Download - AA Section 1-1
![Page 1: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/1.jpg)
Section 1-1The Language of Algebra
![Page 2: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/2.jpg)
VARIABLE:
![Page 3: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/3.jpg)
VARIABLE: A symbol (usually a letter) that holds the place of a number or expression.
![Page 4: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/4.jpg)
VARIABLE: A symbol (usually a letter) that holds the place of a number or expression. Think of a variable as a place holder
![Page 5: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/5.jpg)
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:
![Page 6: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/6.jpg)
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
![Page 7: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/7.jpg)
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 +,−,×,÷
![Page 8: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/8.jpg)
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:
![Page 9: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/9.jpg)
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”
![Page 10: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/10.jpg)
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.
![Page 11: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/11.jpg)
Example 1Express the cost of s boxes of cereal at r dollars per box.
![Page 12: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/12.jpg)
Example 1Express the cost of s boxes of cereal at r dollars per box.
s cans i r dollarscans
![Page 13: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/13.jpg)
Example 1Express the cost of s boxes of cereal at r dollars per box.
s cans i r dollarscans
= sr dollars
![Page 14: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/14.jpg)
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?
![Page 15: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/15.jpg)
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
![Page 16: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/16.jpg)
EVALUATING THE EXPRESSION:
![Page 17: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/17.jpg)
EVALUATING THE EXPRESSION: Substituting for variables and finding the result
![Page 18: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/18.jpg)
EVALUATING THE EXPRESSION: Substituting for variables and finding the result
ORDER OF OPERATIONS:
![Page 19: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/19.jpg)
EVALUATING THE EXPRESSION: Substituting for variables and finding the result
ORDER OF OPERATIONS: GEMDAS
![Page 20: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/20.jpg)
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
![Page 21: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/21.jpg)
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
![Page 22: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/22.jpg)
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
![Page 23: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/23.jpg)
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
![Page 24: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/24.jpg)
EQUATION:
![Page 25: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/25.jpg)
EQUATION: A sentence where the two expressions are equal
![Page 26: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/26.jpg)
EQUATION: A sentence where the two expressions are equal
FORMULA:
![Page 27: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/27.jpg)
EQUATION: A sentence where the two expressions are equal
FORMULA: A rule that says a variable will always equal a certain expression
![Page 28: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/28.jpg)
Example 3Use the formula to find the volume of a sphere that is 8 cm in
diameter. V = 43π r3
![Page 29: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/29.jpg)
Example 3Use the formula to find the volume of a sphere that is 8 cm in
diameter. V = 43π r3
d = 8 cm
![Page 30: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/30.jpg)
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
![Page 31: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/31.jpg)
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
![Page 32: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/32.jpg)
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
![Page 33: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/33.jpg)
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
![Page 34: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/34.jpg)
Homework
![Page 35: AA Section 1-1](https://reader030.vdocuments.site/reader030/viewer/2022032419/55a21abc1a28ab985d8b462e/html5/thumbnails/35.jpg)
Homework
P. 9 #1-30