DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.
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DIVIDING RATIONAL DIVIDING RATIONAL NUMBERSNUMBERS
LESSON 9LESSON 9
Dividing IntegersDividing Integers
►Positive Positive ÷÷ Positive = Positive Positive = Positive►Positive Positive ÷÷ Negative = Negative Negative = Negative►Negative Negative ÷÷ Negative = Positive Negative = Positive►Negative Negative ÷÷ Positive = Negative Positive = Negative►An An odd number of Negativesodd number of Negatives divided divided
together gives a together gives a negativenegative result. result.►An An even number of Negativeseven number of Negatives divided divided
together gives a together gives a positivepositive result. result.
EXAMPLES:EXAMPLES:
(10) (10) ÷÷ (+5) (+5) Positive Positive ÷÷ Positive Positive
(+36) (+36) ÷÷ (-6) (-6) Positive Positive ÷÷ Negative Negative
(-12) (-12) ÷÷ (-3) (-3) Negative Negative ÷÷ Negative Negative
(-54) (-54) ÷ ÷ (+9)(+9) Negative Negative ÷÷ Positive Positive
(-12) (-12) ÷÷ (-2) (-2) ÷÷ (-3) (-3) Odd number of Odd number of NegativesNegatives
(-60) (-60) ÷÷ (-2) (-2) ÷÷ (-3) (-3) ÷ ÷ (-2)(-2) Even number of Even number of NegativesNegatives
EXAMPLES:EXAMPLES:
(10) (10) ÷÷ (+5) (+5)
= 2= 2Positive Positive ÷÷ Positive Positive
= Positive= Positive(+36) (+36) ÷÷ (-6) (-6) Positive Positive ÷÷ Negative Negative
(-12) (-12) ÷÷ (-3) (-3) Negative Negative ÷÷ Negative Negative
(-54) (-54) ÷ ÷ (+9)(+9) Negative Negative ÷÷ Positive Positive
(-12) (-12) ÷÷ (-2) (-2) ÷÷ (-3) (-3) Odd number of Odd number of NegativesNegatives
(-60) (-60) ÷÷ (-2) (-2) ÷÷ (-3) (-3) ÷ ÷ (-2)(-2) Even number of Even number of NegativesNegatives
EXAMPLES:EXAMPLES:
(10) (10) ÷÷ (+5) (+5)
= 2= 2Positive Positive ÷÷ Positive Positive
(+36) (+36) ÷÷ (-6) (-6)
= -6= -6Positive Positive ÷÷ Negative Negative
= Negative= Negative(-12) (-12) ÷÷ (-3) (-3) Negative Negative ÷÷ Negative Negative
(-54) (-54) ÷ ÷ (+9)(+9) Negative Negative ÷÷ Positive Positive
(-12) (-12) ÷÷ (-2) (-2) ÷÷ (-3) (-3) Odd number of Odd number of NegativesNegatives
(-60) (-60) ÷÷ (-2) (-2) ÷÷ (-3) (-3) ÷ ÷ (-2)(-2) Even number of Even number of NegativesNegatives
EXAMPLES:EXAMPLES:
(10) (10) ÷÷ (+5) (+5)
= 2= 2Positive Positive ÷÷ Positive Positive
(+36) (+36) ÷÷ (-6) (-6)
= -6= -6Positive Positive ÷÷ Negative Negative
(-12) (-12) ÷÷ (-3) (-3)
= 4= 4Negative Negative ÷÷ Negative Negative
= Positive= Positive(-54) (-54) ÷÷ (+9) (+9) Negative Negative ÷÷ Positive Positive
(-12) (-12) ÷÷ (-2) (-2) ÷÷ (-3) (-3) Odd number of Odd number of NegativesNegatives
(-60) (-60) ÷÷ (-2) (-2) ÷÷ (-3) (-3) ÷ ÷ (-2)(-2) Even number of Even number of NegativesNegatives
EXAMPLES:EXAMPLES:
(10) (10) ÷÷ (+5) (+5)
= 2= 2Positive Positive ÷÷ Positive Positive
(+36) (+36) ÷÷ (-6) (-6)
= -6= -6Positive Positive ÷÷ Negative Negative
(-12) (-12) ÷÷ (-3) (-3)
= 4= 4Negative Negative ÷÷ Negative Negative
(-54) (-54) ÷ ÷ (+9)(+9)
= - 6= - 6Negative Negative ÷÷ Positive Positive
= Negative= Negative(-12) (-12) ÷÷ (-2) (-2) ÷÷ (-3) (-3) Odd number of Odd number of
NegativesNegatives
(-60) (-60) ÷÷ (-2) (-2) ÷÷ (-3) (-3) ÷ ÷ (-2)(-2) Even number of Even number of NegativesNegatives
EXAMPLES:EXAMPLES:
(10) (10) ÷÷ (+5) (+5)
= 2= 2Positive Positive ÷÷ Positive Positive
(+36) (+36) ÷÷ (-6) (-6)
= -6= -6Positive Positive ÷÷ Negative Negative
(-12) (-12) ÷÷ (-3) (-3)
= 4= 4Negative Negative ÷÷ Negative Negative
(-54) (-54) ÷ ÷ (+9)(+9)
= - 6= - 6Negative Negative ÷÷ Positive Positive
(-12) (-12) ÷÷ (-2) (-2) ÷÷ (-3) (-3)
= - 2= - 2Odd number of Odd number of NegativesNegatives
= Negative= Negative
(-60) (-60) ÷÷ (-2) (-2) ÷÷ (-3) (-3) ÷ ÷ (-2)(-2) Even number of Even number of NegativesNegatives
EXAMPLES:EXAMPLES:
(10) (10) ÷÷ (+5) (+5)
= 2= 2Positive Positive ÷÷ Positive Positive
(+36) (+36) ÷÷ (-6) (-6)
= -6= -6Positive Positive ÷÷ Negative Negative
(-12) (-12) ÷÷ (-3) (-3)
= 4= 4Negative Negative ÷÷ Negative Negative
(-54) (-54) ÷ ÷ (+9)(+9)
= - 6= - 6Negative Negative ÷÷ Positive Positive
(-12) (-12) ÷÷ (-2) (-2) ÷÷ (-3) (-3)
= - 2= - 2Odd number of Odd number of NegativesNegatives
(-60) (-60) ÷÷ (-2) (-2) ÷÷ (-3) (-3) ÷ ÷ (-2)(-2)
= 5= 5Even number of Even number of NegativesNegatives
= Positive= Positive
DIVIDING RATIONAL NUMBERSDIVIDING RATIONAL NUMBERS
Change the fraction after the division Change the fraction after the division sign to its sign to its ReciprocalReciprocal and multiply the and multiply the fractions by:fractions by:
Multiply the numerators of the fractions Multiply the numerators of the fractions Multiply the denominators of the Multiply the denominators of the
fractions fractions Place the product of the numerators Place the product of the numerators
over the product of the denominators over the product of the denominators Simplify the Fraction Simplify the Fraction
EXAMPLEEXAMPLE
-3 5
÷÷ 49
-2-5
67
-4-7
-813
÷÷ ÷÷
EXAMPLEEXAMPLE
-3 5
÷÷ 49
-3 5
94
x
-2-5
67
-4-7
-813
÷÷ ÷÷
EXAMPLEEXAMPLE
-3 5
÷÷ 49
-3 5
94
x
-27 20
-2-5
67
-4-7
-813
÷÷ ÷÷
EXAMPLEEXAMPLE
-3 5
÷÷ 49
-3 5
94
x
-27 20
-2-5
67
-4-7
-813
÷÷ ÷÷
-1 720
EXAMPLEEXAMPLE
-3 5
÷÷ 49
-3 5
94
x
-27 20
-2-5
67
-4-7
-813
÷÷ ÷÷
-1 720
-2-5
x76
EXAMPLEEXAMPLE
-3 5
÷÷ 49
-3 5
94
x
-27 20
-2-5
67
-4-7
-813
÷÷ ÷÷
-1 720
-2-5
x76
1430
Notice the fraction is Notice the fraction is positivepositive
EXAMPLEEXAMPLE
-3 5
÷÷ 49
-3 5
94
x
-27 20
-2-5
67
-4-7
-813
÷÷ ÷÷
-1 720
-2-5
x76
1430
715
EXAMPLEEXAMPLE
-3 5
÷÷ 49
-3 5
94
x
-27 20
-2-5
67
-4-7
-813
÷÷ ÷÷
-1 720
-2-5
x76
1430
715
47
x-13 8
Notice the Notice the negative stays in negative stays in the numeratorthe numerator.
Becomes Becomes Positive Positive
EXAMPLEEXAMPLE
-3 5
÷÷ 49
-3 5
94
x
-27 20
-2-5
67
-4-7
-813
÷÷ ÷÷
-1 720
-2-5
x76
1430
715
47
x-13 8
-52 56
EXAMPLEEXAMPLE
-3 5
÷÷ 49
-3 5
94
x
-27 20
-2-5
67
-4-7
-813
÷÷ ÷÷
-1 720
-2-5
x76
1430
715
47
x-13 8
-52 56
-13 14
MORE EXAMPLES
-13
5÷÷ 3
5
-8 5
÷÷35
Change Mixed to an Improper.
-8 5
x53
Reciprocal.
-40 15
==-8 3
== -223
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