1. Bell Work: Use two unit multipliers to convert 44 square miles to square feet.

2. Answer: 44mi x mi x 5280ft/1mi x 5280ft/1mi = 44(5280) ft = 1,226,649,600ft 22 2

3.  Lesson 11: reciprocal and Multiplicative Inverse, Order of Operations, Identifying Multiplication and Addition

4. Reciprocal and Multiplicative Inverse: If one fraction is the inverted form of another fraction, each of the fractions is said to be the reciprocal of the other fraction.

5. For example, 2/3 is the reciprocal of 3/2 -4/11 is the reciprocal of -11/4

6. Since numbers such as 4 can also be written in a form such as 4/1, these numbers also have reciprocals. 3 is the reciprocal of 1/3 -1/5 is the reciprocal of -5

7. The number zero does not have a reciprocal because 1/0 is undefined.

8. Zero is the only real number that does not have a reciprocal.

9. The reciprocal of a number is often called the multiplicative inverse.

10. If a number is multiplied by its reciprocal (its multiplicative inverse), the product is the number 1. 4 x ¼ = 1-5 x -1/5 = 1

11. Order of Operations: If we wish to compute the value of 4 + 3 x 2 We have a problem. It appears that there are two possible solutions. 4 + 6 = 107 x 2 = 14

12. We worked the problem two ways and got two different answers. Neither way is necessarily more correct than the other, but since there are two possible ways to work the problem, mathematicians have found it necessary to agree on one way so that everyone will get the same answer. They have agreed to do the multiplications first and then to do the additions.

13. Thus, to simplify an expression such as 4 x 3 + 5 – 6 + 4 – 3 x 5 + 6 – 4 x 2 We will use a two-step process. First perform all the multiplications to get 12 + 5 – 6 + 4 – 15 + 6 – 8 Now use algebraic addition. = -2

14. Practice: Simplify 4 x 3 + 2 + (-3)5

15. Answer: 4 x 3 + 2 + (-3)5 = 12 + 2 – 15 = -1

16. Practice: 4 x 3 – 2 x 5 + 6 – 5 x 2

17. Answer: 4 x 3 – 2 x 5 + 6 – 5 x 2 = 12 – 10 + 6 – 10 = -2

18. Identifying Multiplication and Addition: If there is no + or – sign between symbols, multiplication is indicated. 4 – 3(5) – 7(-6) – (4)(-5) 4 – 15 – (-42) – (-20) 4 – 15 + 42 + 20 = 51

19. Practice: Solve 13 – 4(-5) – 3(10)

20. Answer: 13 – 4(-5) – 3(10) = 13 – (-20) – (30) = 13 + 20 + (-30) = 3

21. HW: Lesson 11 #1-30 Due Tomorrow