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.

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 (with numbers) 48 : 12 :: 8 : ___ Answer:______

#2 (with shapes) %%% : ************ :: &&&& : ___
Answer:______

#3 (using objects) 15 eggs : 3 eggs :: 45 hogs : ___ hogs
Answer:______

#4 (using fractions) 1/4 : 3/4 :: 1/3 : __/__

Answer: _______

#5 (using number groups) 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.

#6 4,340 divided by 2 = answer:

#7 5,555 divided by 250 = answer:

#8 3,670 times 4,678 = answer:

#9 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.

**
Lincoln's Sum Papers**

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