Variables & Expressions

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Vocabulary:

variablesalgebraic expressionsfactorsproductpowerbaseexponentevaluate

  

In the algebraic expression 4s, the letter s is called a variable.  In algebra, variables are symbols used to represent unspecified numbers or values.  Any letter may be used as a variable. An algebraic expression consists of one or more numbers and variables along with one or more operations.  Here are some examples of algebraic expressions. 5x    3x-7    4+p/q    m x 5n    3ab/5cd In each expression, the quantities being multiplied are called factors, and the result is called the product.   

Write Algebraic Expressions

a.  five less than the number c

            c-5

b.  the sum of 9 and 2 times the number d

            9+2d c.  two-thirds of the original volume v

            2/3v

An expression like x^n is called a power and is read "x to the nth power."  The variable x is called the base, and n is called the exponent.  The exponent indicates the number of times the base is used as a factor.

Symbols Words Meaning

3^1 3 to the first power

3

3^2 3 squared 3*3

3^3 3 cubed 3*3*3

3^4 3 to the fourth power

3*3*3*3

3^5 3 to the fifth power

3*3*3*3*3

3^6 3 to the sixth power

3*3*3*3*3*3

Write each expression algebraically:a.  the product of 3/4 and a to the seventh power

            3/4a^7

b.  the sum of 11 and x to the third power

            11+x^3

Evaluate Powers:

a.  3^4

            81

b.  8^2

            64

Write Verbal Expressions:

a.  8x^2        5

            the quotient of 8 times x squared and 5

b.  y^5 - 16y

            the difference of y to the fifth power and 16 times y

Glencoe/McGraw-Hill 2003