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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, 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
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
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