ABACUS: MYSTERY OF THE BEAD
The Bead Unbaffled - An Abacus Manual

Originally Posted: Fri Aug 1, 2003
Subject: Adding 15% to a number
Yahoo Soroban/Abacus group (message #293)


Being fairly new to the abacus I only started playing around with percentages last year. I hope some members will find this interesting. I also hope that my explanations are not too laborious or muddled

In North America it's common to add 15% tip to the bill when paying in a restaurant. In order to find 15% *of* a number it's fairly straight forward. Just multiply the number by 15 and move the decimal point two placed to the left.

To *add* a percentage to a number is a little more tricky because it involves a tiny bit more agility. In the examples below I'm using the example of adding 15% which is not really that difficult. Of course one could also go about finding 15% of a number and then add the result to the original number but I find that takes more time.

I'll start with a simple example. Then a slightly more difficult one.

(Notice, in all examples I've put a dot(.) next to rod C. Rod C is the unit rod.)


Example:1  42 + 15% = 48.3

Place the number 42 on rods B & C

A B C.D
| | | |
0 4 2.0

Now add 42 to rods C & D to equal 46.2

A B C.D
| | | |
0 4 2 0
  + 4.2
_______
= 4 6.2 (We've just added 10% to 42.) 

Now it gets a little tricky. Add 5% of the original number (42). Just add 1/2 of 4 to rod C & 1/2 of 2 to rod D.

A B C.D
| | | |
0 4 6.2
  + 2.1
________
= 4 8.3 (Answer: 42 + 15% = 48.3)

Example:2  782 + 15% = 899.3

Place 782 on rods A, B & C

A B C.D
| | | |
7 8 2.0

Now add 782 to rods B C & D to equal 860.2

A B C.D
| | | |
7 8 2.0
+ 7 8.2
________
8 6 0.2 (We've just added 10% to 782.)

This one is a little more tricky. Now add 5% of the original number (782). Do it rod by rod and think of it this way:

1/2 of 7 = 3.5 --> add 3.5 to rod B

This is the tricky part. Add 3 to rod B then add 5 to rod C. (Adding 5 to rod C allows for the .5 part of the addition.)

A B C.D 
| | | | 
8 6 0.2 
+ 3 5 
________ 
8 9 5.2 

1/2 of 8 = 4 --> add 4 to rod C

A B C.D 
| | | | 
8 9 5.2 
  + 4 
________ 
8 9 9.2 

1/2 of 2 = 1 --> add 1 to rod D

A B C.D
| | | |
8 9 9.2 
    + 1
________
8 9 9.3  (Answer: 782 + 15% = 899.3) 

So adding 10% or 15% to a number isn't all that difficult. For me at least adding something like 35% took some getting used to. But in the end, again, I've found it manageable. - Totton Heffelfinger

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© August, 2009
Totton Heffelfinger Toronto OntarioCanada
Email
totton[at]idirect[dot]com