# 3: The Fundamentals of Algebra

- Page ID
- 22479

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In this section we’ll learn how to manipulate symbols in order to combine like terms and restore and balance equations.

- 3.0: Prelude to the Fundamentals of Algebra
- Abu Jafr Muhammad ibn Musa al-Khwarizmi was one of the greatest Arab mathematicians of his time. While living in Baghdad during the ninth century AD he became the Chief Librarian at the House of Wisdom, a library and major center of intellectual study. In 820 CE, al-Khwarizmi wrote Al-Kitab al-mukhtasar ti Hisab al-jabr w’al-muqabala, translated to, The Compendious Book on Calculation by Restoration and Reduction, the first book to generalize solving equations using the principles of equality.

- 3.1: Mathematical Expressions
- In this section we turn our attention to translating word phrases into mathematical expressions. We begin with phrases that translate into sums. There is a wide variety of word phrases that translate into sums. When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.

- 3.2: Evaluating Algebraic Expressions
- In this section we will evaluate algebraic expressions for given values of the variables contained in the expressions.

- 3.3: Simplifying Algebraic Expressions
- The commutative property allows us to change the order of multiplication without affecting the product or answer. The associative property allows us to regroup without affecting the product or answer.

- 3.4: Combining Like Terms
- A term is a single number or variable, or it can be the product of a number (called its coefficient) and one or more variables (called its variable part). The terms in an algebraic expression are separated by addition symbols.

- 3.5: Solving Equations Involving Integers II
- We return to solving equations involving integers, only this time the equations will be a bit more advanced, requiring the use of the distributive property and skill at combining like terms.

- 3.6: Applications
- Because we’ve increased our fundamental ability to simplify algebraic expressions, we’re now able to tackle a number of more advanced applications.