deals with the whole numbers. Here is
one example:
Where did the symbolsfor
multiplicationoriginate?
The 17th century seems to be the century
when the basic mathematical symbols
were developed. The best reasons for the
development of such symbols make
sense: they were faster and easier to
write, took up less written space, and
helped the printing process. Although the use of these symbols would eventually be
standardized—so everyone would understand the meaning of certain mathematical
operations—it took a while for this to happen.
For example, in 1686 German mathematician Gottfried Wilhelm Leibniz
(1646–1716) was using the symbol for multiplication and for division. Eventual-
ly, English mathematician and scientist Thomas Harriot (1560–1621; also seen as
Hariot) used the dot to indicate multiplication in his treatise Artis anayticae praxis
(1631). (He also developed the greater than [>] and less than [<] symbols). That same
year, English mathematician William Oughtred (1575–1660) used the symbol “” for
multiplication in his book Clavis mathematicae,in which he was also the first to
mention the plus-minus symbol [±].)
Today, we use a number of symbols for multiplication operations. The most com-
mon symbols are , * , ., and ( ), as in 2 3, 2 * 3, 2 .3, and (2)(3).
How is the term inverseused in arithmetic operations?
Inverse operations are those that “undo” another operation. In particular, subtraction
is the inverse of addition because a b b a; division is also the inverse operation
to multiplication.
The inverse of a numbercan be expressed as follows: The additive inverse of a real
or complex number ais the number that, when added to a,equals 0. In multiplication,
the multiplicative inverse of ais the number that, when multiplied by a,equals 1.
0
1
2
3
4
1
1
2
3
4
2
2
4
6
8
3
3
9
12
4
4
8
12
16
5
5
10
15
20
6
94
Ledgers are commonly used in business for account-
ing purposes. Debits and credits are added and sub-
tracted to keep track of profits and expenses. The
Image Bank/Getty Images.
