Algebra: Chapter 1, Lesson 2, page 9.
The Commutative and Identity Properties
Commutative property is only for addition and multiplication.
`x+5=5+x`
`5*y=y*5`
Remember the identify properties of addition (0) and multiplication (1).
Anything to the 1st power is the number and anything to the 0 power is always = 1.
`z^1=z` and `z^0=1`
To form equivalent expressions, multiply the expression by `1/1` or variable/variable, like `y/y`. For example, convert `z/2` to an equivalent expression using `1/1` or `y/y`. To do this we have:
`z/2=z/2⋅y/y=zy/(2y)`
We can simplify algebraic expressions using the identity property for multiplication. For example, simplify `(xy)/(3y)`
`(xy)/(3y)=(x⋅y)/(3⋅y)=(x/3)⋅(y/y)=x/3`
Don’t forget, please put your first and last name on homework pages and make sure that I can read it. Show all work as well!!
Here is a link to tonight’s homework on Chapter 1, Lesson 2. There are 2 solutions provided. Remember, you need to have Quicktime for either the PC or Mac installed on your computer!
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Algebra 1a: Chapter 1, Lesson 1, page 4.
Symbols and Expressions
In algebra, we use symbols to stand for various numbers. One type of symbol is called a VARIABLE. An expression such as `396/v` and contains at least one variable is called an ALGEBRAIC EXPRESSION. We can replace a variable with a number, this is called SUBSTITUTING for the variable.
Sets of numbers:
- Natural: 1, 2, 3, 4, 5, …
- Whole: 0, 1, 2, 3, 4, 5, …
- Rational: numbers which include natural and whole numbers and can be expressed as a RATIO such as `1/1` or `2/3`
Parenthesis (, ) or [,] or {,} are called GROUPING SYMBOLS and we do things in them first.
PEMDAS, please excuse my dear aunt sally – order of operations. Just like in Language Arts, we have a convention of writing/reading from left to right, we have a convention in math.
We do things in the order of:
- parenthesis
- exponents
- multiplication/division (in order from left to right)
- addition/subtractions (also in order from left to right).
Here is a link to tonight’s homework on Chapter 1, Lesson 1. There are 2 solutions provided. Remember, you need to have Quicktime for either the PC or Mac installed on