1. Chapter 1 Lesson 1 Variables and Expressions
Objective:
Evaluate expressions containing variables and translate verbal phrases into algebraic expressions.

2. Operation Vocabulary – What Each Sign Means+ - x
plus
sum
more than
increased by
total
in all
minus
difference
less than
subtract
decreased by
times
product
multiplied
each of
divided
quotient

3. Examples Translate each phrase into an algebraic expression.
a number decreased by eight
Let n represent the number.
The words ‘decreased by’ suggests subtraction.
The algebraic expression is n – 8.
b. seven more than twice as many dollars.
Let d represent dollars.
The words ‘more than’ suggest addition and the word twice
is another way of saying ‘two times’.
The algebraic expression is 7 + 2d or 2d + 7

4. Examples Translate each phrase into an algebraic expression.
c. a number increased by eight
Let b represent the number.
The words ‘increased by’ suggests addition.
The algebraic expression is b + 8.
d. 15 plus the quotient of 20 and x.
The word ‘plus’ means addition.
The words ‘quotient’ suggest divide.
The algebraic expression is /x or 20/x + 15

5. Examples Translate each algebraic expression into a phrase. e. 7h
Two things beside each other mean multiply.
Answer: seven times h or seven multiplied by h
f. 5 - x
What you have to be careful about here is that you get your
words in the right order. Are you subtracting 5 from x or
x from 5? Whatever is second is being subtracted from the first.
Answer: x subtracted from 5
3m + 2
Answer: two added to three times m OR
two more than three times m OR
three times m plus 2
There are several different ways to write this!

6. A Little Harder…
Draw a picture representing a rectangle whose length is
eight less than four times its width. Write an expression
for the perimeter of the rectangle.
We know something about the length but have no clue about width, so…width is our variable.
Eight less than means subtract. Four times means multiply. So subtract eight FROM four times.
Now, how do you find perimeter?
Add up all the sides!
w + w + 4w – 8 + 4w – 8
Do you remember how to combine like terms?
10w - 16 w
4w - 8