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DIVIDING RATIONAL DIVIDING RATIONAL NUMBERS NUMBERS LESSON 9 LESSON 9

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### Transcript of DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ►...

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