SAMPLE Fundamentals of Math

Fundamentals of Mathematics Chapter 1: Operations with Real Numbers

Merriam Webster defines mathematics as, “the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations”. Pretty fancy talk for trying to say a scientific study of numbers and how numbers behave. Essentially all of mathematics from Algebra to Trigonometry to Calculus all gather their roots from the fundamental concepts defined by the real number system and the mathematical properties that follows. Sorry, academia talk again – basically, all of mathematics boils down to the real number system and its four primary operators: addition, subtraction, multiplication, and division. 1.1 Operations Let’s start by defining a few basic definitions so we are all on the same page. ● Addition – combining two or more numbers (or items) together to make a new total. ● Subtraction – taking one number away from another number. ● Multiplication – a set value combined with itself a set number of times (repeated addition) ● Division – splitting a number into an equal number of groups These four simple operators most of us initially learned in grade school are used in all domains of mathematics. Of course, the days of straightforward questions such as “what is 2+2?” are probably long gone. Today, most of what we encounter come in stories or worded questions like “If all red tags indicate the item is 20% off then how much will this red-tag shirt cost?” So, let’s begin by reviewing a few phrases you are probably already familiar with and remind ourselves what they mean.

Figure 1.1.1: Common Verbal Operator Expressions Addition Subtraction Multiplication Division Combined Difference Multiplied Divided by Increased Decreased Product Into More than Less than Times Per Sum Minus Of Quotient Together Reduced Twice Out of Plus Fewer than Thrice Ratio of Added to Take away Split

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