Miscellaneous

Elementary
GCD
LCM
Definitions

Percents

Ratios

Square Roots

Reverses

Junior High
Cube Roots

Mult By 9 (#1)
Mult By 9 (#2)

Mult By 8

Polynomials

Positive Integral Divisors

Sum Of Positive Integral Divisors

Relatively Prime 

Triangular Numbers

Remainders

Divide By 40

Divide By 25

Divide By 9

High School

Pentagonal Numbers

Hexagonal Numbers

Heptagonal Numbers

Octagonal Numbers

Manipulating Polygonal Numbers

Dividing Factorials #1

Dividing Factorials #2

Solving Triangular Numbers

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_{Dividing Factorials In The Form:}   n! - (n-2)!

                                                                (n-1)!

A.  This reduces to the following:

n(n - 1) - 1

  n - 1

B.  Examples:

_{Ex [1]}  7! - 5! _{= _______}

             6!

a.  The numerator of the answer is 7(6) - 1 = 41.

b.  The denominator of the answer is simply 6.

c.  The answer is ⁴¹/₆.

_{Ex [2]}  10! - 8! _{= _______}

               9!

a.  The numerator is 10(9) - 1 = 89.

b.  The denominator is 9.

c.  The answer is ⁸⁹/₉.