Basic VocabularyBasic Vocabulary

Math is a language, learn the words!Math is a language, learn the words!

““ExpressionExpression” (a math ” (a math “phrase”)“phrase”)

A name or a symbol for a number A name or a symbol for a number

4 x + 3 3x + 4y - 2 4 x + 3 3x + 4y - 2

Do you see an equal sign in an Do you see an equal sign in an expressionexpression??

““StatementStatement” (a math ” (a math sentence)sentence)

A meaningful assertion that is either A meaningful assertion that is either true or false. true or false.

x + 3 = 5x + 3 = 5

The most common “The most common “statementstatement” is an equation.” is an equation.

Another “Another “statementstatement” could be an ” could be an inequalityinequality. .

x + 3 ≤ 5x + 3 ≤ 5

““Equivalent EquationEquivalent Equation””An equation that means the same thing as the first equation.An equation that means the same thing as the first equation.

x = 2x = 2 2x = 42x = 4

An equation that has the same solution as the first equation.An equation that has the same solution as the first equation.

““TermsTerms””

The individual numbers in an The individual numbers in an expression or an expression or equation.expression or an expression or equation.

4 x + 3 3x + 4y - 24 x + 3 3x + 4y - 2

1 term1 term 2 terms2 terms 3 terms3 terms

““MonomialMonomial”” ““BinomialBinomial”” ““TrinomialTrinomial””

““VariableVariable””

A letter or symbol that takes A letter or symbol that takes the place of a number. the place of a number.

x + 3 = 5x + 3 = 5

‘‘x’ is the x’ is the variablevariable

What number What number does ‘x’ represent?does ‘x’ represent?

3x + 4y = 123x + 4y = 12

‘‘x’ and ‘y’ arex’ and ‘y’ arethe the variablesvariables

What numbers do What numbers do ‘‘x’ and ‘y’ represent?x’ and ‘y’ represent?

““Coefficient”Coefficient”

3x + 4y - 23x + 4y - 2

The number in front of a variable in an expression or an equation.

3 is the 3 is the coefficient of ‘x’coefficient of ‘x’

4 is the 4 is the coefficient of ‘y’coefficient of ‘y’

““ConstantConstant””

3x + 4y - 23x + 4y - 2

A term in an expression or an equationA term in an expression or an equation that does not contain a variable that does not contain a variable

-2 is a -2 is a constantconstant(it’s “constantly” -2)(it’s “constantly” -2)2x + 3 = 52x + 3 = 5

Both 3 and 5Both 3 and 5are are constantsconstants

““SumSum””The The answeranswer when you add when you add two or more numbers together. two or more numbers together.

2 + 3 = 52 + 3 = 5

““AddendsAddends””The The numbersnumbers that are added that are added together to get the sum.together to get the sum.

““FactorsFactors””

The The numbersnumbers that are multiplied that are multiplied together to get the answer. together to get the answer.

2 x 3 = 62 x 3 = 6

““ProductProduct””The The answeranswer when factors when factors are multiplied together.are multiplied together.

““QuotientQuotient”” The The answeranswer when when one number is dividedone number is divided by another number. by another number.

66÷÷ 3 = 2 3 = 2

““DividendDividend””The The numbernumber that that is being divided.is being divided.

““DivisorDivisor””

The The numbernumber that that divides the dividend.divides the dividend.

““Inverse Property of Inverse Property of AdditionAddition””

Any number added to its “opposite” (sign) equals zero.Any number added to its “opposite” (sign) equals zero. 5 + (-5) = 0 5 + (-5) = 0

Think of the Think of the additive inverseadditive inverse of a number as the “of a number as the “oppositeopposite””or “or “negativenegative” of the number.” of the number.

What is the What is the additive inverseadditive inverse of -22? of -22?

““Inverse Property of Inverse Property of MultiplicationMultiplication””

Any number multiplied by is reciprocal Any number multiplied by is reciprocal will equal 1.will equal 1. 1

5

15

What is the What is the multiplicative inversemultiplicative inverse of -1/7? of -1/7?

Any number divided by itself will equal 1.Any number divided by itself will equal 1.

16

6

MultiplicationMultiplication

““repeated additionrepeated addition.” .”

= 3 x 5= 3 x 5 5 + 5 + 55 + 5 + 5

or 3 rows of 5 items.or 3 rows of 5 items.

DivisionDivision Multiplication Multiplication by the inverse or by the inverse or reciprocal of a number.reciprocal of a number.

6

112 612 72

This definition is This definition is essential essential when working with fractions!!!when working with fractions!!!

?2

1

6

1

1

2

6

1 3

1

6

2

What is the difference What is the difference betweenbetween

2

xx2

1

Division by 2 Division by 2 is the same thing as is the same thing as multiplication by multiplication by ½.½.

Nothing!Nothing!and ?and ?

(remember the (remember the definition of divisiondefinition of division ? ?

Order of Operations Order of Operations (PEMDAS)(PEMDAS)““PPlease lease EExcuse xcuse MMy y DDear ear AAunt unt SSally.”ally.”

PParenthesesarenthesesEExponentsxponentsMMultiplicationultiplicationDDivisionivisionAAdditiondditionSSubtractionubtraction

1

4

133 2

14

23 2

14

4*3 413

1

4

133 2

14

23 2

1

4

6 2

14

36 1019

14

12

AssociativeAssociative Property of Property of AdditionAddition

2 + 3 + 4We use PEMDAS (parentheses) to “associate” the 2 of the 3 We use PEMDAS (parentheses) to “associate” the 2 of the 3 numbers together so we know which to add together first.numbers together so we know which to add together first.

(2 + 3) + 4(2 + 3) + 4

= 5 + 4= 5 + 4

= 9= 9

2 + (3 + 4)2 + (3 + 4)

= 2 + 7= 2 + 7

= 9= 9

The property says: when adding 3 or more numbersThe property says: when adding 3 or more numbers together, it doesn’t matter which two of numbers you together, it doesn’t matter which two of numbers you add together first (“associate”), you’ll always get the add together first (“associate”), you’ll always get the same answer. same answer.

Associative Property of Associative Property of MultiplicationMultiplication

2 x 3 x 42 x 3 x 4

We use PEMDAS (parentheses) to “associate”We use PEMDAS (parentheses) to “associate” the 2 of the 3 numbers together.the 2 of the 3 numbers together.

(2 x 3) x 4(2 x 3) x 4

= 6 x 4= 6 x 4

= 24= 24

2 x (3 x 4)2 x (3 x 4)

= 2 x 12= 2 x 12

= 24= 24

The property says: when multiplying 3 or more numbersThe property says: when multiplying 3 or more numbers together, it doesn’t matter which two of numbers you together, it doesn’t matter which two of numbers you multiply together first (“associate”), you’ll always get the multiply together first (“associate”), you’ll always get the same answer. same answer.

CommutativeCommutative Property of Property of AdditionAddition

2 + 32 + 3

3 + 23 + 2

Adding Adding twotwo numbers numbers doesn’t matter which number comes first. doesn’t matter which number comes first.

= 5= 5

= 5= 5

Commutative Property of Commutative Property of MultiplicationMultiplication

2 x 32 x 3 = 3 x 2= 3 x 2

multiplying multiplying twotwo numbers numbers the the orderorder of of multiplication does not matter.multiplication does not matter.

Distributive PropertyDistributive Property (of Addition over (of Addition over Multiplication)Multiplication)

This property is important when variables are involved.This property is important when variables are involved.

2(x + 4)2(x + 4)

= 2 x= 2 x ++ (2 * 4)(2 * 4)

= 2x + 8= 2x + 8

Simplify the following:Simplify the following: 2(x + 4)2(x + 4)

Distributive propertyDistributive property

multiplicationmultiplication

Vocabulary:Vocabulary:

Solution of an Equation Solution of an Equation (that has a variable in it):(that has a variable in it):

the value of the variable that makes the equation truethe value of the variable that makes the equation true. .

31xCan you do this problem in your head?Can you do this problem in your head?

DefinitionDefinitionTo solve an Equation To solve an Equation (that has a variable in it): to (that has a variable in it): to findfind the the value of the variable that makes the equation true. value of the variable that makes the equation true.

REMEMBERREMEMBER anything you do in math must obey the anything you do in math must obey the definitions and properties of math.definitions and properties of math.

Solving an equationSolving an equation involves applying properties and involves applying properties and operations to equations to find the value of the variable that operations to equations to find the value of the variable that makes the equation true.makes the equation true.

Equality PropertiesEquality PropertiesAddition Property of EqualityAddition Property of Equality

Subtraction Property of EqualitySubtraction Property of Equality

Multiplication Property of EqualityMultiplication Property of Equality

Division Property of EqualityDivision Property of Equality

These properties only apply to These properties only apply to equationsequations ( (not expressionsnot expressions)) !!! !!!

Do the same thing to the left and right sides Do the same thing to the left and right sides of the equal sign.of the equal sign.

““same thing left, same thing right”same thing left, same thing right”

Definitions:Definitions:Solution to an equationSolution to an equation: the value of the variable : the value of the variable

that makes the equation “true”.that makes the equation “true”.

Equivalent equationEquivalent equation: has the same solution as : has the same solution as the original equation:the original equation:

1024 x 84 xThe solution to both equations is x = 2.The solution to both equations is x = 2.

They are equivalent equations.They are equivalent equations.

VocabularyVocabularyCoefficientCoefficient The number that multiplies a variable The number that multiplies a variable

or is “in front of” the variableor is “in front of” the variable

x3

VocabularyVocabulary

FormulaFormula: An equation that relates two or more : An equation that relates two or more quantitiesquantities, , usually usually represented byrepresented by variablesvariables..

wlArea *rectangle

QuantityQuantity: An measure of a real world physical property : An measure of a real world physical property (length, width, temperature, pressure, weight, mass, etc.). (length, width, temperature, pressure, weight, mass, etc.).

W W

L

LwLP 22rectangle

Verbal ModelVerbal Model: Writing an equation in words before you : Writing an equation in words before you write it in mathematical symbols.write it in mathematical symbols.

VocabularyVocabulary

Polynomials Polynomials POLYPOLY nomials nomials

32958 2345 xxxxx

many many termsterms each with the each with the same variable same variable raised to raised to an positive an positive INTEGERINTEGER power. power.

xxx 53 57

PolynomialsPolynomials

32958 2345 xxxxx

“Leading Coefficient”

“Degree”

VocabularyVocabularyDetermining the number that the Determining the number that the expression simplifies to if you expression simplifies to if you assume a value for ‘x’.assume a value for ‘x’.

32 x

Evaluating an expressionEvaluating an expression

3)4(2

385

Evaluate the expression for x = -4Evaluate the expression for x = -4

““Like” TermsLike” Terms

1523 4545 xxxx

Which of these terms (if any) are “like” terms?Which of these terms (if any) are “like” terms?

SimplifySimplify means add, subtract, multiply, divide means add, subtract, multiply, divide

1523 4455 xxxx

174 45 xx

PowerPowerWhat is a power?What is a power?

PowerPower: An : An expressionexpression formed by repeated formed by repeatedmultiplication of the same multiplication of the same factorfactor..

43xCoefficientCoefficient

BaseBase

ExponentExponent

The exponent applies to the number or variable The exponent applies to the number or variable immediatelyimmediately to its left, not to the coefficient !!!to its left, not to the coefficient !!!

What does it mean?What does it mean?

x3Means: ‘x’ used as an Means: ‘x’ used as an addendaddend 3 times 3 times

x*3 xxx

3x xxx **Means: ‘x’ used as an Means: ‘x’ used as an factorfactor 3 times 3 times