Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time. These variables include things like the relationship between supply of an object and its price. When we use a mathematical statement to describe a relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount. These letters and symbols are referred to as variables. (See the Appendix One for a brief review of constants and variables.)
The mathematical statements that describe relationships are expressed using algebraic terms, expressions, or equations (mathematical statements containing letters or symbols to represent numbers). Before we use algebra to find information about these kinds of relationships, it is important to first cover some basic terminology. In this unit we will first define terms, expressions, and equations. In the remaining units in this book we will review how to work with algebraic expressions, solve equations, and how to construct algebraic equations that describe a relationship. We will also introduce the notation used in algebra as we move through this unit. The numerical part of the term, or the number factor of the term, is what we refer to as the numerical coefficient. This numerical coefficient will take on the sign of the operation in front of it. The term above contains a numerical coefficient, which includes the arithmetic sign, and a variable or variables. In this case the numerical coefficient is –3 and the variables in the term are a and x. Terms such as xz may not appear to have a numerical coefficient, but they do. The numerical coefficient is 1, which is assumed.
An expression is a meaningful collection of numbers, variables, and signs, positive or negative, of operations that must make mathematical and logical sense. Expressions:
contain any number of algebraic terms
use signs of operation—addition, subtraction,...
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