REVIEWER MATH PLUS

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(IMPORTANT, common mistakes)

SIMPLIFICATION of DECIMAL NUMBER

1. All real number in the form of +a.b can be written as a.b
(+ sign need not to be written ex. +2.5 = 2.5

2. All real number in the form of a.b0 can be written as a.b
( 0 on the right after the fractional part is omitted ex. +2.50 = 2.5

3. All real numbers of the form 0a,b can be written as a.b
(0 before the whole number is omitted, ex -025.2 = -25.2

4. All real number in the form of a.0 can be written as a
(0 fractional part, O is omitted, ex. -5.00 = -5 +25.0 = 25

FLOOR FUNCTION (IMPORTANT)
⌊ 12.34 ⌋ 12.34 is between 12 and 13, 
answer is 12, since 12 is the lower value than 13
⌊ -12.22 ⌋ -12.22 is between 12 and 13
answer is -13 since -13 is the lower value than -12 (dont dron the -)
ex.
⌊ -440.05 ⌋ = -441 
⌊ 33.98 ⌋ = 33
⌊ 22.52 ⌋ + ⌊ -17.22 ⌋ = 22 + (-18) = 22 - 18 = 4

ABSOLUTE VALUE
│- a │ = a
All answer will be positive., do not drop the fractional part
example
│-16.9│ = 16.9
│33.5 │ = 33.5
│-999│ = 999

COMBINATION
1. ⌊ - 33.08 ⌋ + │- 33.5 │ = - 34 + (33.5) = -0.5
2. │⌊ - 33.08 ⌋│ = simplify inner first
get the floor function first ⌊ - 33.98 ⌋ = - 34
the the absolute value │⌊ - 34 ⌋│ = 34
3. .⌊ │-16.9│ x (-12.5)⌋ 
get the absolute value of │-16.9│ = 16.9
then multiply by (-12.5) = - 211.25 
since it is still enclosed by floor function .⌊ - 211.25 ⌋
get the floor function ⌊ - 211.25 ⌋ = -212

TERMINATING AND REPEATING DECIMAL
CLUE:
those number with ... is NON TERMINATING
no ... is a terminating
Non terminating, Non repeating.. Number never repeat
NON terminating, Repeating... Number are repeating
Ordering of real Number

Negative number are always less than the positive number
In Negative number -3 is less 0

In positive number 3 is greater than 0
so in negative number the larger the number, the lower the value.

LAW ON ADDING AND SUBTRACTING NEGATIVE NUMBER
1. The sum of two positive number is + ex +2 + (+5) = +7 = 7
The sum of two negative number is - ex. -2 + (-5) = -2 -5 = -7
(Both are added) just retain the sign
2. The sum of a positive and negative number is obtainable by its absolute value. Subtract the lower number from the higher number and follow the sign of higher number.
example
-4 + 8 = 8-4 = 4
4 + (-8) = 4 - 8 = 8-4 = -4 (since the sign of 8 (higher) is -
Subtraction:
8 - (-2) =(change the sign to add) 8 + 2 = 10
If ever you encounter this in subtraction,
2 - 8, you don't need to change sign, it understood that 8 is positive.
and (-) times (+) will also yield - , so be it 2 - 8, 
higher number 8, lower number 2, sign of 8 now (-) = 8-2 = -6,
- 12 - 15 in subtraction is also the same as -12 - (+15), thats why, you just directly do the operation,
-12 - 15 = -27
TRIVIA
Addition
2 + (-8) = 2 - 8 = -6
Subtraction
2 - 8
2 - (+8) = 2 - 8 = -6