**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 it 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 *

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

5 + 0 = 5 , 5-0=5

- 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 in equality 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.

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** for other areas to cover all ASVAB knowledge.