1 / 13

6.3 Dividing Monomials

6.3 Dividing Monomials. CORD Math Mrs. Spitz Fall 2006. Okay, for the HW. Scale: How many correct? 17-20 – 20 points—not bad – you have it! 12-16 – 15 points – You need some practice 7-11 – 10 points. You need some help. Practice some more – rework the problems missed

tovi
Télécharger la présentation

6.3 Dividing Monomials

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. 6.3 Dividing Monomials CORD Math Mrs. Spitz Fall 2006

  2. Okay, for the HW • Scale: How many correct? • 17-20 – 20 points—not bad – you have it! • 12-16 – 15 points – You need some practice • 7-11 – 10 points. You need some help. Practice some more – rework the problems missed • 6 and below – you need some significant help in order to complete this. Take the worksheet and have mom or dad sign it. Rework problems • Turn it in for credit in the box! Record your scores • Quiz after 6.3 is graded next time we meet!

  3. Standard/Objective • Standard: Students will understand algebraic concepts and applications • Objectives: • Students will simplify expressions involving quotients of monomials, and • Simplify expressions containing negative exponents

  4. Assignment • WS 6.3 • Quiz – end of the 6.2 – 20 minutes • Mid-chapter Test after 6.4 • Quiz after 6.6 • Test after 6.9 – short answer – show all work

  5. Consider each of the following quotients. Each number can be expressed as a power of 3. 81 35 27 34 33 = 32 = 9 = 31 = 33 = 3 27 3 32 31 33 Introduction 27 243 = 27 9

  6. Once again, look for a pattern in the quotients shown. If you consider only the exponents, you may notice that 4 – 3 = 1, 3 – 1 = 2, and 5 – 2 = 3 81 35 27 34 33 = 32 = 9 = 31 = 33 = 3 27 3 32 31 33 Introduction 27 243 = 27 9

  7. Now simplify the following: b5 = b2 Quotient of Powers Quotient of Powers: For all integers m and n, and any nonzero number a, b ≠ 0 am = am-n an b · b · b · b · b = b · b · b b · b = b3 These examples suggest that to divide powers with the same base, you can subtract the exponents!

  8. Simplify the following: a4 b3 a1 b2 Example 1 a4b3 = ab2 = a4-1b3-2 Group the powers that have the same base. = a3b1 Subtract the exponents by the quotient of powers property. = a3b Recall that b1 = b.

  9. Study the two ways shown below to simplify a3 a3 Next note: a3 a3 a · a · a = a3-3 = a3 a · a · a a3 = a0 = 1 Zero Exponent: For any nonzero number a, a0 = 1.

  10. Study the two ways shown below to simplify k2 k2 k7 k7 Aha: k2 k · k k2 = k2-7 = k7 k7 k · k · k · k · k · k · k = k-5 1 = k · k · k · k · k Since cannot have two different values, we can conclude that k-5 1 = k5 1 = k5

  11. This examples suggests the following definition: What does this suggest? Negative Exponents: For any nonzero number a and any integer n, a-n 1 = an To simplify an expression involving monomials, write an equivalent expression that has positive exponents and no powers of powers. Also, each base should appear only once and all fractions should be in simplest form.

  12. Simplify the following: s5 -1 -6 r3 1 -1 1 t-2 3 r-7 s5 t-2 3 18 Example 2 -6r3s5 = · · · 18r-7s5t-2 = r3-(-7)s5-5t2 Recall = t2 = r10s0t2 Subtract the exponents. = r10t2 Remember that s0 = 1. - 3

  13. Simplify the following: 4-2 a2 = · 22 a8 1 1 = 64a6 = 43a6 Example 3 (4a-1)-2 Power of a product property (2a4)2 4-2 a2 = Simplify 4a8 = 4-2-1a2-8 Subtract the exponents = 4-3a-6 Definition of negative exponents Simplify

More Related