## Algebra

Contents
 Day 3, WarmUp Exercises Meaning of "A Number" Day 4, WarmUp Exercises Algebra - a mathematics of constants & variables Multiplication Symbols Multiplication & Division of Signed Numbers Exercises

Day 3- Warm Up

 RECOPY WHATEVER YOU DON’T SIMPLIFY

 ANY NUMBER TO THE ZERO POWER, OTHER THAN ZERO, IS 1.

 THINK MONEY!(WHEN COMPUTING FRACTIONS).

Simplify.
1.)

2.) 0 ÷ 4         3.) 4 ÷ 0         4.) 2 ÷ 4

5.) (4 ÷ 12)(3 - 40         6.)

A Number

A Number

## “a number” = “ x” or y, z, a, b, a variable number not 2,3, 5 a constant number

For additional info, read "A Number" Doesn't Mean "Any Old Number."     Algebra begins with this idea. Yes, all the rules of arithmetic hold in algebra, but, the most important idea of variable is introduced.

For additional info, read Know The Invisible (Understood) Ones.     Yes, it looks like an "x" but the invisible ones surrounding the "x" facalitate computation. Examine the understood but unwritten coefficient, exponent, and divisor of 1.

Day 4, WarmUp Exercises
 Simplify 1.)  [(4 + 2)2(3 - 1) ÷ 8 - 32] ÷ 9   work [(4 + 2)2(3 - 1) ÷ 8 - 32] ÷ 9 [(6)2(2) ÷ 8 - 9 ] ÷ 9 [(36)(2) ÷ 8 - 9 ] ÷ 9 [ (72) ÷ 8 - 9 ] ÷ 9 [ 9 - 9 ] ÷ 9 [ 0 ] ÷ 9 0/9 means 0 pieces, 9 equal pieces in one whole, 0 9/0 means 9 pieces, 0 equal pieces in one whole, undefined [ 0 ] ÷ 9 = 0   2.)   4 + 42 + 40 + 41 work sqrt(4) + 4^2 + 4^0 + 4^1 2 + 4^2 + 4^0 + 4^1 2 + 16 + 1 + 4 18 + 1 + 4 19 + 4 23   3.)     work (19 - 6(2))/sqrt(25) (19 - 12))/5 7/5 1.4

Algebra - a mathematics of constants & variables
algebra - a mathematics of variables rather than a mathematics with only constant numbers.
 Numbers constants     1     0     -1     9     2     18.2     20/10     2.3 1 =1 2 is about 1.414 3 is about 1.732 4 = 2 variables         x         n     y     z           a     b   this.form.c.value

Multiplication Symbols

Signed Number Multiplication or Division
 Multiplication or Division (+)(-) = (-) (-)(-) = (+) (+)(+) = (+) (-)(+) = (-)             Count the number or negative signs to be multiplied or divided.     If you have an ODD number of NEGATIVE SIGNS the result is NEGATIVE.     If you have an EVEN number of NEGATIVE SIGNS the result is POSITIVE.

Exercises
 Simplify. MouseOver for answers. 1.     (- 3)(- 2)÷(- 1)     2.     (-3)(4)     3.     - 5(6 - 2)     4.     (-5)2     5.     - 52