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Transcript

M098 Carson Elementary and Intermediate Algebra 3e Chapter 1 Review Vocabulary * Variable Constant Expression Equation Inequality Set {} Real numbers Rational number * * * * * * * * Irrational number Natural numbers Whole numbers Integers Absolute Value Addends Sum Difference Product Quotient Numerator Denominator Multiple Least common denominator (LCD) Factors Prime number Prime factorization Lowest terms Additive inverses Minuend Subtrahend Multiplicative inverses Dividend Divisor Undefined Indeterminate Exponent Base Terms Coefficient Like terms A symbol that can vary in value A symbol that does not vary in value (such as a number) A constant, variable or any combination of constants, variables and arithmetic operations that describes a calculation A mathematical relationship that contains an equal sign A mathematical relationship that contains an inequality symbol (≠, <, >, ≤, ≥) A collection of objects. The symbols used to write a set. All of the numbers represented by the number line Any real number that can be expressed in the form a/b, where a and be are integers and b ≠ 0. Any number that is not rational. The counting numbers {1, 2, 3, 4…} The natural numbers and 0 {0, 1, 2, 3…} The positive and negative natural numbers and 0 {… -3,-2,-1,0,1,2...} A given number’s distance from 0 on a number line. Numbers that are added. The result of an addition. The result of a subtraction The result of a multiplication The result of a division The top number of a fraction The bottom number of a fraction A number that is the product of a given number and an integer The least common multiple of the denominators of a given set of fractions. Numbers that are multiplied A natural number that has exactly two different factors, a and the number itself A factorization that contains only prime factors Given a fraction a/b and b≠0, the only factor common to both a and b is 1. Two numbers whose sum is 0. First number in a subtraction Second number in a subtraction Two numbers whose product is 1. The number being divided The number being divided by The result when a non-zero number is divided by 0. The result when 0 is divided by 0. A symbol written to the upper right of a base number that indicates how many times to use the base as a factor The number in an exponential expression that is repeatedly multiplied. Expressions that are the addends in an expression that is a sum The numerical factor in a term Variable terms that have the same variable(s) raised to the same exponents, or constant terms. Prior Knowledge Comparing Numbers: For any two real numbers a and b, a is greater than b if a is to the right of b on a number line. Which is larger: -12 or -20? V. Zabrocki 2010 page 1 M098 Carson Elementary and Intermediate Algebra 3e Chapter 1 Review Simplify fractions 63 99 Add, Subtract, Multiply Divide real numbers (integers and fractions) Review rules ! 2 2 - 5 vs. (- 5) (Not much in the text on these but stress anyway) 2 2 - 5 : the additive inverse or the opposite of 5 = -25 2 (-5) : the base is -5 = (-5)(-5) = 25 Order of Operations 2. 16 5 2 24 9 33 4 3. 3 4. 3 2 4 3 5. 2 9 15 5 3 1. 6. 1. -4 2 2 2. -28 18 6 3 2 6 2 3 4 25 4. -13/12 2 5. 4 5 20 2 3 6. undefined 2 7. 3 2 16 57 2 8. 15.54 3.7 2 9. 3. 3 9 16 4 81 27 9 7. -50 4 49 100 64 18 3 2 8. 18.8 9. 18 Evaluating expressions 1. 10 1. n2 8n 1 for n 1 2. 2m2 4n for m 3, n 2 2. -26 Determine numbers that will cause an expression to be undefined 1. -3 1. 2. 8 x3 5a a 4a 2 Distributive Property (watch for minus) 1. 73 2m V. Zabrocki 2010 2. 4, 2 1. -21 + 14m page 2 M098 Carson Elementary and Intermediate Algebra 3e Combining like terms 1. 2. 4a 9b a 5 7c 2b 8 7c 5 1 3 2 1 y x 8 2 4 3 4 Chapter 1 Review 1. 3a + 11b – 3 2. 3 3 7 x y 4 8 6 New Concepts V. Zabrocki 2010 page 3