1 / 36

Understanding Hourly Rates and Complex Numbers in Algebra Assignments

This educational material covers practical applications of algebra, including calculating hourly wages from paid work and simplifying complex numbers and square roots. A specific example shows how to determine Shana's hourly rate based on her earnings of $7.79 for three-quarters of an hour. Additional content explains how to manipulate radical expressions, deal with negative square roots, and conceptualize complex numbers. Ideal for students looking to reinforce their algebra skills and understanding of mathematical concepts.

zoltin
Télécharger la présentation

Understanding Hourly Rates and Complex Numbers in Algebra Assignments

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 29 March 2011 Algebra 2

  2. Shana was paid $7.79 for ¾ of an hour of work. At this rate, what is her hourly rate? • $8.54 • $10.39 • $5.84 • $7.04 300 0 of 30

  3. Congratulations!! You completed all the Interims!!!

  4. Agenda • Bellringer • Complex Numbers Review • i , • ix • i * I • Student Practice / Interim Make-up • Interim Results

  5. Complex Numbers 3/30 22 = 4 32 = 9 42 = 16 52 = 25 62 = 36 72 = 49 82 = 64 92 = 81 102 = 100 112 = 121 122 = 144 Simplifying Square Roots You should already have this list. If not, copy this list into your notes. Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  6. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  7. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? 90 / 9 = 10 Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  8. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? 90 / 9 = 10  * = Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  9. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? 90 / 9 = 10  * = Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  10. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? 90 / 9 = 10  * = 3 * = Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  11. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? 90 / 9 = 10  * = 3 * = Final Answer: 3 Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  12. Simplify • 3 • 7 • 7 • 3 60 0 of 30

  13. Simplify • 4 • 5 • 10 • 2 60 0 of 30

  14. Complex Numbers 3/30 Simplify Enter on your calculator. What happens when you press enter ? Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  15. Complex Numbers 3/30 Simplify Enter on your calculator. What happens when you press enter ? Your calculator will not take the square root of a negative number. Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  16. Complex Numbers 3/30 Simplify What we need to do is deal with the negative under the radical. Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  17. Complex Numbers 3/30 Simplify What we need to do is deal with the negative under the radical. Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  18. Complex Numbers 3/30 Simplify Separate the negative sign from the number Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  19. Complex Numbers 3/30 Simplify Mathematicians invented a symbol for . = i Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  20. Complex Numbers 3/30 Simplify = i ∙ 6 Rewrite putting your number first: 6i Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  21. Simplify • 10i • 7i • 9i • 3i 60 0 of 30

  22. Simplify • 4 • 5 • 10 • 2 60 0 of 30

  23. Complex Numbers 3/30 If you raise i to a power, there are only four possible results: i1 = i2 = i3 = i4 = i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  24. Complex Numbers 3/30 If you raise i to a power, there are only four possible results: i1 = i2 = ● = -1 i3 = i4 = i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  25. Complex Numbers 3/30 If you raise i to a power, there are only four possible results: i1 = i2 = ● = -1 i3 = ● ● = - i4 = i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  26. Complex Numbers 3/30 If you raise i to a power, there are only four possible results: i1 = i2 = ● = -1 i3 = ● ● = - i4 = ● ● ● = 1 i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  27. Complex Numbers 3/30 If you raise i to a power, there are only four possible results: i1 = i2 = ● = -1 i3 = ● ● = - i4 = ● ● ● = 1 After 4, the powers start back over at 1 i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  28. Complex Numbers 3/30 i5 = ? i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  29. Complex Numbers 3/30 i5 = ? 5 – 4 = 1, so i5 = i1 i5 = i1 = i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  30. Complex Numbers 3/30 i12 = ? i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  31. Complex Numbers 3/30 i12 = ? 12 – 4 = 8 Subtract 4 i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  32. Complex Numbers 3/30 i12 = ? 12 – 4 = 8, 8 – 4 = 4 Keep subtracting 4 until you get a 1, 2, 3 or 4 i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  33. Complex Numbers 3/30 i12 = ? 12 – 4 = 8, 8 – 4 = 4, so i12 = i4 i12 = i4 = 1 i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  34. Simplify i15 • . • -1 • - • 1 0 of 30

  35. Simplify i21 • . • -1 • - • 1 0 of 30

  36. Student Practice • Complete the 20 questions from the board • You have 30 minutes to finish the assignment

More Related