Table of Contents

Motivation Problem

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Number Line Model

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Absolute Value

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Chip Model

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Additive Inverse

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Compare the Two Models

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Rational Numbers

 

 

 

 

 

Motivation Problem

How may we compare the values of the following two accounts?

Sam had two accounts, a savings account and a loan. She had a certificate of deposit worth $4,360 and a car loan of $8,290. Which account has the greatest value?

The answer to this question depends on how we think about the situation. If we are asking which situation involves more dollars, then $8,290 involves a greater dollar amount than $4,360. However, if we are asking which value is worth more to Sam, obviously the certificate of deposit, which is money she "owns" is worth more than the loan, which is money she "owes".

In mathematical terms, Sam's CD has a positive value and the loan has a negative value. In mathematics, when we look at just the number of dollars and not whether the value is positive or negative we are talking about the absolute values.  

We consider two different models to help us understand the properties of positive and negative numbers. First we consider the number line model and then we consider the chip model (set model).


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