1. March 3, 2009 Experience is the name every one gives to their mistakes. -Oscar Wilde

2. March 3, 2009 Section 3.4 – division Explorations 3.18 & 3.19 Homework

3. March 3, 2009 Test 2 – Thursday, 3/12 (50 min.) Covers: Text 3.3 & 3.4 (Multiplication and Division) Explorations (so far, 3.13, 3.15, 3.18, 3.19) Class Notes

4. 3.4 (cont’d) Explain what is wrong, and why it’s wrong: “50 ÷ 7 is the same as 50 ÷ 10, which is 5. But, I added 3 to the divisor, so now I need to subtract 3: 5 – 3 = 2.”

5. 3.4 (cont’d) Distributive law and Division: Since division is equivalent to multiplication by the reciprocal of the divisor, we can write: a ÷ n = a · (1/n) We have to be careful with distributing, though:

6. 3.4 (cont’d) Distributive law and Division: However, We will discuss fractions in detail after test 2.

7. 3.4 (cont’d) A short video: http://www.youtube.com/watch?v=7WMi5TUJDso&feature= related

8. 3.4 (cont’d) 1 and 0 are special We know that the product of any number and 1 yields the original number. This is known as the multiplicative identity. It is the only number for which this is true! We know that the sum of any number and 0 yields the original number. This is known as the additive identity. It is the only number for which this is true!

9. 3.4 (cont’d) Additionally… The product of 0 and any number is always 0. This is always true, and it is only true for 0. We call this the multiplication property of zero. Since multiplication and division are inverses, however, this property of 0 creates some difficulties.

10. 3.4 (cont’d) Zero is special: 1.If I have 30 party favors to put into 6 bags, how many party favors should I put in each bag? 2.If I have 0 party favors to put into 6 bags, how many party favors should I put in each bag?

11. 3.4 (cont’d) Zero is special: 3.If I have 30 party favors to put into 6 bags, how many party favors should I put in each bag? 4.If I have 30 party favors to put into 0 bags, how many party favors should I put in each bag?

12. 3.4 (cont’d) Problem 2 is silly, but still makes sense, so we can think about a solution: 0 party favors per bag. However, problem 4 is silly and makes no sense – if I have no bags, the rate “favors per bag” is meaningless. For this reason, we say that division by 0 is undefined.

13. 3.4 (cont’d) Another way to think about it: If 30 ÷ 6 = 5, then 30 ÷ 5 = 6; 5 6 = 30; 6 5 = 30. If 30 ÷ 0 = some value, call it V, then 30 ÷ V = 0; V 0 = 30; 0 V = 30. But related facts are supposed to show that multiplication and division are inverses.

14. 3.4 (cont’d) Explorations 3.18 & 3.19 (worksheet)

15. Homework Due Thursday, 3/5: Link to online homework list