Download Algebraic Expression

Lesson 2.1
Core Focus on
Introductory Algebra
Variables and Expressions
Warm-Up
1. What are two words that mean “add”?
and, sum, plus, together, …
2. What is another word for subtraction?
minus, take-away, difference…
3. Find the value of 80 ÷ 10 − 2 × 4.
0
Lesson 2.1
Variables and Expressions
Write expressions involving variables.
Vocabulary
Variable
A letter that stands for a number.
Algebraic Expression
A mathematical expression that contains numbers, operations and
variables.
variable
c  55
expression
Explore!
Translate Those Words
Step 1 Fold a piece of paper in half vertically. Open
up your paper and then fold your paper in
half horizontally. Open the paper up and lay
it flat on your desk.
Addition
Subtraction
Multiplication
Division
Step 2 Label each section of your paper as shown.
Step 3 Place each word or phrase from the list below
into one of the sections on your paper. Be
prepared to explain your placement of each
word or phrase.
less than
sum
decreased by
quotient
more than
divided by
times
difference
increased by
minus
product
fewer than
Step 4 Draw the mathematical symbol used to represent each operation at the bottom
corner of each box.
Explore!
Translate Those Words
Step 5 Eight algebraic expressions are listed below.
There are two representing each operation.
Place the algebraic expressions into the box
that describes each operation.
x−4
30 − g
6÷p
10k
5w
y + 11
Addition
Subtraction
Multiplication
Division
14 + m
h
2
Step 6 In each box, write your own algebraic expression that uses the operation listed
at the top of that box. Compare your expressions with a classmate. Are the
expressions exactly the same? Should they be?
Methods for Showing Multiplication
Dot
4·y
Parentheses
4(y)
Number and adjacent variable
4y
Good to Know!
One of the most commonly used variables is the letter x.
Because the letter x looks so much like the multiplication sign
, you will not use  to represent multiplication when working
with variables. Instead, you will use one of the methods above.
Example 1
Write an algebraic expression for each phrase.
a. five times k
5k or 5(k) or 5·k
b. seven more than x
x+7
c. f divided by 2
f
f ÷ 2 or
2
When multiplying a
number and variable, write
the number first.
Example 1 Continued…
Write an algebraic expression for each phrase.
d. a number y decreased by seventeen
y – 17
e. eleven plus four times w
11 + 4w or 11 + 4(w) or 11 + 4  w
Example 2
Write a phrase for each algebraic expression.
a. 12 + t
the sum of twelve and t
b. 8x
the product of eight and x
Answers may vary. Can you
think of other answers for
each part of this example?
Example 2 Continued…
Write a phrase for each algebraic expression.
c. u – 5
five less than u
d. 3x – 2
three times x minus two
Communication Prompt
When using variables, you should use the dot for
multiplication rather than ×. Why is this? Give an
example to illustrate your answer.
Exit Problems
Write an algebraic expression for each phrase.
1. twelve more than b
b + 12
2. the quotient of x and 5
x
5
Write a phrase for each algebraic expression.
3. 11d
the product of 11 and d
4. w + 9
the sum of w and 9