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Mth 60 Day 4 2.1a, 2.1b Test #1 • Friday – covers everything from Day 1 • Practice Exams on Hawkes…found in WebTest/take an assigned… • Tests – ONLY ONE TRY – No “do-overs!” Variables & Algebraic Expressions 2.1a Definitions • Variable: a symbol representing a number or a set of numbers. Ex: Φ, β, α, X, Y, Z… • Constant: a symbol representing a fixed quantity. Ex: π, 2, -17… • Algebraic expression: a collection of at least one variable, constants, grouping symbols and mathematical operations (+, -, x, /) Definitions • Term: any piece or part of the expression involving only multiplication and/or division with constants and/or variables. • Variable Term: an algebraic expression containing at least one variable. Ex: -99x, ½ y • Constant Term: an algebraic expression without a variable. Ex: -1/3, 77, 18 • The sign preceding (before) the term is part of the term. Ex: 47 xy 15 z 18 Simplifying Expressions 2.1b Simplify Like Terms Like terms – all terms that are constants or terms that contain the same variable(s) with the same power 4x+6xy-7x2y+9y2x 5-4y-2+9y – rearrange Simplify (verb) 5 4y 2 9y Try it… • Be careful with signs… 4 x 2 3x 2 x 2 y 5x 6 x 2 2 2 Distributive Property (Law) If a, b, and c are any real numbers, variable or expression, then a b c ab ac 2(3 4) 2(3) 2(4) Distributive Property • The Distributive Property is used to remove grouping symbols from an expression/ equation before like terms are combined. • EX: Simplify 4 x 5 y 3 2 x 7 y Try it… 5 x y 2 x y Fraction Bar • A fraction bar is a grouping symbol, similar to parentheses. So combine like terms in the numerator first. EX: Simplify 3z 5 z z 4 Try it… m 5m m 6 Summary • Definitions – learn the language. Speak it! Write it! • Review rules for + - x / of signed numbers Coming up… • Test #1 – Due date October 18th is FIRM – early OK but NO late. – Photo ID required for SMART Lab Test. • Day 5 Reading Guide – 2.1c Exit Ticket 1. Simplify: 4 x 2 3x 2. Simplify: 4 x 5 y 32x 7 y 3. Simplify: x 3x 5x 2