aa section 1-1
TRANSCRIPT
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