1. MULTIPLYING RATIONAL NUMBERS LESSON 8

2. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative = Positive  Negative x Positive = Negative  An odd number of Negatives multiplied together gives a negative result.  An even number of Negatives multiplied together gives a positive result.

3. EXAMPLES: (8) x (+5) Positive x Positive (+7) x (-6) Positive x Negative (-4) x (-3) Negative x Negative (-8) x (+9) Negative x Positive (-4) x (-2) x (-3) Odd number of Negatives (-1) x (-9) x (-3) x (-2) Even number of Negatives

4. EXAMPLES: (8) x (+5) = + 40 Positive x Positive = Positive (+7) x (-6) Positive x Negative (-4) x (-3) Negative x Negative (-8) x (+9) Negative x Positive (-4) x (-2) x (-3) Odd number of Negatives (-1) x (-9) x (-3) x (-2) Even number of Negatives

5. EXAMPLES: (8) x (+5) = + 40 Positive x Positive (+7) x (-6) = - 42 Positive x Negative = Negative (-4) x (-3) Negative x Negative (-8) x (+9) Negative x Positive (-4) x (-2) x (-3) Odd number of Negatives (-1) x (-9) x (-3) x (-2) Even number of Negatives

6. EXAMPLES: (8) x (+5) = + 40 Positive x Positive (+7) x (-6) = - 42 Positive x Negative (-4) x (-3) = + 12 Negative x Negative = Positive (-8) x (+9) Negative x Positive (-4) x (-2) x (-3) Odd number of Negatives (-1) x (-9) x (-3) x (-2) Even number of Negatives

7. EXAMPLES: (8) x (+5) = + 40 Positive x Positve (+7) x (-6) = - 42 Positve x Negative (-4) x (-3) = + 12 Negative x Negative (-8) x (+9) = - 72 Negative x Positive = Negative (-4) x (-2) x (-3) Odd number of Negatives (-1) x (-9) x (-3) x (-2) Even number of Negatives

8. EXAMPLES: (8) x (+5) = + 40 Positive x Positve (+7) x (-6) = - 42 Positve x Negative (-4) x (-3) = + 12 Negative x Negative (-8) x (+9) = - 72 Negative x Positive (-4) x (-2) x (-3) = - 24 Odd number of Negatives = Negative (-1) x (-9) x (-3) x (-2) Even number of Negatives

9. EXAMPLES: (8) x (+5) = + 40 Positive x Positve (+7) x (-6) = - 42 Positve x Negative (-4) x (-3) = + 12 Negative x Negative (-8) x (+9) = - 72 Negative x Positive (-4) x (-2) x (-3) = - 24 Odd number of Negatives (-1) x (-9) x (-3) x (-2) = + 54 Even number of Negatives = Positive

10. Multiplying Rational Numbers  Use the SAME RULES for Rational numbers as you did for Integers.  multiply the two numerators and the two denominators.  REMEMBER: If there are negative signs to place them in the numerator.

11. EXAMPLES 3535 x x= 3535 2525 -3 4 -4 7 -3 8 x = =

12. EXAMPLES 3535 x x= 3535 2525 -3 4 -4 7 -3 8 x = = 9 25 POSITIVE x POSITIVE = POSITIVE

13. EXAMPLES 3535 x x= 3535 2525 -3 4 -4 7 -3 8 x = = 9 25 -6 20 POSITIVE x NEGATIVE = NEGATIVE

14. EXAMPLES 3535 x x= 3535 2525 -3 4 -4 7 -3 8 x = = 9 25 -6 20 12 56 NEGATIVE x NEGATIVE = POSITIVE

15. MORE EXAMPLES -4 -5 x x= -3 6 2525 -3 4 -2 3 -3 4 x = = 2 -3 -2 x

16. MORE EXAMPLES -4 -5 x x= -3 6 2525 -3 4 -2 3 -3 4 x = = 2 -3 -2 x -12 30

17. MORE EXAMPLES -4 -5 x x= -3 6 2525 -3 4 -2 3 -3 4 x = = 2 -3 -2 x -12 30 = -2 5 ODD Number of Negatives = Negative Reduced to LOWEST TERMS

18. MORE EXAMPLES -4 -5 x x= -3 6 2525 -3 4 -2 3 -3 4 x = = 2 -3 -2 x 5 12 5 -3 4 x= CHANGE MIXED TO AN IMPROPER FRACTION

19. MORE EXAMPLES -4 -5 x x= -3 6 2525 -3 4 -2 3 -3 4 x = = 2 -3 -2 x 5 12 5 -3 4 x= -36 20 =

20. MORE EXAMPLES -4 -5 x x= -3 6 2525 -3 4 -2 3 -3 4 x = = 2 -3 -2 x 5 12 5 -3 4 x= -36 20 = 4545 Positive x Negative = Negative Change back to mixed and reduce fraction

21. MORE EXAMPLES -4 -5 x x= -3 6 2525 -3 4 -2 3 -3 4 x = = 2 -3 -2 x 5 4545 18 24

22. MORE EXAMPLES -4 -5 x x= -3 6 2525 -3 4 -2 3 -3 4 x = = 2 -3 -2 x 5 4545 18 24 = 3434 Reduce to LOWEST TERMS EVEN Number of Negatives = Positive

23. TRY THESE -4 5 x 3737 -5 8 3 -7 -2 -4 1616 3737 xx x = = =

24. TRY THESE -4 5 x 3737 -5 8 3 -7 -2 -4 1616 3737 xx x = = = -12 35

25. TRY THESE -4 5 x 3737 -5 8 3 -7 -2 -4 1616 3737 xx x = = = -12 35 30 224 = 15 112

26. TRY THESE -4 5 x 3737 -5 8 3 -7 -2 -4 1616 3737 xx x = = = -12 35 30 224 = 15 112 1616 x -10 7 = -10 42 = -5 21