Algebra 1: Chapter 1, Lesson 4, page 19.
The Associative Property
QUIZ #1 ON TUESDAY, MAKE SURE THAT YOUR NOTES AND CALCULATOR ARE WITH YOU! IT IS WORTH 100 POINTS!
We discussed the use of the Associative property by re-grouping terms in paranthesis. We also used both commutative and associative properties together to help simplify expressions for evaluation.
We looked for patterns in expressions again to help speed up our mental math computation speed.
Remember, the associative property ONLY holds true for addition and multiplication. Just like the commutative property, it doesn’t work for subtraction or division.
For any numbers a, b, and c, we have in equation forms for adding and multiplication:
`a+(b+c)=(a+b)+c and a⋅(b⋅c)=(a⋅b)⋅c`
Two of tonight’s homework problems solved by MrE are here! Just click it!!
======================================================================
Algebra 1a: 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!