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Exponents and Order of Operations Exponents • The exponent (little number) indicates how many times the base (big number) appears as a factor. Order of Operations • Parentheses (grouping symbols) • Exponents • Multiplication/Division • Working from left to right in order they appear. • Add/Subtract • Working from left to right in order they appear. Arithmetic Mean • Fancy way of talking about averages. • Mean means average • To average: • add up all the scores and divide by the number of scores. Questions??? A Return to Algebraic Expressions • Term: The number/letter combinations separated by addition signs in an algebraic expression. • In my words: • The “stuff” being added or subtracted together Example: 3x + 5y + 7: terms are 3x, 5y, and 7 Components of an Algebraic Expression • Constant term: fancy name for a number • Variable term: terms with letters • Example: 3xy – 4z + 17 • Variable expression with 3 terms: 3xy, -4z, 17 • 2 variable terms and 1 constant term Variable Terms • Consist of two parts • The variable(letter) part • The number part • Example: − 2xy has a coefficient of 2 − -6j has a coefficient of –6 − W has a coefficient of 1 Algebraic Expressions • Evaluating Algebraic Expressions: • Substitute a given value in for the variable and use order of operations to simplify Translating Verbal Expressions into Variable Expressions • Recognize verbal phrases that translate into mathematical operations. Example of evaluating an expression. Evaluate 3xy – 2x + 7y when x = 2 and y = 3 3(2)(3) – 2(2) + 7(3) 18 – 4 + 21 14 + 21 35 The value of the expression is 35. Questions???? Terms • Like terms • Terms with the same variable part • Same means same letter(s) and power(s) • We simplify variable expressions by combining like terms. • To combine like terms, work with the coefficients of the like terms Combining Like Terms • 3x + 5 – 9x • – 6x + 5 • -5 +3b – 7 – 5b • -5 – 7 = -12 • 3b – 5b = -2b • Answer: -2b – 12 Simplifying Numerical Expressions • Use order of operations. • Simplifies to a single number • Could also be referred to as evaluating Simplifying Algebraic Expressions • Rewrite using as few symbols as possible • Use the distributive property if necessary to remove parentheses. • Combine like terms • More often than not will have numbers and letters in the final answer. Opposite of an expression • -(4a – 3b + 7c) • Change everything on the inside to its opposite • -4a + 3b – 7c Distributive Property • Distributive Property • This property will be used on a continuous basis throughout this course. • a(b + c) = ab + ac − Examples 2(30 + 5) = 2(30) + 2(5) = 60 + 10 = 70 3(x – 4) = 3(x) – (3)(4) = 3x – 12 • Taking the opposite can be considered distributing -1 • -(4a – 3b + 7c) = -1(4a – 3b + 7c) Simplifying using the distributive property • 5x – 9 + 3(2x + 4) • 5x – 9 + (3)(2x) + 3(4) • 5x – 9 + 6x + 12 • 5x + 6x = 11x • -9 + 12 = 3 • Answer: 11x + 3 Distributing a negative • -4(y + 2) = (-4)(y) + (-4)(2) = -4y + (-8) = -4y – 8 Using the Distributive Property to Simplify • 9t – 5r – 2(3r + 6t) • 9t – 5r – 6r – 12t • 9t – 12t = -3t • -5r – 6r = -11r • Answer: -11r – 3t Questions???