Download per of less than more ratio twice decreased increased

Lesson 1.1
Translating to Algebraic Expressions
Key Words
Addition
Subtraction
Multiplication
Division
add
sum of
plus
increased
more
subtract
difference
minus
decreased
less than
multiply
product of
times
twice
of
divide
divided
quotient
ratio
per
Examples:
Let n = a number
1)
twelve less than twice some number
2)
eight more than the ratio of twice a number and five
3)
the difference of 45% of a number and one
Exponential Notation
The expression an, in which n is a counting number means
a • a • a • a..... • a
n factors
In a , a is called the base and n is called the exponent, or power. When no
exponent appears, it is assumed to be 1. Thus a1 = a.
n
Rules for Order of Operations
1.
Simplify within any grouping symbols.
2.
Simplify all exponential expressions.
3.
Perform all multiplication and division working from left to
right.
4.
Perform all addition and subtraction working from left to right.
Examples:
1)
4 2 + 6(7) − 4(1 + 2) =
2)
2(12)
+ 4(6 + 1) 2 − 4(3 − 1) =
3 +1
To EVALUATE an expression or formula, substitute the given value(s) for the
variable(s) and follow the order of operations.
1)
8 xz − y for x = 2, y = 7, z = 3
2)
3a 2 m − 4am 2 for a = 3, m = 2
3)
x 2 − [2(a + b) − ab] 2 for x = 12, a = 2, b = 1
4)
4 x 2 + 2 xy − z for x = 3, y = 2, z = 8
5)
Find the area of a trapezoid if b1 = 12, b2 = 18, h = 8
b1
A=
h
b2
1
h(b1 + b2 )
2