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Hisab al-jabr w’al-muqa-balah

This is the title of a 300 year old book (in Arabic). Translated, it means:. Hisab al-jabr w’al-muqa-balah. “Science of the reunion and the opposition” or “The science of equations”. Does that part of the title look familiar?. algebra.

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Hisab al-jabr w’al-muqa-balah

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  1. This is the title of a 300 year old book (in Arabic). Translated, it means: Hisab al-jabr w’al-muqa-balah “Science of the reunion and the opposition” or “The science of equations” Does that part of the title look familiar? algebra

  2. For algebraic operations, we begin to mix together numbers and letters into our operations, which is a major challenge for students. By now we know that a variable represents a quantity that can change….

  3. A little math magic….. Think of a number from 1 to 5 Add 3 Multiply by 2 Subtract 4 Divide the number in half Subtract the number you started with…

  4. Exponent Laws Multiplying and Dividing Powers

  5. Can you think of some examples of any short- cuts How about cleaning your room? Cutting the grass Dishes? (eat over the sink) It is our nature to search for more efficient ways to do things

  6. The Exponent Laws are an example of a mathematical short-cut.We’ll learn the mechanics of the short cut first, then we’ll examine the applications. Specifically, repeated operations can be compressed using the Exponent Laws The following examples will illustrate

  7. Through the investigation of patterns, we are going to derive the first and second exponent laws…. But first, a few practice runs…

  8. Examine the following patterns to predict what the next symbol will be…. O T T F F …..

  9. M T W T F S …. J F M A M …

  10. Given any pattern, the simplest progression will be the implication.

  11. 1 3 5 7 9 … These examples are called Sequences 0 2 6 12 … 1 8 27 … 8 4 2 1 … 2 4 8 16 32 …

  12. 7 10 10 X 10 X 10 X 10 X 10 X 10 X 10 We are multiplying 10 by itself 7 times, so this can be re-written in exponential form as: power exponent base

  13. 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 = 28 23 X 25 = Examine the exponents… Is there a short cut? Since the bases can vary, we will use a variable to represent all cases In general: 1. XaX Xb = Xa + b

  14. For example: (x3) (x8) = x11 (a4) (a3) = a7 (a5) (a) (a3) = a9 (y4) (x2) = x2y4

  15. 2 X 2 X 2 X 2 X 2 25 22 = 2 X 2 = 23 Is there a short cut? In general: 2. XaXb = Xa - b

  16. For example: (x7) = x5 (x2) (a4) = a1 = a (a3)

  17. Evaluate for t = 3 and s = 2 t2 + s3 = (3)2 + (2)3 = 3 X 3 + 2 X 2 X 2 = 9 + 8 = 17

  18. McGraw-Hill Ryerson Pg 114 5,6,7 Pg 126 2,4

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