# Basic Math and Pre-Algebra GED ACT SAT Test Prep Review Flashcards

Elementary arithmetic
Terms Definitions
 Natural or Counting Numbers 1, 2, 3, 4,... Whole Numbers 0, 1, 2, 3,... Odd Numbers Whole numbers not divisible by 2. 1, 3, 5, 7,... Even Numbers Whole numbers divisible by 2. 0, 2, 4, 6,... Integers ...–2, –1, 0, 1, 2,... Negative Integers ...–3, –2, –1 Positive Integers The natural numbers. Rational Numbers Can be written as a fraction. Fractions, such as 2/4 or 5/6. All integers are rational. 7 may be 7/1. Terminating decimals are rational. Repeating decimals are rational. Irrational Numbers Cannot be written as fraction. Pi and square roots, for example. Commutative Property of Addition ORDER does not make a difference. 1 + 3 = 3 + 1 a + b = b + a Associative Property of Addition GROUPING does not matter. (3 + 1) + 3 = 3 + (1 + 3) (a + b) + c = a + (b + c) Identity Element of Addition 7 + 0 = 7 a + 0 = a Additive Inverse The opposite of any number. a + (–a) = 0 Commutative Property of Multiplication ORDER does not matter. 4 x 5 = 5 x 4 a x b = b x a Associative Property of Multiplication GROUPING does not matter (3 x 4) x 2 = 3 x (4 x 2) (a x b) x c = a (b x c) Identity Element of Multiplication 7 x 1 = 7 a x 1 = a Multiplicative Inverse Reciprocal of the number. Any number x reciprocal equals 1. 3 x 1/3 = 1 a x 1/a = 1 Distributive Property 2(4 + 3) = 2(4) + 2(3) Order of Operations for Grouping Symbols DO parenthesis, then brackets, then braces: ( ) then [ ] then { }. Order of Operations PEMDAS Please Excuse My Dear Aunt Sally Parenthesis then Exponents then Multiplication/Division then Addition/Subtraction. WORK from left to right on mult and div THEN work left to right on add and subtraction. Expanded Notation 674 = 600 + 70 + 4 Rounding 5 or higher, round up Divisibility Rule for 2 Ends in even number, including 0. Divisibility Rule of 3 Sum of digits is divisible by 3. Divisibility Rule of 4 Number formed by last two digits is divisible by 4. Divisibility Rule of 5 Ends in 0 or 5. Divisibility Rule of 6 Divisible by 2 and 3 (use both rules) Divisibility Rule of 7 No simple rule. Divisibility Rule of 8 Number formed by last three digits is divisible by 8. Divisibility Rule of 9 Sum of digits is divisible by 9. Factors Numbers multiplied together to get a product. Prime Number Only divided by itself and 1. Composite Number Divisible by MORE than just itself and 1. Numerator In a fraction, the number on top 2/5 2 is the numerator Denominator In a fraction, the number on bottom. 3/7 7 is the denominator. Proper Fraction Numerator is SMALLER than denominator 5/8 Improper Fraction Numerator is LARGER than the denominator 9/4 Mixed Number Contains whole number and fraction. 5 1/3 Factors Whole numbers that when multiplied together yield the number. Common Factors Factors that are the same for two or more numbers. Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12 Common Factors of 8 and 12: 1, 2, 4 Greatest Common Factor (GCF) Largest common factor of two or more numbers Multiples Multiples of a number are found by multiplying that number by 1, of 2, or 3, etc. Multiples of 3: 3, 6, 9, 12... Least Common Multiple (LCM) Smallest common multiple that is common to two or more numbers. Adding and Subtracting Fractions Change denominators to lowest common denominator (LCD). Add or subtract numerators and keep denominators the same. Dividing Fractions Invert (turn upside down) the second fraction and multiply the two fractions together. Minus Preceding a Parenthesis When a minus sign is before a parenthesis, it applies to everything withing the parenthesis. 7 - (4 + 3 - 2) = 7 - 4 -3 + 2 = Absolute Value Numerical value. Distance in units from zero on number line. |-4| = 4 Exponent 5^3 A number places above and to the right of a number. It is the power that it is to be raised. 5^3 = 5 x 5 x 5 = 125 Exponent Rules x^1 = x x^0 = 1 x^-3 = 1/x^3 Squared A number multiplied by itself. 3^2 = 3 x 3 = 9 Perfect Square The square of a whole number. Cubed A number multiplied times itself twice. 2^3 = 2 x 2 x 2 = 8 Square Root of a Number A number when multiplied by itself gives you the original number. Square root of 16 is 4 because 4 x 4 = 16. x^2 is x squared. x^1/2 is the square root of x. The square root of zero is zero. -4^1/2 is -2. Powers of Ten 10^3 = 10 x 10 x 10 = 1,000 10^-3 = 1/10 x 1/10 x 1/10 = 1/1000 Scientific Notation A number between 1 and 10 multiplied by a power of 10. 3.56 x 10^7 = 35,600,000 Multiply in Scientific Notation (3 x 10^3)(4 x 10^2) = 1.2 x 10^6 Multiply whole #s and add exponents. English Measurements 5,280 feet = 1 mile 16 ounces (oz) = 1 pound (lb) 2,000 pounds - 1 ton (T) 2 cups = 1 pint (pt) 2 pints = 1 quart (qt) 4 quarts = 1 gallon (gal) Metric Measurements kilo = thousand hecto = hundred deka = ten deci = tenth centi - hundredth milli = thousandth Precision Exactness of measurement. The smaller the unit of measurement, the more PRECISE the measurement. Perimeter of a Square P = 4s P is perimeter and s is side. Perimeter of a Parallelogram P = 2l + 2w OR 2(l +w) P is perimeter, l is length, w is width. Area of Triangle A = 1/2bh A is area, b is base, h is height. Perimeter P stands for perimeter. The total distance all the way around the outside of a polygon.
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