the next highest digit column in order to obtain a positive difference in the nearby
column. For example, borrowing is evident in the following operation in the base 10
numbering system (1,234 minus 567, giving the result of 667):
When you subtract the same columns, starting in the right-hand column, the 4 is
too small to subtract from 7; therefore, you need to borrow 10 from the column to the
left, boosting the number 4 to 14. The column to the left then loses 10, and 2 is left.
Again, the 2 is too small to subtract from 6, so 10 is borrowed from the next column
to the left, boosting the number 2 to 12. The last number to the left is dropped down
by 10, giving 11; the 5 is subtracted from the 11, resulting in 6 in that column.
Where did the symbols plus ()and minus ()originate?
One of the first books to use the plus and minus signs was written in 1489 in Johann
Widmann’s (c. 1460–?) Mercantile Arithmetic. Originally, he used the signs and
to indicate excesses and deficits (what we would call credit and debit) in business deal-
ings. But some historians believe the sign initially evolved from the French et,or
“and,” because the written “e” and “t” resemble the sign.
Although they were probably used before in general mathematics, the first person
known to have used the and symbols in writing algebraic expressions lived in the
early 1500s: Dutch mathematician Vander Hoecke. The symbols finally went into gen-
eral use in England when Robert Recorde’s (1510–1558; also seen erroneously as
Record) book The Whetstone of Wittewas published; this is the same book responsible
for bringing the equal () sign to the forefront of mathematics (see above).
What is multiplication?
The word “multiply” comes from the Latin roots multi(“many”) and pli(“folds”). Eng-
lish poet Geoffrey Chaucer (1340?–1400) may have used the word first as a verb in his A
Treatise on the Astrolab(1391). In multiplication, two natural numbers are multiplied
together (the numbers are called factors; the less-used terms for two such numbers are
multiplicand and multiplier), producing what is called a product. Multiplication is
actually a form of repeated addition. For example, 2 3 means 2 2 2 (or 6).
What are multiplication tables?
Multiplication tables are just what the name implies: a table of multiplication. Most of
these tables have a specific purpose: mainly, to multiply numbers in the rows and
columns by each other to find a product. One of the simplest multiplication tables
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