3. - is a real number that is less than
zero.
- are usually written with a minus
sign (-) in front.
Examples:
-1, -2, -3, -4, -5 …

5. • Negative numbers appear for the first time in
history in the Nine Chapters on the
Mathematical Art
• In the Nine Chapters red rods used to denotes
negative numbers and black rods for positive
numbers.

6. • In Hellenistic Egypt, the
Greek mathematician in the third
century A.D. referred to an equation that was
equivalent to 4x + 20 = 0 (which has a negative
solution) in , saying that the equation
was absurd.
• During the 7th century AD, negative numbers were
used in India to represent debts.
• The Indian mathematician Brahmagupta, discussed
the use of negative numbers to produce the
general form quadratic formula that remains in use
today. He also found negative solutions
of quadratic equations and gave rules regarding
operations involving negative numbers and zero.

7. Examples:
A debt minus zero is a debt.
A fortune subtracted from zero is a debt.
• He called positive numbers "fortunes," zero
"a cipher," and negative numbers "debts."
• During the 8th century A.D, the Islamic
world learned about negative numbers
from Arabic translations of Brahmagupta's
works.

8. • The 10th century Islamic Mathematicians were
using negative numbers for debts. The earliest
known Islamic text that uses negative numbers
is A Book on What Is Necessary from the
Science of Arithmetic for Scribes and
Businessmen by
• In the 12th century A.D. in India,
also gave negative roots for quadratic
equations but rejected them because they
were inappropriate in the context of the
problem.

9. • In the 15th century, Nicolas Chuquet, a
Frenchman, used negative numbers
as exponents and referred to them as “absurd
numbers.”
• In the 18th century it was common practice to
ignore any negative results derived from
equations, on the assumption that they were
meaningless.