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Lesson 1.1 Translating to Algebraic Expressions Key Words Addition Subtraction Multiplication Division add sum of plus increased more subtract difference minus decreased less than multiply product of times twice of divide divided quotient ratio per Examples: Let n = a number 1) twelve less than twice some number 2) eight more than the ratio of twice a number and five 3) the difference of 45% of a number and one Exponential Notation The expression an, in which n is a counting number means a • a • a • a..... • a n factors In a , a is called the base and n is called the exponent, or power. When no exponent appears, it is assumed to be 1. Thus a1 = a. n Rules for Order of Operations 1. Simplify within any grouping symbols. 2. Simplify all exponential expressions. 3. Perform all multiplication and division working from left to right. 4. Perform all addition and subtraction working from left to right. Examples: 1) 4 2 + 6(7) − 4(1 + 2) = 2) 2(12) + 4(6 + 1) 2 − 4(3 − 1) = 3 +1 To EVALUATE an expression or formula, substitute the given value(s) for the variable(s) and follow the order of operations. 1) 8 xz − y for x = 2, y = 7, z = 3 2) 3a 2 m − 4am 2 for a = 3, m = 2 3) x 2 − [2(a + b) − ab] 2 for x = 12, a = 2, b = 1 4) 4 x 2 + 2 xy − z for x = 3, y = 2, z = 8 5) Find the area of a trapezoid if b1 = 12, b2 = 18, h = 8 b1 A= h b2 1 h(b1 + b2 ) 2