
Writing
Algebraic Expressions 

Unit 7
> Lesson 4 of 8 
Problem: 
Ms. Jensen likes to divide her class into groups of 2. Use
mathematical symbols to represent all the students in her class.


Solution: 
Let g represent the number of groups in Ms. Jensen's class. 

Then 2 · g, or 2g can represent "g groups of
2 students". 
In the problem above, the variable g represents the number of groups in Ms. Jensen's class.
A variable is a symbol used to represent a number in an expression or an equation.
The value of this number can vary (change). Let's look at an example in which we use a variable. 
Example 1:

Write each phrase as a mathematical expression.



Phrase 
Expression 
the sum of nine and eight 
9 + 8 
the sum of nine and a number x 
9 + x 

The expression 9 + 8 represents a single number (17). This expression is a
numerical expression,
(also called an arithmetic expression).
The expression 9 + x represents a value that can change. If x is
2, then the expression 9 + x has a value of 11. If x is 6, then
the expression has a value of 15. So 9 + x is an
algebraic expression.
In the next few examples, we will be working solely with algebraic expressions. 
Example 2:

Write each phrase as an algebraic expression.



Phrase 
Expression 
nine increased by a number x 
9 + x 
fourteen decreased by a number p 
14  p 
seven less than a number t 
t  7 
the product of 9 and a number n 
9 · n or 9n 
thirtytwo divided by a number y 
32 ÷ y or


In Example 2, each algebraic expression consisted of one number, one operation and
one variable. Let's look at an example in which the expression consists of more than one number and/or
operation. 
Example 3:

Write each phrase as an algebraic expression using the variable n.



Phrase 
Expression 
five more than twice a number 
2n + 5 
the product of a number and 6 
6n 
seven divided by twice a number 
7 ÷ 2n or 
three times a number decreased by 11 
3n  11 

Example 4:

A small company has $1000 to distribute to its employees as a bonus. How much money will
each employee get?


Solution:

Let e represent the number of employees in the company. The amount of money each
employee will get is represented by the following algebraic expression:




Example 5:

An electrician charges $45 per hour and spends $20 a day on gasoline. Write an algebraic expression
to represent his earnings for one day.


Solution:

Let x represent the number of hours the electrician works in one day. The electrician's
earnings can be represented by the following algebraic expression:


Solution:

45x  20

Summary: 
A variable is a symbol used to represent a number in an expression or an equation. The
value of this number can change. An algebraic expression is a mathematical expression that
consists of variables, numbers and operations. The value of this expression can change.

Exercises
Directions: Choose the algebraic expression that correctly represents the phrase provided. Select your answer by clicking on its button. Feedback to your answer
is provided in the RESULTS BOX. If you make a mistake, choose a different button. 
1. 
Fifteen less than twice a number



2. 
Three times a number, increased by seventeen



3. 
The product of nine and a number, decreased by six



4. 
Thirty divided by seven times a number



5. 
Jenny earns $30 a day working part time at a supermarket. Write an algebraic expression to represent
the amount of money she will earn in d days.



This indepth lesson is by Gisele Glosser. You can find me on Google.
