This document introduces basic concepts of variables, expressions, and exponents. It provides examples of writing verbal expressions algebraically and vice versa. Key terms introduced include variables, algebraic expressions, factors, products, powers, bases, and exponents. Examples demonstrate writing expressions for word problems, evaluating powers, and finding the number of squares in a multiplication problem written as an exponent. The purpose is to learn the fundamentals of translating between verbal and algebraic representations.

1. Chapter 01 – Section 01
Variables and Expressions

2. © William James Calhoun
To translate verbal expressions into mathematical
expressions and vice versa.
This section is the basics of the basics.
Terms to become familiar with:
• variables – symbol used to express an unspecified number
• algebraic expressions – one or more numbers and variables along with
one or more arithmetic operations
• factors – quantities that are being multiplied
• product – the result of factors being multiplied

3. © William James Calhoun
EXAMPLE 1α: Write an algebraic expression for each verbal
expression.
a. three times a number x subtracted from 24
b. 5 greater than half of a number t
EX1EX1ββ

4. © William James Calhoun
EXAMPLE 1β: Write an algebraic expression for each verbal
expression.
a. m increased by 5
b. the difference of x and 9
c. 7 times the product of x and t

5. © William James Calhoun
EXAMPLE 2α: Write a verbal expression for each algebraic expression.
a. (3 + b) ÷ y
b. 5y + 10x
EX2EX2ββ

6. © William James Calhoun
EXAMPLE 2β: Write a verbal expression for each algebraic expression.
a. 9t
b. 8 + a
c. 7 – 3y

7. © William James Calhoun
More terms you will need to become familiar with:
• power – an expression with a superscript representing a number
multiplied by itself a certain number of times
Examples of powers: 54
and x3
• base – the number or variable that is multiplied
• exponent – the superscript number that signifies the number of times
multiplication should occur
45
= 4 * 4 * 4 * 4 * 4
four is multiplied by itself five times
{
= 1024

8. © William James Calhoun
EXAMPLE 3α: Write a power that represents the number of smallest
squares in the large square.
EX3EX3ββ
Count the number of squares along one side.
There are 8 squares in each row.
Count the number of squares along the other side.
There are 8 squares in each column.
To find the number of smallest squares, you would
multiply 8 * 8.
8 * 8 can be written as a power by
1) writing the base, 8, once
2) writing the number of times multiplied, 2,
once superscripted
Answer:
82

9. © William James Calhoun
EXAMPLE 3β: Write a power that represents the number of smallest
squares in the large square.

10. © William James Calhoun
EXAMPLE 4α: Evaluate 34
.
EX4EX4ββ
Method 1
Write the problem out in long form.
3 * 3 * 3 * 3
Multiply in small steps.
3 * 3 = 9
9 * 3 = 27
27 * 3 = 81
Method 2
Use your calculator.
Hit the “3” key.
Hit the power key – “^” or “yx
”.
Hit the “4” key.
Hit the “=“ key.
Answer: 81.

11. © William James Calhoun
EXAMPLE 4β: Evaluate each expression.
a. 35
b. 53

12. © William James Calhoun
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