Lesson 1: Vocabulary

Topic: Expressions and One-Step Equations (Unit 1) E. Q.: Why is it important to be able to translate word problems into expression or equations? Name: _____________________________ Date: _____________________________ Class: _____________________________ Chp. 7 Lesson 1 – Vocabulary

 Order of Operations: Please Excuse My Dear Aunt Sally parentheses, exponents, multiplication & division, addition and subtraction ( ), x 2, ∙ and ÷, + and –  Reverse Order of Operations: - and +, ÷ and ∙, x 2, and ( )

 numerical expression - an expression that contains only numbers (constants) and may contain operations. Ex. (2  3) + 1 3,976 ÷ 7 78  algebraic expression - an expression that contains one or more variables and may contain operation symbols and constants.  Ex y 35  w + z x

equation: A mathematic sentence formed by placing an equal sign between two expressions. Ex = 4,x + 3 = 9,5y – 10 = 15 evaluate – to substitute a number for the variables in an expression and then simplify constants - a quantity, or number, that does not change variables - a letter or symbol used to represent a number Ex. y, x, m, Z

 inverse operations – Operations that undo each other. Ex. addition & subtraction, multiplication & division  solution - A number that when substituted for a variable makes the equation true. Ex. x – 3 = 7 when x = 10  solve – To find all of the solutions of an equation and by finding all of the values that make the equation true.

 function – A rule that relates two quantities so that each input value corresponds exactly to one output value. Examples: y = 2.54x, m = r - 3  input – The value substituted into a function (independent variable). Examples: y = 2.54x The input is the value of x. m = r – 3 The input is the value of r.  output – The value that results from the substitution of a given input into a function (dependent variable). Examples: y = 2.54x The output is the value of y. m = r – 3 The output is the value of m.  Linear Function--A function whose graph is a straight line.

 ordered pair – A pair of numbers that can be used to locate a point on a coordinate plane. ↔ ↕ Ex. (x, y) (input, output) (6, 3)  domain – The set of x values (input value or independent variable) for a given function.  range – The set of y values (output value or dependent variable) for a given function.

 Coefficient : The number found by multiplying just the numbers in a term together. For example: given the product 4∙x∙8, its equivalent term is 32x. The number 32 is called the coefficient of the term 32x  Multiplicative Identity :Multiplying a number by 1 leaves it unchanged: a × 1 = 1 × a = a

Factors : Factors are numbers you can multiply together to get another number Example: 2 and 3 are factors of 6, because 2 × 3 = 6. A number can have MANY factors! Example: What are the factors of 12? 3 and 4 are factors of 12, because 3 × 4 = 12. Also 2 × 6 = 12 so 2 and 6 are also factors of 12. And 1 × 12 = 12 so 1 and 12 are factors of 12 as well. So 1, 2, 3, 4, 6 and 12 are all factors of 12 And -1, -2, -3, -4, -6 and -12 also, because multiplying negatives makes a positive. Looking ahead_____________________________________________________________ In Algebra, factors are what you can multiply together to get an expression. (x+3) and (x+1) are factors of x 2 + 4x + 3:

 Distributive Property The Distributive Law: says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately Example: 3 × (2 + 4) = 3×2 + 3×4 So the "3" can be "distributed" across the "2+4" into 3 times 2 and 3 times 4.