 # ASVAB Math Study Guide

Our ASVAB Math study guide encompasses the simple to complex nature of mathematically-inclined concepts including fractions, percentages, certain math properties, basic algebra, exponents, and logarithms. Do take your time to thoroughly read each topic and understand the given examples.

The ASVAB Mathematics Knowledge section tests your understanding of numerous math areas, concluding algebra and geometry. It is available for both the computerized version (CAT-ASVAB) and the paper-and-pencil version. The CAT ASVAB math test concludes with 16 questions and you have 20 minutes to finish it. The paper-and-pencil version has 25 questions in 24 minutes.

Calculators are not allowed to use in the Mathematics Knowledge section. The best way to prepare for the test is to familiarize yourself with as many  Math questions as you can. Your score on this test is counted to your AFQT Score and directly affects your percentile rank. Be sure you are well prepared for this section before entering the real exam.

## What kind of math is on the ASVAB?

Our ASVAB Math study guide encompasses the simple to complex nature of mathematically-inclined concepts including fractions, percentages, certain math properties, basic algebra, exponents, and logarithms. Do take your time to thoroughly read each topic and understand the given examples.

### Fraction

Multiplication of Fractions

Try to recall these simple fractional terms: Where the variable above the fraction is called the Numerator and the variable below is called the Denominator.

To try this out, let’s try multiplying these fractions: We first multiply the numerators and then the denominators to find the answer.

Take Note:

Try to always reduce the result to its lowest possible terms. Given this example, both numerator and denominator don’t have common factors thus, this fraction can no longer be reduced.

Division of Fractions

For example: This can be done by changing the division sign (÷) into a multiplication sign (×) and then reciprocating the second number. Like the example given above, this case cannot further be reduced.

Mixed Fractions

A fundamental way to deal with mixed fractions is by turning them into an improper fraction which is a different kind of fraction that has a greater numerator than the denominator.

Supposed that we have this mixed fraction: We can convert it through the multiplication of the whole number(3) with the denominator(4) and subsequently, adding the product of the latter with the numerator( 3). As a result, the denominator from the first mixed fraction will be the same as the improper fraction.

Improper to Mixed Fraction Conversion

As we see from the preceding examples, we’ve converted a mixed fraction (known as mixed number) to an improper fraction. But now, we’ll learn about the reciprocal of the matter.

Let’s try this example:

12/7

We can simply convert it by dividing the numerator with the denominator. Meaning, we first divide 7 with 12 resulting in 1 then bring down 5. After this, you’ll put the remainder which is 5 beside the quotient (1) in a fraction manner as a numerator and retain the denominator which is 7.

### Percentage

The percentage formula is utilized when expressing a number between one and zero. More so, it is used to know the parts of a whole in a more specific way. Denoted with the symbol (%), it is primarily used to determine and compare the ratios.

Percentage(P) = (IV ⁄ TV) × 100, where IV is the initial or pre-given value and TV is the total value.

Sample problem:

In a singing competition, there are 20 contestants. Out of them, 11 are boys. Determine the percentage of boys in the said contest.

Solution:

Total number of contestants in the class = 20

No. of Boys in the competition = 11

% of boys in the competition = (11 ⁄ 20) × 100 = (1100 ⁄ 2000) = 0.55 or 55%

### Basic Properties of Numbers

Generally, there are four properties of numbers: associative, commutative, identity, and distributive. Such properties are important rudiments upon advancing to a higher level of mathematics.

Associative Property

Addition: When two or more numbers undergo addition or multiplication, regardless of the way they are arranged, the sum will remain unchanged.

5 + (4 + 1) = 10 or (5 + 4) + 1 = 10

Commutative Property

Multiplication. When two numbers undergo multiplication or addition, regardless of their group, their product or sum remains the same.

8 x 6 = 48 or 6 x 8 = 48

Identity Property

1. Addition and Subtraction. The sum and difference, respectively of any value with zero being that number

5 + 0 = 5 , 5-0=5

2. Multiplication and Division. The product and quotient of any value with one being that number.

15 x 1 = 15, 15/1= 15

Distributive Property

This property entails the solution in an expression such as a(b + c) or literally following the PEMDAS rule.

3 x (4 + 5) = 27 or 3 x 4 + 3 x 5 = 27

### Algebra

It is the study of mathematical symbols along with rules encapsulating variables with distinct contexts and is also referred to as the backbone of mathematics.

Solving for x in a Basic Equation

Oftentimes, we get to solve x in every exam or test given by our teacher or professor. Basically, the main objective is to get the value of x through ‘reverse PEMDAS manipulation. In other words, whatever is done on the left side, will also be performed on the right side of the equal sign.

Sample Problem:

x + 7 = 10

With this, we are trying to determine the possible x value that when subtracted to 7, will have a difference of 10. This may be logically easy but we’ll try getting the x value by itself. For that to happen, we have to remove 7 from the left side by subtracting 7 on both sides.

x + 7 = 10

x + 7 – 7 = 10 – 7

x = 3

Determining the x value in an Inequality Equation

The solving process in finding x is similar to an inequality. One thing it differs is that, through division or multiplication by a negative value, the direction of the inequality’s sign changes.

Sample Problem:

2x + 20 ≥ 40

Like equality’s first step, we start by subtracting 20 on both sides.

2x + 20 ≥ 40

2x + 2  −20 ≥ 40 −20

2x ≥ 20

After that, we then divide 2 into both sides. The inequality’s direction remains unaffected due to the fact that we’ve divided it with positive value.

x ≥ 10

### Exponents

Generally, it involves two numbers and is used when multiplying a number by itself. More so, it is stated as “a raised to the power of n” or aⁿ

One example is, 6 cubed:

6^3
= 6 x 6 x 6
= 216

Next example, 7 squared:

72
= 7 × 7
= 49

Take note:

A value raised to the power of 1 equals itself such as 51= 5 x 1= 5, itself

A value raised to the power of 0 equals 1 such as 70 = 1

You can simply subtract the exponents whenever the base is the same such as

95 / 93
= 95-3
= 92

To check:
95 = 9 x 9 x 9 x 9 x 9 and 93 = 9× 9× 9
95 / 93 = (9 x 9 x 9 x 9 x 9) / (9 x 9 x 9)= 9 × 9 = 92

### Square Roots

To put it simply, the square root is the mathematical inverse of taking a square root, meaning —square root “nullifies” squared values.

Let’s try, 4 squared or 42

42 = 4 × 4 = 16

To put it into perspective, we can figure out what number is necessary to be squared, when we successfully determine the square root of a given number,

Advice: Try asking yourself, “What numerical value squared could give us the given value such as 16?

### Logarithm

Logarithm denoted as log(x) serves as the function in contrast to exponentiation, and is referred as the power to which a given value must be raised to obtain the necessary rate. It is widely known as a math operation that figures out the frequency or number of times a certain value termed as a base, undergoes multiplication by itself. It is also used in various statistical methods that track arithmetic processes in a particular mathematical context.

Common Logarithms

Mathematically, these are types of logarithms limited to base 10.

Also written as: Natural Logarithms

It is a special form of logarithm in which the base is a constant e, where e is an irrational number. The natural log of a number x is written as: Take note that, ln is the inverse of e.

Negative Logarithms

Logarithms don’t usually settle with negative values but this serves as an exemption, such that all values situated between 0 and 1 are deemed as negative algorithms.

## ASVAB Math Practice Test by ABC Elearning

Our ASVAB Mathematics Knowledge study guide and free ASVAB math knowledge practice test will help you understand thoroughly the problems in this area. You can retake our practice test unlimited times to boost your knowledge and confidence.

Take more of our ASVAB practice test or read more ASVAB Study Guide for all 9 ASVAB sections to completely prepare for your coming exam.

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