Authoring, Researching, Reporting and other Worn
Learning On-Line Activity by Howard Taylor

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While with the Lincoln family, you will do some math practice.  Abe has been showed how to do ciphering to the rule of three.  Here's how you can learn how to do it too.

Abraham Lincoln stated in his 1859 autobiography,". . . Of course when I came of
age I did not know much. Still somehow, I could read, write, and cipher to
the Rule of Three."
   By ciphering (cipher'n) Abraham learned to "work with numbers." 
His learned math skills centered on the math processes of PROPORTION.  He
could cipher numbers to the RULE OF THREE. 

To cipher to the rule of three for 3, 9, and 2 is to complete the phrase "3
is to 9 as 2 is to __," with the answer being the quantity 6. In other words, ciphering to the rule of three is to solve a proportion such as 3/9 = 2/x,
where x=6. Cipher the rule of three for 4, 6, and 3. Cipher the rule of three
for a, b, and c. 

Go here for more explanation of the Rule of Three. 

The rule
of three can include the processes of addition, subtraction, multiplication
and even division.  It also shares algebraic procedures and the working with fractions and decimals.  The Rule of Three can be the basis for understand numbers and mathematical processes. 

Abe would like for you to work these ciphering problems with him, "under
the shade of the old oak tree."  Mr. Lincoln has allowed Abe to do some school work for the afternoon.

#1--  A Starter to understand proportions and then the RULE of THREE
Proportions (also called RATIOS in modern math)

Example:    3  is to  4  as 10 is to  ___          or   3 : 4 :: 10: ___        the answer is 11. 
The way to do a simple addition ratio is to figure out the relationship of the first number to the second.  In
this problem, 3 is 1 less than 4, therefore in figuring the ratio (unknown) on the right side, you add 1.      How does
this apply to the Rule of Three?   The problem has three known elements:  the 3, the 10 and the 4.   The
unknown is the answer, in this problem is 11.

Example:   4  is to  16   as   5   is to   ___    or     4 : 16 :: 5 : ___         the answer is 20.  
The way to do this multiplication ratio is to see the relationship of 4 to 16.   16 is 4 times greater than 4. 
Therefore, the ratio for the right side will be 4 times 5, or 20.  
How does this apply to the Rule of Three?  
The problem has three known elements:  the 4, the 16 and the 5.   The unknown is the answer, in this
problem is 20.

Example:   24  is to  8  as  36  is to  ___    or   24 : 8 :: 36 : ___          the answer is 12.  
The way to do this division ratio is to see the relationship of 24 to 8.  8 is 1/3rd  of 24, therefore the right
side of the ratio would be figured by dividing 36 by 3.  The answer is 12.      It could be written in the form
of fractions (algebraically)  

24  ::  36
  8  :: 

 Here are some actual problems for the Cipher'n Student to tackle.  Have fun!
#1          48 : 12 ::  8 :  ___           Answer:______

#2          %%%  : 
************  ::  &&&& :  ___     Answer:______

#3          15 eggs :  3 eggs  ::  45 hogs :  ___ hogs   Answer:______

#4           1/4 : 3/4 ::  1/3 :  __/__       Answer: _______

000000 : 00  ::  18 : ___     Answer:  _______  

Young Abraham Lincoln learned to do long multiplication and division
very well and accurately.   Write these problems with division brackets
and work them.  You need to know your multiplication facts to do these. 

4,340  divided by 2 =          answer:

5,555 divided by 250 =       answer:

3,670  times 4,678 =      answer:

2250  times 9,021=        answer:

You can make up your own problems.  To be a little more
modern, use a calculator to check your answer.

To see if you can write your "long multiplication or division"
problems as neatly and correctly as Abraham Lincoln, go here
to see his math paper here.