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# 1: Foundations

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In this chapter, you will review the language of algebra and take your first steps toward working with algebraic concepts.

• 1.0: Prelude to the Foundations of Algebra
Scientists are designing ways to use 3D printers to build on the moon or Mars. Already, animals are benefiting from 3D-printed parts, including a tortoise shell and a dog leg. Builders have even constructed entire buildings using a 3D printer. The technology and use of 3D printers depends on the ability to understand the language of algebra. Engineers must be able to translate observations and needs in the natural world to complex mathematical commands that can provide directions to a printer.
• 1.1: Use the Language of Algebra
This chapter is intended to be a brief review of concepts that will be needed in an Intermediate Algebra course.
• 1.2: Integers
So far, we have only used the counting numbers and the whole numbers. Our work with opposites gives us a way to define the integers. The whole numbers and their opposites are called the integers. The integers are the numbers …−3,−2,−1,0,1,2,3…
• 1.3: Fractions
A fraction is a way to represent parts of a whole.
• 1.4: Decimals
Decimals are another way of writing fractions whose denominators are powers of ten.
• 1.5: Properties of Real Numbers
• 1.E: Foundations (Exercises)