Transcript Unit 1: Language & Notation of Algebra Vocabulary • What is a variable? – a letter that represents a # (value) • What is a.

Unit 1:
Language &
Notation of Algebra
Vocabulary
• What is a variable?
– a letter that represents a # (value)
• What is a constant?
– A value (#) that does not change
• What is a coefficient?
– A # that is multiplied by a variable
• What is a numerical expression?
– May contain only constants and/or operations
• What is an algebraic expression?
– May contain variables, constants, and/or operations
Operation Review
put together/combine
(plus, sum, increased by, more)
put together equal groups
(times, product, equal groups of, per)
find out how much more or less
(minus, difference, less than,
decreased)
separate into equal groups
(divided by, quotient, split, ratio)
Translating from Algebraic Symbols to
Words
Give two ways to write each algebraic expression into words.
Ex. A
x+3
x increased by three
The sum of 3 and a number
Ex. B
n - 15
n decreased by 15
the difference of n and 15
Ex. C
2y
Twice a number
The product of 2 and y
Ex. D
g ÷ 10
g divided by 10
The quotient of g and
10
Translating from Words to Algebraic Symbols
Ex. A
Four more than twice a number.
4  2x
Ex. B
The difference of 15 and a number.
15  x
Ex. C
The product of five and a number.
5x
Ex. D
A number divided by thirty.
Ex. E
Eight less than twice a number is sixteen.
Ex. F Twenty less than a number is sixty.
x
30
2 x  8  16
x  20  60
Order of Operations
Parenthesis (perform operations inside grouping symbols)
Exponents (simplify powers and roots)
Multiply
Divide
Add
Subtract
multiply and divide from left to right
addition and subtraction from left to right
Unit Review
Evaluate:
4x2  3 y  z if x  2, y  1, z  5
Evaluate:
7 x  4 y(12  2x)  62 if x  3, y  4
Translate: Nine less than five times a number is eleven
Translate:
3 y  16  5
24
-111
5 x  9  11
Three times a number decreased by sixteen is five
A prepaid phone card has a credit of 200 minutes. Write an expression for the number of
minutes left on the card after t minutes have been used.
200  t
A cleaning service charges $49.00 to clean a one-bedroom apartment. If the work takes
longer than 2 hours, the service charges $18.00 for each additional hour. What would be the
total cost for a job that took 4 hours to complete?
$85