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.
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.
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
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.
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:
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.
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.
In a singing competition, there are 20 contestants. Out of them, 11 are boys. Determine the percentage of boys in the said contest.
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.
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
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
- 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
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
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.
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.
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
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 x 6 x 6
Next example, 7 squared:
= 7 × 7
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 = 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
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 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.
Mathematically, these are types of logarithms limited to base 10.
Also written as:
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.
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.
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