the Least Common Denominator (LCD) of two rational expressions

Math

Paper instructions:

1. Many students struggle with word problems. One key to being successful with these types of problems is converting them into mathematical statements and knowing how to solve them. For instance, knowing that the word “is” can be translated into “=” helps convert from one notation to the other. Create a linear equation for a common real-world problem and share how you found the solution. What words in a word problem tell you to add or subtract? What words tell you to multiply or divide?

2. Math, and specifically Algebra, is used every day in people’s lives. Explain why you agree or disagree with that statement and provide examples to justify your stance. Include a useful example with numbers to support your claims.

3. In your own words, explain the process of factoring a trinomial with a leading coefficient that is not equal to one. Why is this process more difficult than when the leading coefficient is equal to one? Give an example. How could we apply FOIL in this context?

4. Statistical studies have shown that intelligence is not a predictor of math success; but motivation, study skills, and hard work are strong predictors. There is no such thing as a “math person” or a “nonmath person.” Math is a matter of learning and learning how to learn. What have you seen in the first two topics to either affirm or reject this evidence? What tools in the classroom are you using to aid your learning? Give an example.

5. A rational expression is a fraction of two polynomials. If you need to add or subtract two rational expressions, how would you do it? Describe, in your own words, the process for finding the Least Common Denominator (LCD) of two rational expressions. How is factoring related to this process? Give an example of adding two rational expressions with different denominators.

6. The quizzes and exams are timed. What are successful strategies and resources that you have found useful for taking the weekly quizzes and exams? What steps can you take to improve your quiz scores? What have you already tried that has worked or not worked and why?

7. What is a rational exponent? How are rational exponents related to radicals? Give an example of how an expression with a rational exponent can be rewritten as a radical expression, and simplify the expression, if possible

8. Complex numbers are what you get when you add real and imaginary numbers. What is an imaginary number? How are they different or similar to real numbers? What applications do they have?

9. Select a quadratic equation and solve it using the “completing the square” method. Show your work in full details.

10. What are like terms in mathematics and when are like terms required? What two criteria are required for terms to be like?

11. State the quadratic formula. Take your example from last week’s completing the square, or pick a new quadratic equation, and solve it using the quadratic formula.

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13. Logarithms and exponents are inversely related. What does this mean mathematically, and how can we use an inverse to solve a problem? What are the properties of logs? Demonstrate this by solving an example of a logarithmic equation and label which property of logarithms you are using in each step.

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