Math 8 SOL 8.14 (1-2, 1-3, 1-5, 4-5, 4-6)
Ms. Graham/
Translate Phrases, Simplify Expressions NOTES
Mr. Barlock
Name: _______________________________ Block: _______ Date: _____________
Translating Verbal Phrases into Algebraic Expressions
Vocabulary:
Algebraic Expression
A mathematical sentence containing numbers, _______________, and
________________ (such as addition, subtraction, multiplication, and division)
that are grouped together to show the value of something.
Key words to recognize:
Addition
Subtraction
Multiplication
Division
Examples:
Phrase
The product of eight and seven
Key Word
product
Expression
_______________________
The difference of nine and a number
__________
_______________________
The sum of a number and four
__________
_______________________
The quotient of ten and a number
__________
_______________________
Four less than a number
__________
_______________________
The quotient of a number and six
__________
_______________________
The sum of two different numbers
__________
_______________________
Examples:
b) six dollars an hour times the number of hours
a) five years older than her brother
Define the variable: ________________
Define the variable: ________________
Translate: _______________________
Translate: _______________________
1
Math 8 SOL 8.14 (1-2, 1-3, 1-5, 4-5, 4-6)
Translate Phrases, Simplify Expressions NOTES
Translating Verbal Phrases into Algebraic Equations
Ms. Graham/
Mr. Barlock
Vocabulary:
Algebraic Equation
A mathematical sentence that contains an _____________ sign (______).
Look for key words such as “is” or “is the same as” to know we are creating an equation, which
is made up of two expressions and an __________ sign (=).
Example: A number less 8 is 22  _______________
Word problem: Niagara Falls is one of the most visited waterfalls in North America, but it is
not the tallest. Yosemite Falls is 2,249 feet taller. If Yosemite Falls is 2, 425 feet high, write
an equation to find the height of Niagara Falls.
You try: translate the verbal phrase into an algebraic expression or equation.
a) 18 seconds faster than Tina’s time
b) the quotient of twice a number and 9
c) an adult cat has 2 fewer teeth than a human
d) the sum of 6 and a number is 2
e) the original price decreased by $5 is $34
f) 5 shirts at $d each is $105.65
2
Math 8 SOL 8.14 (1-2, 1-3, 1-5, 4-5, 4-6)
Translate Phrases, Simplify Expressions NOTES
Review Simplifying Fractions
Ms. Graham/
Mr. Barlock
1. Are the three fractions equivalent?
2. Which figure is divided into the least number of parts?
3. Which fraction would you say is in simplest form, and why?
A fraction is in simplest form when the ______________ ____________ _____________
(_____) of the numerator and denominator is _____.
Simplifying Algebraic Fractions
Algebraic fractions have _______________ in them
We simplify them in a similar way as numeric fractions
9
b) Simplify Algebraic Fraction
a) Simplify Numeric Fraction:
 Simplify numbers, if any
12


Way 1: Divide by GCF
9
9 3 3


12 12  3 4
You Try:
a) Simplify:
Way 2: Factor into
primes and “slash”

75
105
b)
3
Simplify variables using “way 2”: factor and “slash”
16xy3
36x2 yz
Math 8 SOL 8.14 (1-2, 1-3, 1-5, 4-5, 4-6)
Ms. Graham/
Translate Phrases, Simplify Expressions NOTES
Mr. Barlock
A monomial is an expression that consists of a number, a variable, or a product of numbers
and/or variables.
Examples of monomials:
NOT monomials:
Multiplying and Dividing Monomials
Multiply 23  24
Divide
26
22
23  24 = (__*__*__)*(__*__*__*__) = ____
Multiply x3∙x2 = _____________ = ________
Rule: When multiplying powers with the same
__________, keep the base and add the
_____________.

Rule: When dividing powers with the same
__________, keep the base and subtract the
______________.
If there are numbers or more than one
variable type, do each separately:

Example: (2xy2)(-3x2y3) =
(2)(-3)(x)(x2)(y2)(y3) = -6x3y5
If there are numbers or more than one
variable type, do each separately:
Example:
 4x5 y 7  2x2 y 5

5
10x3 y 2
You try: Simplify by multiplying or dividing exponents…
a) 73  7
b) x5  x2
57
d) 4
5
e)
c) (-4n3)(2n6)
y5
y3
f) 
4
2k 8
10k 5