• Algebra Notes Page

Chapter 9 Lesson 6
(PIZZAZ worksheet solutions)
MOVING WORDS:
Remember to have positive and negative solutions when taking a square root: Isolate the radicand, then isolate the variable if necessary. Simplify the radical into simple radical form by factoring out perfect squares (4, 9, 25, etc.) Fractions and irrational expressions may be acceptable answers: Did you hear about the teacher who told the students ten jokes with no pun in ten did.

April 22, 2013

Graphing Parabolas      January 30th, 2014
Systems of Linear Inequalities worksheet: January 31st, 2013
Lesson 6-6 "Linear Inequalities"   Final Exam Review KEYs    Unit 3 Inequalities
Lesson 3.3 Solving Inequalities by Multiplying and Dividing:         Unit 2 Equations

Lesson 2-1 Solving Two Step Equations   Lesson 2-1 "Solving One Step Equations"      Unit 1 Chapter 1

Notes #6 -- September 11, 2012
"Combining Like Terms"

Think of x2 as a large square, x as a 1*x rectangle, and 1 as a small square (so 5 = 5 squares): Now imagine a truck carrying three rectangles and two squares.  How many shapes would two such trucks distribute?  So in algebra we combine like terms like so: Notes #5 -- September 10th, 2012
"Properties of Real Numbers"

So the Natural Number is is closed under addition and multiplication.
If you add two natural numbers, you get another natural number.  The answer is in the same set of numbers.
If you multiply two natural numbers, the product is also a natural number.  This isn't always true for subtraction.  If you subtract two integers, you always get another integer.
The set of integers is closed under subtraction.  This isn't always true for division.
Rationals are closed under addition, subtraction, multiplication, and division.
But you can't always take the square root of a rational number and get another rational number.
However, the set of Reals is closed under +, -, *, /, and square rooting.

There are three other properties of real numbers.      These two properties only hold true for addition and multiplication.
They can be disproved (or refuted) for subtraction and division.  Come up with two counterexamples that prove the commutative property isn't true for subtraction and division.

The last property is the Distributive Property of Multiplication over Addition.    Notes #4 -- September 6th, 2012
"Roots and Irrationals"
HW Review p. 29  and now some notes ...  The square root sign was invented by Christian Rudolph and made to look like the letter "r",
for the Latin word for root, "radix."  Notes #3 -- September 4th, 2012
Powers and Exponents      Notes #2 -- August 30th, 2012
Multiplying and Dividing Real Numbers

Multiplication is adding multiple times.  For example, 3(2) is adding two three times (2+2+2).
So +3(+2) = +6 since a postive times a postive is also positive. What about a positive times a negative?
3(-2) is subtracting two three times, or -2 -2 -2.  So that's -6.  Positive times negative is negative.  How about -3(+2)? A negative times a positive? This means do the opposite of adding 2 three times.
The opposite of adding 2 is subtracting 2.  And -2 -2 -2 = -6.  So -3(2) is -6.  (-)(+) is negative.  Finally, how about a negative times a negative, e.g. -3(-2).  This means do the opposite of subtracting 2 three times.
So add two three times.  2+2+2 is +6.  Therefore, a negative times a negative is positive.  In summary: The inverse of multiplication is division.  Division follows the same rules for positives and negatives as multiplication.    