CIPHERING WITH ABE in 1819
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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: _______
#5 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.
