Chapter 01 – Section 01

Variables and Expressions

© 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

© 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

© 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

© William James Calhoun

EXAMPLE 2α: Write a verbal expression for each algebraic expression.a. (3 + b) ÷ y

b. 5y + 10x

EX2EX2ββ

© William James Calhoun

EXAMPLE 2β: Write a verbal expression for each algebraic expression.a. 9t

b. 8 + a

c. 7 – 3y

© 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

© 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, once2) writing the number of times multiplied, 2,

once superscripted

Answer:

82

© William James Calhoun

EXAMPLE 3β: Write a power that represents the number of smallest squares in the large square.

© William James Calhoun

EXAMPLE 4α: Evaluate 34.

EX4EX4ββ

Method 1Write the problem out in long form.3 * 3 * 3 * 3Multiply in small steps.3 * 3 = 99 * 3 = 2727 * 3 = 81

Method 2Use your calculator.Hit the “3” key.Hit the power key – “^” or “yx”.Hit the “4” key.Hit the “=“ key.Answer: 81.

© William James Calhoun

EXAMPLE 4β: Evaluate each expression.

a. 35 b. 53

© William James Calhoun

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