Section 1-1The Language of Algebra

VARIABLE:

VARIABLE: A symbol (usually a letter) that holds the place of a number or expression.

VARIABLE: A symbol (usually a letter) that holds the place of a number or expression. Think of a variable as a place holder

VARIABLE: A symbol (usually a letter) that holds the place of a number or expression. Think of a variable as a place holder

ALGEBRAIC EXPRESSION:

VARIABLE: A symbol (usually a letter) that holds the place of a number or expression. Think of a variable as a place holder

ALGEBRAIC EXPRESSION: A combination of numbers and variables, using arithmetic operators to combine them

VARIABLE: A symbol (usually a letter) that holds the place of a number or expression. Think of a variable as a place holder

ALGEBRAIC EXPRESSION: A combination of numbers and variables, using arithmetic operators to combine them +,−,×,÷

VARIABLE: A symbol (usually a letter) that holds the place of a number or expression. Think of a variable as a place holder

ALGEBRAIC EXPRESSION: A combination of numbers and variables, using arithmetic operators to combine them +,−,×,÷

ALGEBRAIC SENTENCE:

VARIABLE: A symbol (usually a letter) that holds the place of a number or expression. Think of a variable as a place holder

ALGEBRAIC EXPRESSION: A combination of numbers and variables, using arithmetic operators to combine them +,−,×,÷

ALGEBRAIC SENTENCE: Expressions related with “verbs”

VARIABLE: A symbol (usually a letter) that holds the place of a number or expression. Think of a variable as a place holder

ALGEBRAIC EXPRESSION: A combination of numbers and variables, using arithmetic operators to combine them +,−,×,÷

ALGEBRAIC SENTENCE: Expressions related with “verbs”

=,≠,≥,etc.

Example 1Express the cost of s boxes of cereal at r dollars per box.

Example 1Express the cost of s boxes of cereal at r dollars per box.

s cans i r dollarscans

Example 1Express the cost of s boxes of cereal at r dollars per box.

s cans i r dollarscans

= sr dollars

Example 2Matt Mitarnowski has $65 in the bank. If he saves $30 each month, how

much money, excluding interest, will he have in the bank after m months?

Example 2Matt Mitarnowski has $65 in the bank. If he saves $30 each month, how

much money, excluding interest, will he have in the bank after m months?

65 + 30m dollars

EVALUATING THE EXPRESSION:

EVALUATING THE EXPRESSION: Substituting for variables and finding the result

EVALUATING THE EXPRESSION: Substituting for variables and finding the result

ORDER OF OPERATIONS:

EVALUATING THE EXPRESSION: Substituting for variables and finding the result

ORDER OF OPERATIONS: GEMDAS

EVALUATING THE EXPRESSION: Substituting for variables and finding the result

ORDER OF OPERATIONS: GEMDAS

1. Grouping symbols ( ), [ ], √, etc. are done first, from the inside-out

EVALUATING THE EXPRESSION: Substituting for variables and finding the result

ORDER OF OPERATIONS: GEMDAS

1. Grouping symbols ( ), [ ], √, etc. are done first, from the inside-out

2. Powers

EVALUATING THE EXPRESSION: Substituting for variables and finding the result

ORDER OF OPERATIONS: GEMDAS

1. Grouping symbols ( ), [ ], √, etc. are done first, from the inside-out

2. Powers

3. Multiply and divide from left to right

EVALUATING THE EXPRESSION: Substituting for variables and finding the result

ORDER OF OPERATIONS: GEMDAS

1. Grouping symbols ( ), [ ], √, etc. are done first, from the inside-out

2. Powers

3. Multiply and divide from left to right

4. Add and subtract from left to right

EQUATION:

EQUATION: A sentence where the two expressions are equal

EQUATION: A sentence where the two expressions are equal

FORMULA:

EQUATION: A sentence where the two expressions are equal

FORMULA: A rule that says a variable will always equal a certain expression

Example 3Use the formula to find the volume of a sphere that is 8 cm in

diameter. V = 43π r3

Example 3Use the formula to find the volume of a sphere that is 8 cm in

diameter. V = 43π r3

d = 8 cm

Example 3Use the formula to find the volume of a sphere that is 8 cm in

diameter. V = 43π r3

d = 8 cm r = 1/2 d = 4 cm

Example 3Use the formula to find the volume of a sphere that is 8 cm in

diameter. V = 43π r3

d = 8 cm r = 1/2 d = 4 cm

V = 43π (4)3

Example 3Use the formula to find the volume of a sphere that is 8 cm in

diameter. V = 43π r3

d = 8 cm r = 1/2 d = 4 cm

V = 43π (4)3 ≈ 268.0825731

Example 3Use the formula to find the volume of a sphere that is 8 cm in

diameter. V = 43π r3

d = 8 cm r = 1/2 d = 4 cm

V = 43π (4)3 ≈ 268.0825731 cm3

Homework

Homework

P. 9 #1-30