1. DIVIDING RATIONAL NUMBERS
LESSON 9

2. Dividing Integers Positive ÷ Positive = Positive
Positive ÷ Negative = Negative
Negative ÷ Negative = Positive
Negative ÷ Positive = Negative
An odd number of Negatives divided together gives a negative result.
An even number of Negatives divided together gives a positive result.

3. EXAMPLES: Positive ÷ Positive Positive ÷ Negative Negative ÷ Negative
(10) ÷ (+5)
Positive ÷ Positive
(+36) ÷ (-6)
Positive ÷ Negative
(-12) ÷ (-3)
Negative ÷ Negative
(-54) ÷ (+9)
Negative ÷ Positive
(-12) ÷ (-2) ÷ (-3)
Odd number of Negatives
(-60) ÷ (-2) ÷ (-3) ÷ (-2)
Even number of Negatives

4. EXAMPLES: Positive ÷ Positive = Positive Positive ÷ Negative
(10) ÷ (+5)
= 2
Positive ÷ Positive
= Positive
(+36) ÷ (-6)
Positive ÷ Negative
(-12) ÷ (-3)
Negative ÷ Negative
(-54) ÷ (+9)
Negative ÷ Positive
(-12) ÷ (-2) ÷ (-3)
Odd number of Negatives
(-60) ÷ (-2) ÷ (-3) ÷ (-2)
Even number of Negatives

5. EXAMPLES: Positive ÷ Positive Positive ÷ Negative = Negative
(10) ÷ (+5)
= 2
Positive ÷ Positive
(+36) ÷ (-6)
= -6
Positive ÷ Negative
= Negative
(-12) ÷ (-3)
Negative ÷ Negative
(-54) ÷ (+9)
Negative ÷ Positive
(-12) ÷ (-2) ÷ (-3)
Odd number of Negatives
(-60) ÷ (-2) ÷ (-3) ÷ (-2)
Even number of Negatives

6. EXAMPLES: Positive ÷ Positive Positive ÷ Negative Negative ÷ Negative
(10) ÷ (+5)
= 2
Positive ÷ Positive
(+36) ÷ (-6)
= -6
Positive ÷ Negative
(-12) ÷ (-3)
= 4
Negative ÷ Negative
= Positive
(-54) ÷ (+9)
Negative ÷ Positive
(-12) ÷ (-2) ÷ (-3)
Odd number of Negatives
(-60) ÷ (-2) ÷ (-3) ÷ (-2)
Even number of Negatives

7. EXAMPLES: Positive ÷ Positive Positive ÷ Negative Negative ÷ Negative
(10) ÷ (+5)
= 2
Positive ÷ Positive
(+36) ÷ (-6)
= -6
Positive ÷ Negative
(-12) ÷ (-3)
= 4
Negative ÷ Negative
(-54) ÷ (+9)
= - 6
Negative ÷ Positive
= Negative
(-12) ÷ (-2) ÷ (-3)
Odd number of Negatives
(-60) ÷ (-2) ÷ (-3) ÷ (-2)
Even number of Negatives

8. EXAMPLES: Positive ÷ Positive Positive ÷ Negative Negative ÷ Negative
(10) ÷ (+5)
= 2
Positive ÷ Positive
(+36) ÷ (-6)
= -6
Positive ÷ Negative
(-12) ÷ (-3)
= 4
Negative ÷ Negative
(-54) ÷ (+9)
= - 6
Negative ÷ Positive
(-12) ÷ (-2) ÷ (-3)
= - 2
Odd number of Negatives
= Negative
(-60) ÷ (-2) ÷ (-3) ÷ (-2)
Even number of Negatives

9. EXAMPLES: Positive ÷ Positive Positive ÷ Negative Negative ÷ Negative
(10) ÷ (+5)
= 2
Positive ÷ Positive
(+36) ÷ (-6)
= -6
Positive ÷ Negative
(-12) ÷ (-3)
= 4
Negative ÷ Negative
(-54) ÷ (+9)
= - 6
Negative ÷ Positive
(-12) ÷ (-2) ÷ (-3)
= - 2
Odd number of Negatives
(-60) ÷ (-2) ÷ (-3) ÷ (-2)
= 5
Even number of Negatives
= Positive

10. DIVIDING RATIONAL NUMBERS
Change the fraction after the division sign to its Reciprocal and multiply the fractions by:
Multiply the numerators of the fractions
Multiply the denominators of the fractions
Place the product of the numerators over the product of the denominators
Simplify the Fraction

11. EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷

12. EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -3 5 9 4 x

13. EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -3 5 9 4 x
-27 20

14. EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -3 5 9 4 x
-27 20 7 20 -1

15. EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 -2 -5 7 6 -3 5 9 4 -27 20 ÷ ÷ ÷-1

16. EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -2 -5 7 6 -3 5 9 4 x x 14 30
-27 20
Notice the fraction is positive 7 20 -1

17. EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -2 -5 7 6 -3 5 9 4 x x 14 30
-27 20 7 15 7 20 -1

18. EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -2 -5 7 6 4 7
-13 8 -3 5 9 4 x x x 14 30
-27 20
Notice the negative stays in the numerator.
Becomes Positive 7 15 7 20 -1

19. EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -2 -5 7 6 4 7
-13 8 -3 5 9 4 x x x 14 30
-52 56
-27 20 7 15 7 20 -1

20. EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -2 -5 7 6 4 7
-13 8 -3 5 9 4 x x x 14 30
-52 56
-27 20 7 15
-13 14 7 20 -1

21. MORE EXAMPLES 3 5 3 5 -8 5 3 5 5 3 -8 5 2 3 -40 15 -8 3 ÷ ÷ -1 -2 x =
Change Mixed to an Improper. -8 5 3 5 ÷ 5 3 -8 5
Reciprocal. x 2 3
-40 15 -8 3 -2 = =