Integers are numbers without fractions or decimals and include all positive whole numbers, negative whole numbers, and zero. Examples of integers are -5, 0, and 8. On the ASVAB, you may be asked to perform arithmetic operations (addition, subtraction, multiplication, division) using integers or identify which numbers belong in certain categories.<\/span><\/p>\n A rational number can be written as a fraction a\/b, where a and b are integers and b is not zero. For example, 3\/4, -2, and 0.25 are all rational numbers. Even terminating or repeating decimals are rational because they can be written as fractions.<\/span><\/p>\n These are numbers that cannot be expressed as simple fractions. Their decimal expansions are non-repeating and non-terminating. Examples include \u221a2 and \u03c0 (pi). You don\u2019t need to memorize many irrational numbers for the ASVAB, but knowing the distinction helps when answering questions about number sets.<\/span><\/p>\n The set of real numbers includes both rational and irrational numbers. Real numbers are any number you can find on the number line. Understanding how different categories of numbers relate can help you eliminate wrong answer choices.<\/span><\/p>\n Operations with signed numbers are common on the ASVAB. Here\u2019s how they work:<\/span><\/p>\n Mistakes with negative signs are common, especially when multiple steps are involved.<\/span><\/p>\n The absolute value of a number is its distance from zero on the number line, regardless of direction. It\u2019s always non-negative.<\/span><\/p>\n On the ASVAB, you might see absolute value in equations or simple expression evaluation. Pay attention to whether the question is asking for the value itself or the result after operations.<\/span><\/p>\n A factor of a number divides it evenly without a remainder. For example, factors of 12 are 1, 2, 3, 4, 6, and 12. The ASVAB may ask you to find the greatest common factor (GCF) or list all factors.<\/span><\/p>\n A multiple is the result of multiplying a number by an integer. Multiples of 4 include 4, 8, 12, 16, and so on. Questions may ask you for the least common multiple (LCM) or the next number in a list of multiples.<\/span><\/p>\n A prime number has exactly two distinct positive divisors: 1 and itself. Common primes include 2, 3, 5, 7, 11, 13, 17. You should memorize the first ten or so prime numbers for quick recall.<\/span><\/p>\n Prime factorization\u2014the process of breaking a number down into prime factors\u2014might also appear in questions involving GCF and LCM.<\/span><\/p>\n Knowing divisibility rules can save time on the ASVAB when you need to test whether one number divides evenly into another.<\/span><\/p>\n Remainders are what\u2019s left after division. If 14 \u00f7 4 = 3 R2, that means 4 goes into 14 three times with 2 left over. The test may ask you to interpret this or solve problems involving remainders.<\/span><\/p>\n Being fluent in converting and simplifying fractions is essential.<\/span><\/p>\n Exponents indicate repeated multiplication:<\/span><\/p>\n Key exponent rules:<\/span><\/p>\n A square root is the number that gives the original number when multiplied by itself:<\/span><\/p>\n Cube roots and higher may appear, but square roots are most common on the test.<\/span><\/p>\n Used to simplify very large or small numbers:<\/span><\/p>\n You\u2019ll need to convert between standard form and scientific notation and perform operations like multiplying or dividing in scientific notation.<\/span><\/p>\n A factorial is the product of all positive integers up to a given number:<\/span><\/p>\n Factorials appear in counting, arrangement, and probability problems.<\/span><\/p>\n PEMDAS is a guideline for evaluating expressions:<\/span><\/p>\n Example:<\/span><\/p>\n Ignoring the proper order leads to incorrect answers.<\/span><\/p>\n Used to expand or simplify expressions:<\/span><\/p>\n Changing the order of addition or multiplication doesn\u2019t change the result:<\/span><\/p>\n Changing grouping in addition or multiplication doesn\u2019t affect the result:<\/span><\/p>\n Recognizing these can help you simplify complex expressions.<\/span><\/p>\n A ratio compares two values:<\/span><\/p>\n A proportion is an equation of two equal ratios:<\/span><\/p>\n A rate is a ratio of two different units:<\/span><\/p>\n You’ll solve many proportion and rate problems in ASVAB word problems.<\/span><\/p>\n Percentages are tested often, especially in word problems and practical applications.<\/span><\/p>\n Average = (Sum of values) \/ (Number of values)<\/span><\/p>\n The middle number in an ordered list. If the list has an even number of elements, average the two middle ones.<\/span><\/p>\n The most frequent value. There can be multiple modes or none.<\/span><\/p>\n These are often used in word problems involving sets of data.<\/span><\/p>\n Probability measures the likelihood of an event occurring:<\/span><\/p>\n For two events A and B:<\/span><\/p>\nRational Numbers<\/b><\/h4>\n
Irrational Numbers<\/b><\/h4>\n
Real Numbers<\/b><\/h4>\n
Arithmetic with Positive and Negative Numbers<\/b><\/h3>\n
\n
\n
\n<\/span> Example: -3 + (-5) = -8<\/span> <\/li>\n
\n<\/span> Example: -7 + 4 = -3<\/span> <\/li>\n<\/ul>\n<\/li>\n
\n<\/span> Example: 6 – (-2) becomes 6 + 2 = 8<\/span> <\/li>\n\n
\n<\/span> Example: (-3) \u00d7 (-4) = 12<\/span> <\/li>\n
\n<\/span> Example: 5 \u00f7 (-1) = -5<\/span> <\/li>\n<\/ul>\n<\/li>\n<\/ul>\nAbsolute Value<\/b><\/h3>\n
\n
Factors, Multiples, and Prime Numbers<\/b><\/h3>\n
Factors<\/b><\/h4>\n
Multiples<\/b><\/h4>\n
Prime Numbers<\/b><\/h4>\n
Divisibility Rules and Remainders<\/b><\/h3>\n
\n
Fractions and Decimals<\/b><\/h3>\n
Converting Between Fractions and Decimals<\/b><\/h4>\n
\n
\n<\/span> Example: 3\/4 = 0.75<\/span> <\/li>\n
\n<\/span> Example: 0.6 = 6\/10 = 3\/5<\/span> <\/li>\n<\/ul>\nArithmetic with Fractions<\/b><\/h4>\n
\n
\n<\/span> Example: 1\/2 + 1\/3 = 3\/6 + 2\/6 = 5\/6<\/span> <\/li>\n
\n<\/span> Example: 2\/3 \u00d7 3\/4 = 6\/12 = 1\/2<\/span> <\/li>\n
\n<\/span> Example: 3\/4 \u00f7 2\/5 = 3\/4 \u00d7 5\/2 = 15\/8<\/span> <\/li>\n<\/ul>\nExponents, Roots, and Scientific Notation<\/b><\/h3>\n
Exponents<\/b><\/h4>\n
\n
\n
Roots<\/b><\/h4>\n
\n
Scientific Notation<\/b><\/h4>\n
\n
Factorials<\/b><\/h3>\n
\n
Order of Operations (PEMDAS)<\/b><\/h3>\n
\n
\n
Properties of Operations<\/b><\/h3>\n
Distributive Property<\/b><\/h4>\n
\n
Commutative Property<\/b><\/h4>\n
\n
Associative Property<\/b><\/h4>\n
\n
Ratios, Proportions, and Rates<\/b><\/h3>\n
Ratios<\/b><\/h4>\n
\n
Proportions<\/b><\/h4>\n
\n
\n<\/span> Cross-multiplying confirms the equality: 2 \u00d7 6 = 3 \u00d7 4<\/span> <\/li>\n<\/ul>\nRates<\/b><\/h4>\n
\n
Percentages<\/b><\/h3>\n
Conversions<\/b><\/h4>\n
\n
Calculations<\/b><\/h4>\n
\n
Measures of Central Tendency<\/b><\/h3>\n
Mean<\/b><\/h4>\n
Median<\/b><\/h4>\n
Mode<\/b><\/h4>\n
Probability Basics<\/b><\/h3>\n
\n
Examples<\/b><\/h4>\n
\n
Independent Events<\/b><\/h4>\n