- In our younger days, we had to study Arithmetic.
- Reading, (W)riting and (A)rithmetic were the Three R’s.
- The Burmese version is Ah Thone Lone (for Ah Phut, Ah Yay and Ah Twet.
- For some reason, we had to study some subjects in English and Burmese.
- Our elders used the textbook by Workman.
- We use the book by U Pann Yi (who adapted/translated Workman’s book).
Rapid Mental Calculation
- During our younger days, there was an Indian lady who could do large calculations in her head.
- There was Trachtenberg’s method of rapid mental calculation.
To keep his sanity in a prison, Tratchenberg developed a method to perform arithmetic operations quickly.
- Before the advent of calculators and computers, it was advantageous to learn some short cuts.
- (a) To find the square of a number ending in five.
- 115 x 115 = (11 x 12) x 100 + 25 = 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
- (b) use “Casting out the nines” 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.
Some use abacus. There are several variations.
(a) Most abacus has two sets of bead :
Two beads (with a weight of 5)
Five beads (with a weight of 1)
(b) Some use less beads :
One bead (with a weight of 5)
Four beads (with a weight of 1)
(c) Currently, some after-school classes in the USA teach abacus
Mechanical, electro-mechanical and electronic calculators became computational aids. The early calculators were beaten by a proficient abacus user.
Computers, PCs and smart devices are ubiquitous.