Basic mathematics

- Long division

* If you draw a digit from the dividend and the reminder is still < divisor, add 0 in the quotient, if you draw 2 digits and the reminder < divisor, add 00 in the quotient.
ex.: 3219.2/32 = 100.6, 323.2/32 = 10.1
* If the dividend has 0s at its end, after you finish dividing the non-zero part, add the rest 0s to the quotient, beware of adding a 0 that was use in previous division stage of the long division. And, if there's a decimal part, add the rest 0s.
ex.: 16000/32 = 500, 16000.32/32 = 500.01

Rounding:

- Round off to nearest ...
- The bias in the total value of full rounded list of numbers
- floor(), ciel(), int(), frac(), trunc(), round(), mod()
* frac(x) = x - floor(x) or frac(x) = x - int(x)
* sometimes with negatives int(x) = floor(x), becareful with int, it differs from calculator to another.

ALGEBRA LAWS:

- Commutative (+,*), Associative (+,*), Distributive (+,*,-) Laws

Identity:

- The opposite of x (additive inverse) with addition yields the additive identity (0).
- The reciprocal of x (multiplicative inverse) with multiply yields the multiplicative identity (1).

Factors:

- Divisibility (2,5,3,11)
- Decomposing a Number into Its Prime Factors
- GCF and LCM

Decimals and fractions:

- Reduce fraction to/write it in lowest terms
- Compare two fractions
- Increase fraction to ... new terms (also when a fraction denominator turned to be the same of denominator of another in adding or subtracting)
- Mixed fraction (convert mixed number with negative fraction) (a b/c = a*c+b/c) (a -b/c = a*c-b/c)
- Multiplying and Dividing Mixed Numbers
- Carried Away: Adding Mixed Numbers
- Borrowing from the Whole: Subtracting Mixed Numbers
- LCD (by cross-multiply, increasing fraction to new terms, LCM)

- Convert fraction to decimal and vice versa
- Converting a recurring decimal into a fraction
- Adding and subtracting decimals, multiply and division

Scientific notation:

- Scientific notation/ Multiplying and Dividing and adding

Percentages:

- Percentages and ratio of 10
- Multiples of 100% (convert to fraction)
- x% of y = (x/100)*y
- x of y = (x*100)/y = x%
- Changes in percentages (increasing and decreasing)

1) Calculate the percentage of the new number. For example, if the original number was 482 and it changed to 458, do this to know how much in percents 458 to 482:
(458*100)/482 = x%
change the improper fraction to mixed fraction to have sensible value.

2) Subtract the result of the previous step from 100 and change improper fraction to mixed fraction for sensible number. (Use abs function)

3) You can divide the result by 100 to have the ration in times, like to know that the increasing or decreasing was half time or quarter time ... etc but it's sensible only in some numbers, it won't be sensible for our example.

Round numbers also to have sensible numbers.