Transcript Algebra
Algebra Algebra is a part of mathematics that uses letters or symbols to represent changing or unknown values. Variable Variable • a letter used to represent a value that can change or vary • in 4x – 1, the letter x is a variable Identify the variable: 2x 3y -2x2 6a Term Term • a number and a variable together or just a number • Examples: 4x 7 -3y 17w2 v Give three other examples of a term Numerical Coefficient Numerical Coefficient • The number in front of the variable. • If no number is visible it is assumed to be 1. • Examples: 5x has a numerical coefficient of 5 -3xyz has a numerical coefficient of -3 z has a numerical coefficient of 1. What is the numerical coefficient of: 2y -63f w -t Literal Coefficient Literal Coefficient • The non-numeric factor of a term • Examples: in 4x the literal coefficient is x in 3x2, the literal coefficient is x2 What is the literal coefficient of: 3y -8u 6ab 7x2y3z4 Expression Expression • Numbers and variables (terms), combined by operations • Examples: 2x + 3 two terms x - y + z three terms x - yz two terms How many terms are in the following? 3x + 7 4x – 5t + 2 6d – 7x2 + 3 Alge-Tiles 1 -1 x -x x2 - x2 We can represent a term or an expression by drawing the number of tiles the term or expression indicates: 3x means 3 groups of x 2x2 means 2 x2 tiles -4 means 4 negative ones 5x + 2 3x2 – 6x + 3 Making Zero Similar to integers, the positive and negative Alge-Tiles combine to “make zero”. Examples: What expressions are represented by the following groups of tiles? 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) Draw tiles to represent the following expressions: 1) 5x + 2 2) -6x – 4 3) 4x2 – 3x + 6 4) -7x2 + 5x – 6 5) -2x2 – 3x – 11 6) 8x2 – 6x + 9 7) -3x + 4x 8) -5x + 12x 9) 10x2 + 6x2 10) 5x + 3x 11) -3x2 + 4x2 12) -3x – 5x 1) 5x + 2 2) -6x – 4 3) 4x2 – 3x + 6 4) -7x2 + 5x – 6 5) -2x2 – 3x – 11 6) 8x2 – 6x + 9 7) -3x + 4x 8) -5x + 12x 9) 10x2 + 6x2 10) 5x + 3x 11) -3x2 + 4x2 12) -3x – 5x