writers before Rahn as a minus sign.) In 1668, when Rahn’s book was translated into
English with additions by English mathematician John Pell (1610–1685), the division
symbol was retained. Some say Pell greatly influenced Rahn to develop the symbol,
but most historians agree that there is little evidence of such a connection.
Slash—Another sign for division, the slash (/) was actually first used for fractions,
such as 2/3 or 1/2. It can be extended into other, larger or smaller numbers, such as
123/112 and 0.112/0.334. Little is known about its origins, but it is known that this
symbol was sometimes used for subtraction, until it became standard practice for rep-
resenting division.How did the symbolsfor long divisiondevelop?
In the 19th century, United States textbooks typically showed long division with the
divisor, dividend, and quotient on the same line, separated by parentheses, as in
36)108(3. In the same century, in examples of short division, a vinculum (line) was
placed under the dividend, with the vinculum almost attached to the bottom of the
parenthesis. The quotient was written under the vinculum, as per the following:By late in the 19th century, the vinculum was almost attached to the top of the
parenthesis and the quotient was written above the vinculum, as per the following:These symbols are similar to what we see in our elementary dealings with long
division, but our vinculum is attached to the parenthesis. Interestingly enough, there is
no name for the symbol used for long division ( ) ).What are the least common multipleand denominator?
The smallest common multiple (whole number) of two or more whole numbers is
called the lowest (or least) common multiple (LCM). For example, for the numbers 3
and 8, the multiples of 8 are 8, 16, 24, 32, and so on; the multiples of 3 are 3, 6, 9, 12,
15, 18, 21, 24, 27, and so on. Therefore, the LCM of 3 and 8 is 24.
The least common denominator(LCD) is mainly used to carry out the addition or
subtraction of fractions. In order to do these operations, the fractions need to have the
same denominator. (For more information about fractions, see below.) The easiest way
to work on such calculations is to determine the lowest number possible for the
denominator—a number called the least common denominator (LCD)—which is
actually the common factor by which two numbers are divisible. For example, to add
1/6 and 1/8, we have to find the least common multiple of the denominators. In this45591(^5) g
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