1. Beginning Algebra Division of Real Numbers

2. Objective 1. To divide two real numbers. Objective 3. To simplify expressions containing division using the rule for order of operations. 1.7 Division of Real Numbers Objective 2. To divide fractions. Objective 4. To translate sentences from English into symbols and them simplify.

3. Multiply Signed Numbers Write the + sign and Product of the numbers (Always positive) Write the - sign and Product of the numbers (Always negative) Like signsUnlike signs

4. Multiply Signed Numbers Write the + sign and Product of the numbers (Always positive) Write the - sign and Product of the numbers (Always negative) Like signsUnlike signs

5. Divide signed numbers: Multiply by reciprocal a  1 b a b c d  a b d c  To Divide

6. Divide signed numbers: 8  2 = ( - 9)  ( - 3) = (16)  ( - 4) = ( - 12)  6 =

7. 8  2 = 8  = 4 2 1 is positive.  positive Positive Divide: (Multiplyby reciprocal)

8. ( - 9)  ( - 3) = Divide: ( - 9)  = + 3 (Multiplyby reciprocal) 3 - 1- 1 is positive.  negative Negative

9. 16  ( - 4) = 16  = - 4 4 - 1- 1 Divide: (Multiplyby reciprocal)  negative Positive is negative.

10. ( - 12)  6 = ( - 12)  = - 2 6 1 Divide: (Multiplyby reciprocal) is negative.  positive Negative

11. Divide: (Multiply by reciprocal) 8  2 = 8  = 4 ( - 12)  6 = ( - 12)  = - 2 1 6 (16)  ( - 4) = (16)  = - 4 - 1 4 ( - 9)  ( - 3) = ( - 9)  = + 3 - 1 3.

12.  = 1 is positive. Positive Divide: (Multiply 3 4 by reciprocal) 8 6  = 4 3 8 6 positive  2 1 2 1 Simplify:

13. Divide: (Multiply is positive. Negative =  6 - 1- 1 9 - 7- 7 = 3 14 + 9 - 7- 7 by reciprocal)  1 - 6- 6 3 - 2- 2 negative  Simplify:

14. Divide: (Multiply 4 - 5- 5 by reciprocal)  negative Positive is negative.  13 10  = 13 10 5 - 4- 4 2 5 = 26 25 - Simplify:

15. Divide: (Multiply is negative.  positive Negative  = 10 - 3- 3 5 12  10 - 3- 3 by reciprocal) 5 12 = 8 - 1- 1 -1 4 2 1 Simplify:

16. Divide: (Multiply by reciprocal)  = 4 3 8 6 1  = 3 4 8 6 3 14  = 9 - 7- 7 8 - 1- 1 8 - 1- 1 26 - 25 =  5 - 4- 4 13 10 =  5 12 10 - 3- 3. = 9 - 7- 7 8  = 4 - 5- 5 13 10  = - 3- 3 5 12 

17. Simplify with several operations: -7(-3) -35 -7(-3) -35 Reduce and divide 1 5 -3 5 =.

18. Simplify with several operations: 20 - 5(-3) 10(-3) Add numerator. -7 6 = 20 + 15 10(-3) Multiply numerator first. 7 2 35 10(-3) Reduce and multiply..

19. Operation of Mixed Signed Numbers: [Count the negatives.] (- 2)(- 2) (- 3)(- 3)( 3) (- 7)(- 7) (4)(4) (- 9)(- 9)  positive Even + 8 7 = (4)(4) ( 2)( 2) (3)(3)( 3) ( 7)( 7) ( 9)( 9) + 1 3 Attach + to product of unsigned numbers and simplify: 1 1

20. [Count the negatives.] (2)(2) (- 4)(- 4) ( 3)( 1) (- 5)(- 5) Odd  negative - 3 5 = (- 8)(- 8) Operation of Mixed Signed Numbers: (2)(2) (4)(4) ( 3)( 1) (5) (8) - 4 1 1 1 Attach - to product of unsigned numbers and simplify:

21. Investment Investment: If 8 people invest $500 each in a stamp collection and after a year the collection is worth $3,800, how much did each person lose? Problem Involving Subtraction Translating English Sentences: $200 The original value of the stamps depreciated by the amount of $200 in the first week. You lost $25.. 8(500) - 3800 8 4000 - 3800 8 = = 200 8 = 25

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