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

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DIVIDING RATIONAL DIVIDING RATIONAL NUMBERS NUMBERS LESSON 9 LESSON 9

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

Page 1: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

DIVIDING RATIONAL DIVIDING RATIONAL NUMBERSNUMBERS

LESSON 9LESSON 9

Page 2: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

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.

Page 3: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

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

Page 4: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

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

Page 5: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

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

Page 6: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

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

Page 7: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

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

Page 8: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

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

Page 9: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

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

Page 10: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = 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

Page 11: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

EXAMPLEEXAMPLE

-3 5

÷÷ 49

-2-5

67

-4-7

-813

÷÷ ÷÷

Page 12: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

EXAMPLEEXAMPLE

-3 5

÷÷ 49

-3 5

94

x

-2-5

67

-4-7

-813

÷÷ ÷÷

Page 13: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

EXAMPLEEXAMPLE

-3 5

÷÷ 49

-3 5

94

x

-27 20

-2-5

67

-4-7

-813

÷÷ ÷÷

Page 14: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

EXAMPLEEXAMPLE

-3 5

÷÷ 49

-3 5

94

x

-27 20

-2-5

67

-4-7

-813

÷÷ ÷÷

-1 720

Page 15: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

EXAMPLEEXAMPLE

-3 5

÷÷ 49

-3 5

94

x

-27 20

-2-5

67

-4-7

-813

÷÷ ÷÷

-1 720

-2-5

x76

Page 16: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

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

Page 17: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

EXAMPLEEXAMPLE

-3 5

÷÷ 49

-3 5

94

x

-27 20

-2-5

67

-4-7

-813

÷÷ ÷÷

-1 720

-2-5

x76

1430

715

Page 18: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = 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

Notice the Notice the negative stays in negative stays in the numeratorthe numerator.

Becomes Becomes Positive Positive

Page 19: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = 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

Page 20: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = 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

-13 14

Page 21: DIVIDING RATIONAL NUMBERS LESSON 9. Dividing Integers ► Positive ÷ Positive = Positive ► Positive ÷ Negative = Negative ► Negative ÷ Negative = Positive.

MORE EXAMPLES

-13

5÷÷ 3

5

-8 5

÷÷35

Change Mixed to an Improper.

-8 5

x53

Reciprocal.

-40 15

==-8 3

== -223