ALGEBRA IS A METHOD OF WRITTEN CALCULATIONS that help us reason about numbers. At the very outset, the student should realize that algebra is a skill.  And like any skill -- driving a car, baking cookies, playing the guitar -- it requires practice. A lot of practice. Written practice.  That said, let us begin.

What is algebra ?

• The first thing to note is that in algebra we use letters as well as numbers. But the letters represent numbers. We imitate the rules of arithmetic with letters, because we mean that the rule will be true for any numbers.

Expressions, Identities, Formulae, Equations

Expressions, Identities, Formulae, EquationsAn expression… Is an algebraic statement consisting of at least one

variable and one number. It has no equals sign and so cannot be solved.

An equation…Is an algebraic statement consisting of an

expression and a variable (or another expression) separated by an equal symbol. It can be solved to find the particular values of the variable for which

it is true.A formula…Relates one variable (letter) to another. It consists

of one variable and an expression separated by an equal symbol.

An identity…Is an equation that is always true for any variables

(letter values) you choose.

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

Ex- • 8 + n = 122)A variable can use any letter of the

alphabet.Ex-• n + 5• x – 7• w - 25

Definitions

Definitions3) Algebraic expression – a group of

numbers, symbols, and variables that express an operation or a series of operations.

Ex- m + 8 , r – 34)Evaluate an algebraic expression –

To find the value of an algebraic expression by substituting numbers for variables.

• m + 8 m = 2 2 + 8 = 10

• R – 3 r = 5 5 – 3 = 2

• Simplify – Combine like terms and complete all operations

m = 2• m + 8 + m 2 m + 8• (2 x 2) + 8 4 + 8 = 12

Definitions

Words That Lead to Addition in algebra

• Sum• More than• Increased• Plus• Altogether

Words That Lead to Subtraction in algebra

• Decreased• Less• Difference• Minus• How, many, more

SOME EXAMPLESOF

ALGEBRIC EXPRESSIONS

Write an Algebraic Expression for These Situations

• Scott’s brother is 2 years younger than Scott

• The sum of two numbers is 12

• The difference between two numbers is 5

s - 2

v + c = 12

m – n = 5

Complete This Table

x x + 65

102132

11162738

48 y

2275 x

27)1(3 b

14264 aa

)73(5)2(4 27 aa

722 2 k

01ie

12 x

814 x

521

x

5.0sin x

ba 32

1262 xx

xe

2

245sin

86)43(2 aa

baba xxx

aaa 52431

IRV

maF

rc 2

atuv

a

acbbx

2

42

2mce

n

xx i

222 cba

bcCosAcba 2222

aa 0aa 1

cmxy

10 x

Thank you for your attention