What is division?
The word “divide” comes from the Latin root vidua(referring to a separation; the
word “divide” shares its major root with the word “widow”) and di,a prefix that is a
contraction of dis,meaning “apart” or “away.” In division, the number being divided is
called the dividend,while the number dividing it is called the divisor. The end result is
called the quotient. For example, in 20/5 4, 20 is the dividend, 5 the divisor, and 4
the quotient.
Division in mathematics is a relatively new concept for the masses; it was only
taught at university levels after the 16th century. The first to offer division to the pub-
lic was German mathematician Adam Ries (1492–1559; also seen as Risz, Riesz, Riese,
or Ris) in his work Rechenung nach der lenge, auff den Linihen vnd (sic) Feder,often
shortened to Practica. His work reached more people for an important reason: Instead
of the usual practice of writing a mathematical book in Latin, he wrote his book in
German, thus reaching a wider audience.
Where did the symbolsfor divisionoriginate?
The history behind the division symbols is long and complicated. The following lists
how the major ones developed:
Closed parentheses—The arrangement “8)24,” meaning 24 divided by 8 in this
case, was used by Michael Stifel (1486 or 1487–1567) in Arithmetica integra(1544).
The obelus—By 1659 Swiss mathematician Johann Heinrich Rahn (1622–1676)
introduced the division symbol (, called an obelus) in his book Teutsche Algebra.
The symbol was a combination of “:” and “”. (This division symbol was used by many 95
MATH BASICS
Why can’t you divide by zero?
D
ividing by zero is like the old saying “You can’t get something from noth-
ing.” Mathematically speaking, it’s the same way: You can’t “divide by noth-
ing.” In fact, when something is divided by zero, the answer is always undefined.Here are a few ways of looking at this: There is a rule in arithmetic that
a(b/a) b. So if we say that 1/0 5, then 0(1/0) 0 5 0. In other words, if
you could divide by 0, this rule would not work. Another way to look at the “no
to 0 as a divisor” problem is through multiplication: if 10/2 5, we know that 5
2 10; the same for 5/1 5, thus we know that 5 1 5. But if you take
5/0, that would mean that the answer times 0 would equal 5, but anything times
0 is equal to zero. Because there is no answer to this dilemma, mathematicians
say you can’t divide by zero.