Abu Ja’far Mu ḥ ammad ibn Mūsā al-Khwārizmī ( AD) محمد بن موسى الخوارزمي Developed by Ivan Seneviratne

Father of Algebra Al-Khwarizmi was a Persian mathematician, astronomer, astrologer and geographer born around 780, in either Khwarizm or Baghdad, and died around 850. His systematic and logical approach gave shape to the discipline of algebra. He also made major contributions to the fields of trigonometry, astronomy, astrology, geography and cartography.

Kitab Al-Jabr wal Muqabala Written by al-Khwarizmi in 9 th century, this was the first book on systematic solution of linear and quadratic equations. The word ‘Algebra’ is a part of the title of this textbook which was translated into Latin in Europe. Algorithmus is a Latin transcription of his name.

What is Algebra? Algebra is a branch of Mathematics that describes the relationships between things that vary over time. Variables are denoted by letters and symbols. Algebra is a study in logic a practical system for solving problems. "al-jabr" means "completion", it is the process of removing negative terms from an equation.

Algebraic Expression An algebraic expression is a combination of variables, numbers, and at least one operation. 43  x Coefficient Variable Constant

Essential Vocabulary Variables A variable is a symbol that represents a number. Constants Fixed values, like 2, 7 or . Coefficients Constant factors that multiply a variable or powers of a variable. Like Terms Same variables

Laws of Algebra Distributive: x(y+z) = xy+xz, (x+y)z = xz+yz Associative: (x+y)+z = x+(y+z) (xy)z = x(yz) Commutative: x+y = y+x xy = yx Identity: x+0 = 0+x = x x 1 = 1x = x Inverse: x+(-x) = (-x)+x = 0 x(x -1 ) = (x -1 )x = 1

Placement Rule Always write the variable after the number. b x 6 write 6b Using parentheses b ( 6 ) write 6b 6 ( b ) write 6b

9 Let’s Think & Discuss  Give an example of an expression that is algebraic.  Give an example of an expression that is not algebraic.  Compare the two expressions: how are the same and how are they different.

This presentation is developed by Ivan Seneviratne © 2006 purely for personal use.