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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Multiplying Consecutive Integers By 8:

A.  There is a pattern that develops when multiplying consecutive integers by 8.

1.  This method works only if you are multiplying increasing consecutive integers (MUST start with 1) by 8 and adding the last digit back.

2.  The answer will be in the form: 987...., where the number of digits is equal to the number of digits be multiplied by.

Ex [1]  1234 x 8 + 4 = __________.

a.  Since there are 4 digits we write 9876.  (Notice there are only 4 digits in the answer.)

b.  The answer is 9876.

Ex [2]  12345678 x 8 + 8 = __________.

a.  Since there are 8 digits we write 98765432.

b.  The answer is 98765432.