Writing Algebraic Writing Algebraic ExpressionsExpressions

Objectives:Objectives:•know algebra termsknow algebra terms•write an algebraic expression for a word phrasewrite an algebraic expression for a word phrase• write a word phrase for an expressionwrite a word phrase for an expression

DefinitionsDefinitions

Variable – A variable is a letter Variable – A variable is a letter or symbol that represents a or symbol that represents a number (unknown quantity).number (unknown quantity).

8 + 8 + nn = 12 = 12

DefinitionsDefinitions

A variable can use any letter of A variable can use any letter of the alphabet.the alphabet.

nn + 5 + 5

xx – 7 – 7

ww - 25 - 25

DefinitionsDefinitions

Algebraic expression – a group of Algebraic expression – a group of numbers, symbols, and variables numbers, symbols, and variables that express an operation or a that express an operation or a series of operations.series of operations.m + 8m + 8r – 3r – 3

DefinitionsDefinitions

Algebraic equation – an Algebraic equation – an algebraic form containing an = algebraic form containing an = signsign

g + 6 = 45g + 6 = 45 76 – t = 5076 – t = 50

DefinitionsDefinitions

Terms – are algebraic forms Terms – are algebraic forms separated by + and – signs, the separated by + and – signs, the signs being includedsigns being included

3x + 2y - 93x + 2y - 9 -6t - 4s + 5f - 2 -6t - 4s + 5f - 2

DefinitionsDefinitions

Like terms – are terms with exactly Like terms – are terms with exactly the same variable formthe same variable form

7x, 5x, 6x, -12x, -6x7x, 5x, 6x, -12x, -6x -t, 3t, -8t, 9t-t, 3t, -8t, 9t

4r, 6y, -9r, 2y, -y, s, 18y, 4s, -94r, 6y, -9r, 2y, -y, s, 18y, 4s, -9

DefinitionsDefinitions

Constant term / constant – term Constant term / constant – term which does not contain a variablewhich does not contain a variable

2x + 4y -9 2x + 4y -9 4h + 24h + 2 3e – 2t3e – 2t

DefinitionsDefinitions

coefficient – numerical part of a coefficient – numerical part of a term including its signterm including its sign

5w - 95w - 9 7y – 3z – h7y – 3z – h -5r + 2s - 8-5r + 2s - 8

Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua.

When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.

An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua.

NotesNotes

In order to translate a word In order to translate a word phrase into an algebraic phrase into an algebraic expression, we must first expression, we must first know some key word know some key word phrases for the basic phrases for the basic operations.operations.

On the back of your notes:On the back of your notes:AdditionAddition SubtractionSubtraction

MultiplicationMultiplication Division Division

Addition Phrases:Addition Phrases:More thanMore than

Increase byIncrease by

Greater thanGreater than

AddAdd

TotalTotal

PlusPlus

SumSum

Subtraction Phrases:Subtraction Phrases:Decreased byDecreased by

Difference betweenDifference between

Take Away Take Away

LessLess

SubtractSubtract

Less than*Less than*

Subtract from*Subtract from*

Multiplication Phrases:Multiplication Phrases:ProductProduct

TimesTimes

Multiply Multiply

OfOf

Twice or doubleTwice or double

TripleTriple

Division Phrases:Division Phrases:QuotientQuotient

DivideDivide

Divided byDivided by

Split equally Split equally

NotesNotesMultiplication expressions should Multiplication expressions should be written in side-by-side form, be written in side-by-side form, with the number always in front of with the number always in front of the variable.the variable.

33aa 2 2tt 1.5 1.5cc 0.4 0.4ff

NotesNotes

Division expressions should Division expressions should be written using the fraction be written using the fraction bar instead of the traditional bar instead of the traditional division sign.division sign.

2

c5

t 3

x

Write Algebraic ExpressionsWrite Algebraic Expressionsfor These Word Phrasesfor These Word Phrases

Ten more than a numberTen more than a number

A number decrease by 5A number decrease by 5

6 less than a number6 less than a number

A number increased by 8A number increased by 8

The sum of a number & 9The sum of a number & 9

4 more than a number4 more than a number

n + 10

w - 5

x - 6

n + 8n + 9

y + 4

ExamplesExamplesAddition phrasesAddition phrases::

3 more than 3 more than xx

the sum of 10 and a number the sum of 10 and a number cc

a number a number nn increased by 4.5 increased by 4.5

ExamplesExamplesSubtraction phrasesSubtraction phrases::

a number a number tt decreased by 4 decreased by 4

the difference between 10 and a the difference between 10 and a number number yy

6 less than a number 6 less than a number z z

ExamplesExamplesMultiplication phrasesMultiplication phrases::

the product of 3 and a number the product of 3 and a number tt

twice the number twice the number xx

4.2 times a number 4.2 times a number ee

ExamplesExamplesDivision phrasesDivision phrases::

the quotient of 25 and a number the quotient of 25 and a number bb

the number the number yy divided by 2 divided by 2

2.5 divide 2.5 divide gg