Ch 1.1-1.9

Algebra I Chapter 1 Mrs. Cataldo CLASS NOTES CHAPTER 1.1-1.9 1.1 Addition: Show 6 + 7 with a picture: Show 6 + 7 on a number line: Define sum: The sum does not depend on either the _________ of the numbers or the _________ in which they are _________. The expression x + 7 means “_________________________.” The letter x is called a ______________ because it can be replaced by various numbers. 1.2 Subtraction: Show 4 -1 with a picture: Show 5 – 3 on a number line: Define difference: The difference _________ depend on the _________ of the numbers. 1.3 Multiplication: Symbols for multiplication: Show 3 x 4 with a picture: Define product: Another way to picture a product is by means of _____________. The product of two or more numbers, like their _______, does not depend on either their _________ or the _________ in which they are _______________. Steps for story problems: 1. What do we want to know? 2. What do we know? 3. Write an expression. 4. Solve. Volume: The volume of a cube is the length * width * height. Units are cubed. Example, 5 in x 2 in x 3 in = 30 in3. 1.4 Division: Symbols for division: Draw a picture of 6 /3. Define quotient: The quotient of two numbers, like their _____________, depends on the _________ of the numbers. Although quotients are found by division, they can be checked by ____________. 1.5 Exponents: 33 = _____________________ The difference between multiplication and raising to a power: Explain 3 x 3 Explain 33 _________________________________________________________ Explain x2 _________________________________________________________ Explain ax _________________________________________________________ Explain xn _________________________________________________________ 1.6 Zero and One: The counting numbers, also called the ___________ numbers begin with _______. Identity Property of Zero: For every number x, x + 0 = _______. This also applies to x – 0 = _______. Multiplication Property of Zero: For every number x, x • 0 = _______. Division with zero: Dividing zero by a number results in ___________________________________. Dividing a number by zero results in ___________________________________. 0/0 is _________________________. Identity Property of Zero: For every number x, x • 1 = _______. Any x/1 = _______. 1.7 Several Operations Solve this in as many ways as you can, ignoring the order. Which is the correct answer when using the order of operations rules? 2 • 12 + 3 • 10 Order of Operations: • Powers (if there are any) • Next do the _________________ and divisions in order from _________ to _____________. • Finally do the ____________ and subtrations in order from _________ to _____________. _______________ help change the order of operations. 1.8 Parentheses In an expression containing ______________, the ______________ indicate that the operations enclosed within them are to be done _____________ anything else. Fraction bar exception: Fraction bars act as parentheses for numbers above and below the bar. That is, do the operations above and below the bar first. Please Excuse My Dear Aunt Sally – Helps us remember the order of operations 1) 2) 3) 4) 5) 6) 1.9 Distributive Rule The Distributive Rule (Addition): The Distributive Rule (Subtraction):