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Arithmetic

For archive (Updated on February 16, 2019)

Early days 

Arithmetic ( written as ‘rithmetic) was part of the 3-R Campaign.

Arithmetic was known as Thinchar Tit (Part One of the Mathematics examination).

One text in English was by Workman.

It was adapted and/or translated by U Pann Yi into Burmese.

To find the square of a number ending in five:

Take the number to the left of the rightmost five.
Multiply that number by (number + 1).
Append 25 to the result.

Example : to find the square of 115,
Take 11 and multiply it by 12. Then append 25 to get 13225.

It can be done easily in the head.
It follows from Algebra.
(10a + 5) (10a + 5) = 100a^2 + 100a + 25 = 100a(a+1) + 25

115 x 115 = (11 x 12) x 100 + 25 = 13225.

Casting out the nines

Before the availability of calculators and computers, manual arithmetic operations have to be checked for accuracy.
“Casting out the nines” is a quick way to check if multiplication is correct.
It follows from “Modulo Arithmetic”.
A number, which is a power of 10, when divided by 9 gives a remainder of 1.


10 = 9 + 1
100 = 99 + 1

100000 = 99999 + 1

So checking the modulo of the multiplier, multiplicand and the result is usually sufficient to detect errors.

Abacus

There are several flavors.

Most abacus has two sets of bead for a row :
Two beads (with a weight of 5) on one side
Five beads (with a weight of 1) on the other side
It allows “deferred carries”.

Some use less beads :
One bead (with a weight of 5) on one side
Four beads (with a weight of 1) on the other side
Carries must be done immediately.

Currently, some after-school classes in the USA teach abacus.

Notes

During our younger days, there was an Indian lady named Thakundala, who could do large calculations in her head.

To keep his sanity in a prison, Tratchenberg developed a method to perform arithmetic operations quickly.

The early calculators were often beaten by a proficient abacus user.

Mechanical, electro-mechanical calculators gave way to electronic calculators and computers.

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