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# Algebra (saylor.org)

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This introductory mathematics course is for you if you have a solid foundation in arithmetic (that is, you know how to perform operations with real numbers, including negative numbers, fractions, and decimals). Numbers and basic arithmetic are used often in everyday life in both simple situations, like estimating how much change you will get when making a purchase in a store, as well as in more complicated ones, like figuring out how much time it would take to pay off a loan under interest.

This introductory mathematics course is for you if you have a solid foundation in arithmetic (that is, you know how to perform operations with real numbers, including negative numbers, fractions, and decimals). Numbers and basic arithmetic are used often in everyday life in both simple situations, like estimating how much change you will get when making a purchase in a store, as well as in more complicated ones, like figuring out how much time it would take to pay off a loan under interest.

The subject of algebra focuses on generalizing these procedures. For example, algebra will enable you to describe how to calculate change without specifying how much money is to be spent on a purchase–it will teach you the basic formulas and steps you need to take no matter what the specific details of the situation are. Likewise, accountants use algebraic formulas to calculate the monthly loan payments for a loan of any size under any interest rate. In this course, you will learn how to work with formulas that are already known from science or business to calculate a given quantity, and you will also learn how to set up your own formulas to describe various situations by translating verbal descriptions to mathematical language. In the later units of this course, you will discover another tool used in mathematics to describe numbers and analyze relationships: graphing. You will learn that any pair of numbers can be represented by a point on a coordinate plane and that a relationship between two quantities can be represented by a line or a curve.

Units 6, 7, and 8 may seem more abstract than the earlier ones, as you will deal with expressions that contain mostly variables and not too many numbers. While the procedures you will master in these units might seem to have little practical application, you have to keep in mind that they result in formulas that describe very real situations in business, accounting, and science. Knowing how to perform various operations with algebraic expressions will eventually enable you to solve quadratic and even more complex equations. You will explore a variety of real-world scenarios that can be described by these kinds of equations. For example, if a ball is thrown up in the air, solving a quadratic equation will help you find out when it will hit the ground. As another example, if you know the area of a rectangular garden, then you can use a quadratic equation to find the length of each side.