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# Why It Matters: Algebra Essentials

## Why learn about the essentials of algebra?

Yuan Dynasty iron magic square showing Persian/ Arabic numbers (ca. 1271 - 1368)
It is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. Farmers, cattlemen, and tradesmen used tokens, stones, or markers to signify a single quantity—a sheaf of grain, a head of livestock, or a fixed length of cloth, for example. Doing so made commerce possible, leading to improved communications and the spread of civilization. Three to four thousand years ago, Egyptians introduced fractions. They first used them to show reciprocals. Later, they used them to represent the amount when a quantity was divided into equal parts. But what if there were no cattle to trade or an entire crop of grain was lost in a flood? How could someone indicate the existence of nothing? From earliest times, people had thought of a "base state" while counting and used various symbols to represent this null condition. However, it was not until about the fifth century A.D. in India that zero was added to the number system and used as a numeral in calculations. Clearly, there was also a need for numbers to represent loss or debt. In India, in the seventh century A.D., negative numbers were used as solutions to mathematical equations and commercial debts. The opposites of the counting numbers expanded the number system even further.

### Learning Objectives

Real Numbers
• Classify a real number
• Perform calculations using order of operations
• Use the properties of real numbers
• Evaluate and simplify algebraic expressions
Exponents and Scientific Notation
• Use the rules of exponents to simplify exponential expressions
• Use scientific notation
Radicals and Rational Exponents
• Evaluate and simplify square roots
• Rationalize a denominator that contains a square root
• Rewrite a radical expression using rational exponents