Transcript Notes: Translating Expressions

Variable Expressions
2009 SOL A.1
Varina High School
Tammy Wallace
Vocabulary
• A variable is a symbol, usually a letter, used to
represent a quantity. This quantity represents an
element of any subset of the real numbers.
• An algebraic expression may contain numbers,
variables, operations, and grouping symbols. An
algebraic expression may be evaluated by
substituting values for the variables in the
expression.
How are algebraic
expressions used in Algebra?
• Algebraic expressions can be translated to verbal
expressions or word phrases
• Verbal expressions or word phrases, which describe
characteristics of given conditions, can also be
translated into algebraic expressions for the
purpose of evaluation.
In expressions, there are many different
ways to write multiplication:
1. 𝑎𝑏
2. 𝑎 ∙ 𝑏
3. 𝑎 𝑏 or 𝑎 𝑏
4. (𝑎)(𝑏)
5. 𝑎 x 𝑏
We are not going to use the multiplication
symbol (#5) any more. Why do you think we
will not use this anymore?
Division, on the other hand, is
written as:
1)
𝑥
3
2) 𝑥 ÷ 3
Here are some phrases you may have listed.
The terms with * are ones that are often used.
Addition
Subtraction Multiplication
Division
Exponents
sum
difference
produce
quotient
power of ___
increase
decrease
times
divided
squared
plus
minus
multiplied
ratio
cubed
add
subtract
more than
less than
total
Writing Algebraic Expressions
Steps for Writing Algebraic Expressions:
1. Read for understanding
2. Define the variable
3. Translate the words into
numbers/variables/operations
4. Write as an expression
Define a variable and write an
algebraic expression for each phrase.
two times a number plus 5
Read for understanding
two times
a number
plus 5
Define the variable. This can be whatever you want it to be
Let x = “a number”
Translate to numbers
two times
2∙
a number
plus 5
𝑥
+5
Write as an expression
𝟐𝒙 + 𝟓
7 less than three times a number
(NOTE: when the words “more than” or “less than” are
used, write the expression opposite than how you
read it)
Read for understanding
7 less than
3 times
a number
Define the variable
Let x = “a number”
Translate to numbers
7 less than
𝑠𝑜𝑚𝑒𝑡ℎ𝑖𝑛𝑔 − 7
3 times
a number
3∙
𝑥
Write as an expression
𝟑𝒙 − 𝟕
The absolute value of the sum of
a number a 5
Read for understanding
the absolute value of
the sum of
a number and 5
Define the variable
Let x = “a number”
Translate to numbers
the absolute value of
?
the sum of
? +?
Write as an expression
𝒙+𝟓
a number and 5
𝑥 and 5
The quotient of a number cubed
and 12.
Read for understanding
quotient of
a number
cubed and 12
Define the variable
Let x = “a number”
Translate to numbers
quotient of
?
?
a number
cubed and 12
𝑥
?3 𝑎𝑛𝑑 12
Write as an expression
𝒙𝟑
𝟏𝟐
The square root of the product
of 6 and a number squared.
Read for understanding
the product of
square root of
Define the variable
6 and a number
squared
Let x = “a number”
Translate to numbers
square root of
?
the product of
6 and a number
squared
?∙?
6 and 𝑥 2
Write as an expression
𝟔𝒙𝟐
Write an verbal expression for each
algebraic expression
𝟖+𝒂
Answers may vary
Write an verbal expression for each
algebraic expression
𝒎
𝟒
Answers may vary
Write an verbal expression for each
algebraic expression
𝟑
𝒏−𝟓
Answers may vary
Write an verbal expression for each
algebraic expression
𝒙𝟐 + 𝟔
Answers may vary