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Complex Fractions, The Golden Mean and Radical and Rational Expressions

1. Complex fractions have some interesting patterns. Evaluate each complex fraction in the sequence below. This is an interesting sequence of fractions because the numerators and denominators are a famous sequence of whole numbers, and the fractions get closer to a number called "the golden mean". After you have evaluated the first five, you no doubt will see a pattern in the resulting fractions as decimals. Write your observations about the sequence of fractions and about the sequence of decimal fractions (see attachment for the problems).

2. Reflect on what you know about rational expressions and their applications, and then consider how you might apply rational expressions to your daily life. Explain this application, and discuss what the equation might be.

3. Give an example of any difficulty you might have with grasping the concepts used in radical expressions. How would you explain square roots, cube roots, n roots, and radicals to a student who is having difficulty understanding these concepts. What are some limitations of square root?

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Complex Fractions, The Golden Mean and Radical and Rational Expressions are investigated.

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