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. • 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?” 1.1 Operations Let’s start by defining a few basic definitions so we are all on the same page.

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

Recognizing these key words can help us translate what we are hearing/asking in our everyday lives to turn our questions into actionable problems. For example, the manager knows that the restaurant has 24 tables in total and there will be four waitresses on staff today. How many tables per waitress will there be? By recognizing the number per number (or object per person) phrasing here helps us identify this is a division problem, since we know _____ per _____ means to divide.

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