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1.2- Algebraic Expressions and Models It is time to start remembering Numerical Expressions • A numerical expression consists of numbers, operations, and grouping symbols. • For example, an exponent is a numerical expression that represents repeated factors in multiplication 2 22222 5 Base Exponent Power Algebraic Expressions • A variable is a letter that represents one or more numbers. • When a number replaces a variable it is called the value of the variable. • An expression with variables is called a ____________________________. • When variables are replaced by numbers, you are evaluating the expression and finding the value. Write the expression Substitute values of variables S________ Order of Operations (What we use when evaluating the expressions) • • • • • • P E M D A S *Multiply/Divide and Add/Subtract from left to right! Please excuse my dear Aunt Sally? Simplifying Algebraic Expressions 3x 5x 4 x 10 2 Terms Coefficient Like Terms Constant Terms 2 Models • An expression that represents a real-life situation is a mathematical model. • When you create the expression, you are modeling the real-life situation. Examples • Evaluate the expression using exponents. 3 4 ( 3) (7a 7a ) (5z 5z) 4 Examples • Evaluate the expression. ( 2) 5 1 (3 2) 14 (7 5) 1 2 Examples • Evaluate the expression for the given value of x. 3x 0.5( x 1); x 3 Examples • Evaluate the expression for the given value of x. (25x 3) x; x 3 Examples • Evaluate the expressions for the given values of x and y. (2 y) 5x; x 2, y 1 3 Examples • Write an expression for the area of the right triangle, then evaluate it for x=6. x 4x 1 Examples • You want to buy either a CD or a cassette as a gift for each or 10 people. CD’s cost $13 each and cassettes cost $8 each. Write an expression for the total amount you must spend. Then evaluate the expression when 4 people get CDs. Homework • Worksheet 1.2B (Left Column 1-28) Answers