Abacus ... Bead Arithmetic

Chinese Zhusuan, knowledge and practices of mathematical calculation through the abacus

I bought mine decades ago when I lived in San Francisco. It seemed like one of those fun things to have and play with / learn from at some future time when I could concentrate undisturbed. Young ones today refer to that as 'me time'.

It amazes me at times that education is able to produce children with working knowledge of how math works and how language is structured to speak, write, or sign. Every now and again I take a look at what methods are being used to teach math at different levels.

For me, for example, I find the need to do ratios and proportions. I measure food and I calculate medication doses. Back in the day, we learned about the means and the extremes.

In mathematics, means and extremes refer to specific terms in a proportion. In a proportion expressed as
a:b = c:d

The extremes are the first and last terms, which are a and d.

The means are the middle terms, which are b and c.

The means-extremes property states that the product of the means is equal to the product of the extremes,
i.e., b × c = a × d.

This property is useful for solving proportions and understanding relationships between ratios

Later on in life, the notation changed, but the action/method by which one derives the answer is the same. It's called cross multiplication.

To cross multiply 2 fractions, multiply the numerator of the fraction on the left side of the equal sign by the denominator of the fraction on the right side. Then multiply the denominator of the left fraction by the numerator of the right fraction. Set the 2 products equal to one another and solve for the unknown variable.



I believe that we often become so fixated on the notation that we forget the method and its rationale. Imagine growing up in the United States where large numbers (those to the left of decimal) have the numbers separated by a comma in groups of three. Thus

Twenty-seven million four hundred thirty-nine thousand two hundred eleven would be written as

27,439,211

In many places outside the USA, the seven has a(n) horizonal bar in the middle. To the American, that makes the seven look like the capital letter F.



How about the European number one?



Some folks go overboard with the oblique at the top



I'm sure the North Americans never saw this in their classrooms.



In the USA, I'm not quite sure if the numerals are the same in print as they are in script (cursive).



The cursive training tends to lean more towards leaning. Note that the number one is a single, vertical downward stroke.

These numbers can be represented with beads on a rod. On my abacus there is a(n) horizontal bar (the beam) that separates the values of 0-4 from the values of 5-9.



My abacus does not have house points (in fact I had to look it up). It can be used as a comma that separates larger numbers by columns of three or it can be used as a decimal point.