EXPRESS ME ALGEBRAICALLY!!

ALGEBRA

Find the definition of the following terms:

• Algebra• variable• replacement set• substitution• constant• symbols of

grouping• symbols of

relationship

• algebraic term• algebraic

expression• factors• numerical

coefficient• literal coefficient 

ALGEBRADefined as a branch of

mathematics which generalizes the facts in arithmetic.

In the language of algebra, letters along with numbers and operation symbols are used to create expressions.

VARIABLECan stand for different numbers at different times.

Represents any number from a given replacement set.

EXAMPLES:

Any letter in the ENGLISH ALPHABET such as X, Y, Z, A, B, and C.

x + 7b2 – 4ac

REPLACEMENT SET

The set of values of the variable.

SUBSTITUTIONReplacing a variable by a constant.

EXAMPLES: let x ={1, 2, 3} replacement set

x + 7x= 1 x = 2 x = 3x + 7 x + 7 x + 71 + 7 2 + 7 3 +7 8 9 10

CONSTANTA symbol which has exactly one number in its replacement set.

EXAMPLES:

7, 4, and 1 1. = 3. 141592654…

SYMBOLS OF GROUPING

Parentheses: ( )

Brackets: [ ]

Braces: { }

Bar or fraction bar: ____

EXAMPLES:

1 1 – { 1 2 – [ 4 – (8 + 9 ) ] – 1 3 }1 1 – { 1 2 – [ 4 – 1 7 ] – 1 3 }1 1 – { 1 2 – 1 3 + 1 3 }1 1 – 1 2- 1

SYMBOLS OF RELATIONSHIP

≠ Is not equal to≤ Is less than or equal to≥ Is greater than or equal

to< Is less than> Is greater than= Equals, is equal to, is

EXAMPLES:

x + 7 < 1 0 x = 11 + 7 < 1 08 < 1 0 √

FACTORSThe numbers and symbols in a product.

EXAMPLES:

(-3) (2) = -6

Factors product(-3 x ) (2 x ) = -6 x2

Factors product

NUMERICAL COEFFICIENT

The number in an algebraic term.

LITERAL COEFFICIENT

A letter used to represent a number

EXAMPLES:

4 x

Numerical coefficient Literal coefficient

-45 abc

Numerical coefficient Literal coefficient

ALGEBRAIC TERMEither a single number, a letter, or a product of several numbers or letters.

EXAMPLES:

x + 7

algebraic term term2x + 3y – 4z

term term term

ALGEBRAIC EXPRESSION

A statement containing one or more terms connected by plus or minus signs.

EXAMPLES:

x + 7

Algebraic expression2x + 3y – 4z

expression

ALGEBRAIC EQUATION

A statement containing one or more terms connected by plus or minus signs with the symbol of equality.

EXAMPLES:

x + 7 = 10

Algebraic Equation2x + 3y – 4z = 20

Equation

ALGEBRAIC term expression

equation 2x, 29 2x + 29 2x + 29 = 50

x, y x - y x - y = -10

a2 , 2b, 5 a2 + 2b - 5 a2 + 2b – 5 = 9

ASSIGNMENT E-Math Book, page 165, Vocabulary and Concepts no.s 1-10. Page 167, VII: Identifying literal coefficients, no.s 59-63 and page 165, IX: Identifying numerical coefficients, no.s 65-69.