: triangles, circles, rectangles, and squares. Problems will involve finding area, perimeter, volume, or angles, and all are basic learning goals for solving real-world geometry problems.

An example is as follows:

You will also have to apply geometry in word problems, which might involve finding dimensions of objects or areas of land, like the amount of fencing needed for a yard or the volume of water in a tank. These are the aspects that make the knowledge of geometry useful, particularly for tests and practical, everyday problem-solving.

### Unit Conversion

Unit conversion involves changing base units in some measurement systems, either metric or imperial, and this will be one of the important skills tested in the ASVAB Arithmetic Reasoning section. In general, unit problems involve converting one unit of length, weight, volume, or time into another and can be important in solving realistic situations that involve distances, weights, or capacities. Being able to understand unit conversion gives you the guarantee that you will be able to interpret data that comes out in so many varied ways and manipulate it.

An example is as follows:

Generally, when working on unit conversion problems, you would be asked to convert from one unit into another using conversion factors. These conversion factors are merely ratios that tell you how one unit is related to another. Some of the common conversions that you’ll need to know will be listed below:

- Length:

1 mile = 1,760 yards = 5,280 feet

1 yard = 3 feet

1 foot = 12 inches

1 kilometer = 1,000 meters

1 meter = 100 centimeters

- Weight:

1 pound = 16 ounces

1 ton = 2,000 pounds

1 kilogram = 1,000 grams

1 kilogram ≈ 2.2 pounds

- Volume:

1 gallon = 4 quarts = 8 pints = 16 cups

1 liter = 1,000 milliliters

1 quart ≈ 0.946 liters

- Time:

1 hour = 60 minutes

1 minute = 60 seconds

### Number Properties

Number properties are some of the basic concepts of mathematics and these concepts are especially important in working on many problems on the ASVAB Arithmetic Reasoning test. A property of a number describes how it acts under a specific operation, such as addition, subtraction, multiplication, or division. Knowing number properties will help you think through how to solve a problem and sometimes use a shortcut to simplify calculations. Following are some of the number properties you are most likely to encounter: commutative, associative, distributive, identity, and inverse.

- Commutative property: works with addition and multiplication and simply says that the order of the numbers doesn’t change the outcome:

Addition: a + b = b + a

Multiplication: a × b = b × a

- Associative property works with addition and multiplication and states that how the numbers are grouped doesn’t alter the outcome. So you can regroup numbers when adding or multiplying to make calculations easier:

Addition: (a + b) + c = a + (b +c)

Multiplication: (a × b) × c – a × (b × c)

- Distributive Property is most commonly used when there is an operation of multiplication over addition or subtraction in an equation or expression:

a × (b + c) = a × b + a × c

- Identity Property describes numbers that, when added to or multiplied by, do nothing to the value of another number.

Addition: The identity for addition is 0 because a + 0 = a

Multiplication: The identity for multiplication is 1 because a × 1 = a

- Inverse Property: contains numbers that, when applied, produce the identity.
- A prime number is any number greater than 1 that is divisible only by 1 and itself. Examples include 2, 3, 5, 7, and 11. Prime numbers are important when dealing with factors and divisibility questions on the ASVAB. Being able to identify if a number is a prime or composite non-prime number makes some arithmetic problems easier particularly when trying to find greatest common factors or least common multiples.

An example is as follows:

### Equations

Equations test an individual’s ability in terms of understanding, setting up, and solving the mathematical relationships among numbers. Typically, an equation is a mathematical statement that has been set out to show how two expressions are equal; variables, such as x and y, may be used to stand for unknown values. You’ll encounter some simple and some more complicated equations that require some basic algebra skills to solve.

An example is as follows:

## How to study for the ASVAB Arithmetic Reasoning?

Success in the Arithmetic Reasoning subtest of the ASVAB will require both content and practice of problem-solving skills. Ongoing review and focused practice build your confidence and assure better performance on test day. Here are some key strategies from our ASVAB study guide:

### Review math fundamentals

Reviewing math fundamentals is very important in preparation for the ASVAB Arithmetic Reasoning section, as it forms a basis for more complex problem-solving.

- Basic operations like addition, subtraction, multiplication, and division need to be mastered for one to effectively solve multi-step problems.
- Fractions, decimals, and percentages are usually tied in with one another, so converting and solving them according to the situation is a common sight.

This foundational math concept will strengthen one’s accuracy and speed, thus providing self-confidence to tackle even those harder problems on the test.

### Practice word problems

The practice of word problems is a kind of practice that will enable you to use your knowledge of mathematics in real-life situations. Word problems generally involve translating written information into a mathematical equation using skills such as interpreting distances, rates, time, costs, and quantities. These practices will not only widen your velocity and accuracy in solving the problems but also present an opportunity for a better chance of recognizing patterns and strategies that you can adopt for various question types.

### Take the ASVAB Arithmetic Reasoning practice tests

Taking practice tests is an essential part of your preparation strategy in that it allows you to become familiar with the nature of the examination and the types of questions that are going to come. The practice test resembles the main examination in many ways; hence, it serves as a means of putting your acquired knowledge and problem-solving skills into practice under the influence of timing. Practice tests also acclimate you to the pacing and types of questions you will face on the test so that on testing day, you are more prepared to pace yourself and reduce anxiety.

Practice ASVAB Arithmetic Reasoning now

## FAQs

### 1. How to pass Arithmetic Reasoning on the ASVAB?

You should focus on understanding the concepts of mathematics fractions, percentages, and word problems to get the highest passing probability. Practice on a regular basis coupled with timed drills will facilitate handling time effectively and solving questions with efficiency. Access here for more useful strategies to boost your chance of passing.

### 2. Can you use a calculator on the ASVAB Arithmetic Reasoning?

No, calculators are not allowed during the administration of the ASVAB. You must be able to perform mental calculations and work problems manually. Deeper your understanding of the ASVAB calculator policy by clicking this post.

### 3. How is Arithmetic Reasoning scored on the ASVAB?

Your score is based on the number of correct answers, and it counts toward both your AFQT score and line scores, which determine your qualification for certain military jobs. Understanding more about the ASVAB score and how the score affects job prospects.

### 4. How long is Arithmetic Reasoning on the ASVAB?

In the computer version, you have 55 minutes to answer 15 Arithmetic Reasoning questions. In the paper version, you are given 36 minutes to answer 30 questions. Have more insights about the ASVAB test length on our post here.

## Conclusion

Mastering the Arithmetic Reasoning section will go a long way in helping you get a good overall score, and that is possible if you take a proper approach towards it. Pay greater attention to some fundamental areas of math such as fractions, percentages, ratios, and equations. Regular practice will whet your problem-solving skills and increase your test-taking speed. Finally, use our ASVAB Arithmetic Reasoning study guide to help you move one step closer to your military career goals. Good luck!