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7 Math Vocabulary # 2 (Expressions and Equations).notebook 7th Grade Math Vocabulary Ahrens Operation A calculation by a mathematical process. Expressions and Equations calculators perform operations Expressions and Equations Glossary x exponents are operations too Operation Operation Order of Operations A mathematical process. The rules of which calculation comes first in an expression. Addition Subtraction Multiplication Division + 3 y = y y y Parentheses, Exponents, Multiplication or Division, Addition or Subtraction + _ x ÷ ÷ 21 3 = 7 7x = 21 11 = 3y + 2 4 x 5 = 20 5 + x = 5 Please Excuse My Dear Aunt Sally sign 11 1 = 3b + 1 Operation Order of Operations Order of Operations Expression The rules of which calculation comes first in an expression. Numbers, symbols and operations grouped together that show the value of something. Parentheses Exponents Multiplication Division Addition Subtraction "Please Excuse My Dear Aunt Sally" Order of Operations 7 + (6 x 52 3) 7 + (6 x 25 3) 7 + (150 3) 7 + (147) 150 2 3 2 + 1 An expression is one side of an equation. 2 x 3 = 6 Expressions DO NOT have equals signs. Expression 1 7 Math Vocabulary # 2 (Expressions and Equations).notebook Ahrens Algebraic Expression Expression An expression that consists of one or more: numbers, variables, and operations. Numbers, symbols and operators (such as + and ×) grouped together that show the value of something. 7x 2 9b 0.5a 7 x 6 4x Remember! 3y + 2 7x 7x = 21 "7 times x" "7 divided by x" 11 = 3y + 2 3 + 2 = y x 2 number: operation: variable: number: operation: variable: number: operation: variable: 11 1 = 3z + 1 Expressions equals sign: Algebraic Expression Evaluate Inverse Operations To find the value/amount of something. Operations that "undo" each other. They are opposites. You cannot "evaluate" an algebraic expression if you do not know the value of the variable. If x=3, then 2x is 2 times 3; so 2x = 6 Addition reverses subtraction + + Subtraction reverses addition Evaluate The operation that reverses the effect of another operation. Addition _ Subtraction Multiplication x ÷ Division 5 + x = 5 + 5 + 5 x = 10 Inverse Operation x x Multiplication reverses division 9 32 9 Square roots reverses squaring Inverse Operations Inverse Operation + Division reverses multiplication Squaring 32 reverses square roots 11 = 3y + 2 2 2 9 = 3y ÷ 3 ÷ 3 3 = y Variable A letter or symbol that represents a changeable or unknown value. 4x + 2 x x variable x = ? 2x = 6 Variable 2 7 Math Vocabulary # 2 (Expressions and Equations).notebook Ahrens Isolate the Variable Variable To move the variable to one side of the equation, and all of the numbers to the other side. A symbol for a number that is unknown. any letter towards end of alphabet! x y u z v *Sometimes Greek! Inverse x operation 7x = 21 Expression 1: Only the variable 2y = 12 11 = 3y + 2 2 2 To isolate the variable, use inverse operations & properties of numbers. y = 6 11 1 = 3z + 1 Expression 2: Everything else Variable Isolate the Variable Solution Solution Set A value you can put in place of a variable that would make the statement true. A set of values that can make a statement true. x + 4 = 9 Solution: x = 5 3y 6 Solution: y 2 The answer to a math problem. The #s in a solution set are written in curly brackets. { } Constant A fixed value, a number on its own, whose value does not change. A constant may either be positive or negative. constant 3y constant Constant y={4,5,6,7} Solution Set Constant 11m 7 y2 = 16 y = {4,4} Solution 2 + 4x 3 < y < 7 There is no constant. A number that is on its own within an expression or equation. 4 Tricky! 69 110 π 1/2 0.45 7 8 A fixed value. 7x These are not constants. These are coefficients! 7x = 21 3z 11 = 3y + 2 3y 11 1 = 3z + 1 Constant 3 7 Math Vocabulary # 2 (Expressions and Equations).notebook Ahrens Term Coefficient A number multiplied by the variable. 4x + 2 x4 coefficient Coefficients are in front of the variable. 4 x = x+x+x+x A single number or variable, or a variable with a coefficient. 4x 4x + y 1 term Term Like Terms Like Terms Terms that have the same variable raised to the same power Like terms 4x + y different variables 3 terms 2 terms Coefficient 4x2 + x2 4x + y 1 4x + x2 different powers Terms whose variables (and their exponents) are the same. 3x x 1/2x 15.7x 5x 2.3x Like Terms 5x3 5 x3 27x3 2x3 1/4x3 5x3 2.7x3 NOT 5x2 LIKE TERMS! 5x Like Terms Equation Equation Two expressions that are equivalent to each other. Equivalence is shown with an equal sign. A mathematical statement, in symbols, where two things are exactly the same (or equivalent). 4x= 8 equivalent expressions 4 = x3 5x4 x3 no equivalence 1 + 2 = 3 22 = 20 + 2 7x = 21 (where x = 3) 4 + 9 = 13 = 11 3y + 2 (where y = 3) equivalent expressions 11 1 = 3z + 1 Equation Equation 7 + 4 = 90 5 = 3 + 10 3x + 6 = 11 (where x = 3) (where z = 3) 4 7 Math Vocabulary # 2 (Expressions and Equations).notebook Distributive Property Equivalent Equal; the same amount or value. 3+3=3x2 = For all real numbers a, b, c, a(b+c) = ab + ac and a(b c) = ab ac. a(b + c) = ab + ac Formula To find all numbers or variables that divide into all of the parts of an expression. = 13x + 8z 2x + 4y = 7(x + 5) 2 • x + 2 • 2 • y cannot be factored (terms have nothing in common). A special type of equation that shows the relationship between different variables. Numbers and symbols that show how to work something out. Distance Formula: distance = rate x time d = r x t PRIME = = 7 • x + 7 • 5 3(x + 4) = 48 (3)(x) + (3)(4) = 48 3x + 12 = 48 3x = 36 x = 12 Distributive Property Factoring 7x + 35 3(2 + 4) = (3)(2) + (3)(4) = 6 + 12 = 18 3(2 4) = (3)(2) (3)(4) = 6 12 = 6 a(b c) = ab ac Equivalent The distributive property in reverse. Ahrens Area of a circle Formula: Celsius to Fahrenheit Formula: 5 C = (F 32) 9 Area = π(radius)2 A = πr2 2(x + 2y) Factoring Formula Addition Property Subtraction Property If a=b, then a+c=b+c for all real numbers a, b, and c. The same number can be added to each side of the equation without changing the solution of the equation. If a=b, then ac=bc for all real numbers a, b, and c. The same number can be subtracted from each side of the equation without changing the solution of the equation. a = 2 b = 2 c = 4 a = b a + 4 = b + 4 2 + 4 = 2 + 4 6 = 6 a = b x 3 = 5 + 3 + 3 x = 8 Addition Property z 14 = 6 + 14 + 14 z = 20 a = 2 b = 2 c = 4 a = b a 4 = b 4 2 4 = 2 4 2 = 2 a = b x + 3 = 5 3 3 x = 2 z + 7 = 20 7 7 z = 13 Subtraction Property 5 7 Math Vocabulary # 2 (Expressions and Equations).notebook Ahrens Multiplication Property Division Property If a=b, then ac=bc for all real numbers a, b, and c. Each side of an equation can be multiplied by the same number without changing the solution of the equation. If a=b, and c=0, then a/c=b/c for all real numbers a, b, and c. Each side of an equation can be divided by the same nonzero number without changing the solution of the equation. a = 2 b = 2 c = 4 a = b a x 4 = b x 4 2 x 4 = 2 x 4 8 = 8 z ÷ 2 = 10 x 2 x 2 z = 20 a = b x ÷ 3 = 5 x 3 x 3 x = 15 a = 2 b = 2 c = 4 a = b a = b x x 3 = 5 ÷ 3 ÷ 3 x = 5/3 a ÷ 4 = b ÷ 4 2 ÷ 4 = 2 ÷ 4 .5 = .5 Multiplication Property Minimum The lowest or least amount or value. Greater than or equal to smaller larger larger A comparison of two numbers that are not, or may not, be equal. smaller z = 20 Division Property Inequality Greater than z x 2 = 10 ÷ 2 ÷ 2 Less than or equal to You must drive at least 40 mph. Less than Inequality Minimum includes the smallest possible value. You must be at least this tall to ride. It means ____ or more. Minimum Maximum Dependent Variable The highest or greatest amount or value. The variable whose value varies based on the value of another variable. Maximum includes the highest value. It means ____ or less. Maximum Equations Graphing y = x The dependent variable is always along the y axis. 2 The value of y is determined by the value of x. Function Tables The (x) (y) dependent 1 1 variable is 4 always the 2 9 3 output (y). 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 Dependent Variable 6 7 Math Vocabulary # 2 (Expressions and Equations).notebook Ahrens Function Table Rule Organizes the special relationship between x and y values. Each of its input values gives back exactly one output value. Defines the relationship between the input and the output, using an algebraic equation. It says what happens to the input in a function. (x) (y) 1 1 2 4 3 9 The output (y) depends on the input (x). x is the independent variable, on the left, and y is the dependent variable, on the right. 3 Rule: In pu t y = 4x+2 ut p ut O 9 Rule: y = x2 Function Table Rule: (x) (y) y = 3x (x) (y) 1 3 2 6 3 9 1 6 2 10 3 14 Rule Input Output The input is the independent variable in a function (x). The output is the dependent variable in a function (y). In The (x) (y) output (y) 1 1 depends 4 2 on the input (x). 3 9 3 put y = x 2 Input The value of y is determined by the value of x. Input ut tp Ou 9 Rule y = x2 The (x) (y) output (y) 1 1 depends 4 2 on the input (x). 3 9 y = x 3 In pu t t pu 2 Output The value of y is determined by the value of x. t Ou 9 Rule y = x2 Output 7