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Chapter 1.6

Chapter 1.6. Area and Algebra. Geometry so far. So far we have used diagrams and pictures to help us understand geometric topics better Now we can use these geometric ideas of area to connect with the laws of algebra you’ve already seen. Discussion: What is meant by a “law of algebra”.

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Chapter 1.6

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  1. Chapter 1.6 Area and Algebra

  2. Geometry so far • So far we have used diagrams and pictures to help us understand geometric topics better • Now we can use these geometric ideas of area to connect with the laws of algebra you’ve already seen

  3. Discussion:What is meant by a “law of algebra” • Of course not ever equation deserves to be called a law of algebra • What does it mean to “solve” an equation? Can an equation have more then one solution? • Solve the equation x-2=0. How many solutions does it have? • Solve the equation x^2=9. How many solutions are there? • Solve 2x= x+x. • Solve the equation x/x = 1

  4. Is it true or false? • Putting any number into the equation x-2=0 besides 2 make this statement false. The only true statement is 0=0 which happen only when x=2 • At the same time any number will work for 2x=x+x. • x/x=1 is true for any number besides zero. Dividing by zero does not make sense. (special case you may see in calculus)

  5. 2 definitions to know • Domain-The set of all numbers for which an equation makes sense (is either true or false) • Identity- An equation that is true for all numbers in it’s domain • From the previous examples 2x=x+x and x/x=1 are identities, while x-2=0 and x^2=9 are not.

  6. Which of the following are identities?

  7. We can extend this to two variables Is this an identity? On the other hand, what about

  8. It’s the law • Law (in algebra)- an identity that people consider important. Our old friend the DISTRIBUTIVE LAW Open to page 57 and read starting at the bottom paragraph “Several years ago…”

  9. Ms. Bocciarelli

  10. Another algebraic expression

  11. Test those algebra skills

  12. NO!!! • Exponentiation is NOTdistributiveover addition. is not

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