multiplying rational numbers lesson 8. multiplying integers positive x positive = positive ...

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MULTIPLYING RATIONAL MULTIPLYING RATIONAL NUMBERS NUMBERS LESSON 8 LESSON 8

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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

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Page 1: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

MULTIPLYING MULTIPLYING RATIONAL NUMBERSRATIONAL NUMBERSLESSON 8LESSON 8

Page 2: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

Multiplying IntegersMultiplying Integers Positive x Positive = PositivePositive x Positive = Positive Positive x Negative = NegativePositive x Negative = Negative Negative x Negative = PositiveNegative x Negative = Positive Negative x Positive = NegativeNegative x Positive = Negative An An odd number of Negativesodd number of Negatives multiplied multiplied

together gives a together gives a negativenegative result. result. An An even number of Negativeseven number of Negatives multiplied multiplied

together gives a together gives a positivepositive result. result.

Page 3: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLES:EXAMPLES:

(8) x (+5)(8) x (+5) Positive x PositivePositive x Positive

(+7) x (-6)(+7) x (-6) Positive x NegativePositive x Negative

(-4) x (-3) (-4) x (-3) Negative x NegativeNegative x Negative

(-8) x (+9)(-8) x (+9) Negative x PositiveNegative x Positive

(-4) x (-2) x (-3)(-4) x (-2) x (-3) Odd number of NegativesOdd number of Negatives

(-1) x (-9) x (-3) x (-2)(-1) x (-9) x (-3) x (-2) Even number of NegativesEven number of Negatives

Page 4: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLES:EXAMPLES:

(8) x (+5)(8) x (+5)= = + 40+ 40

Positive x PositivePositive x Positive= = PositivePositive

(+7) x (-6)(+7) x (-6) Positive x NegativePositive x Negative

(-4) x (-3) (-4) x (-3) Negative x NegativeNegative x Negative

(-8) x (+9)(-8) x (+9) Negative x PositiveNegative x Positive

(-4) x (-2) x (-3)(-4) x (-2) x (-3) Odd number of NegativesOdd number of Negatives

(-1) x (-9) x (-3) x (-2)(-1) x (-9) x (-3) x (-2) Even number of NegativesEven number of Negatives

Page 5: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLES:EXAMPLES:

(8) x (+5)(8) x (+5)= = + 40+ 40

Positive x PositivePositive x Positive

(+7) x (-6)(+7) x (-6)= = - 42- 42

Positive x NegativePositive x Negative= Negative= Negative

(-4) x (-3) (-4) x (-3) Negative x NegativeNegative x Negative

(-8) x (+9)(-8) x (+9) Negative x PositiveNegative x Positive

(-4) x (-2) x (-3)(-4) x (-2) x (-3) Odd number of NegativesOdd number of Negatives

(-1) x (-9) x (-3) x (-2)(-1) x (-9) x (-3) x (-2) Even number of NegativesEven number of Negatives

Page 6: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLES:EXAMPLES:

(8) x (+5)(8) x (+5)= = + 40+ 40

Positive x PositivePositive x Positive

(+7) x (-6)(+7) x (-6)= = - 42- 42

Positive x NegativePositive x Negative

(-4) x (-3) (-4) x (-3) = + 12= + 12

Negative x NegativeNegative x Negative= Positive= Positive

(-8) x (+9)(-8) x (+9) Negative x PositiveNegative x Positive

(-4) x (-2) x (-3)(-4) x (-2) x (-3) Odd number of NegativesOdd number of Negatives

(-1) x (-9) x (-3) x (-2)(-1) x (-9) x (-3) x (-2) Even number of NegativesEven number of Negatives

Page 7: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLES:EXAMPLES:

(8) x (+5)(8) x (+5)= = + 40+ 40

Positive x PositvePositive x Positve

(+7) x (-6)(+7) x (-6)= = - 42- 42

Positve x NegativePositve x Negative

(-4) x (-3) (-4) x (-3) = + 12= + 12

Negative x NegativeNegative x Negative

(-8) x (+9)(-8) x (+9)= - 72= - 72

Negative x PositiveNegative x Positive= = NegativeNegative

(-4) x (-2) x (-3)(-4) x (-2) x (-3) Odd number of NegativesOdd number of Negatives

(-1) x (-9) x (-3) x (-2)(-1) x (-9) x (-3) x (-2) Even number of NegativesEven number of Negatives

Page 8: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLES:EXAMPLES:

(8) x (+5)(8) x (+5)= = + 40+ 40

Positive x PositvePositive x Positve

(+7) x (-6)(+7) x (-6)= = - 42- 42

Positve x NegativePositve x Negative

(-4) x (-3) (-4) x (-3) = + 12= + 12

Negative x NegativeNegative x Negative

(-8) x (+9)(-8) x (+9)= - 72= - 72

Negative x PositiveNegative x Positive

(-4) x (-2) x (-3)(-4) x (-2) x (-3)= = - 24- 24

Odd number of NegativesOdd number of Negatives= = NegativeNegative

(-1) x (-9) x (-3) x (-2)(-1) x (-9) x (-3) x (-2) Even number of NegativesEven number of Negatives

Page 9: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLES:EXAMPLES:

(8) x (+5)(8) x (+5)= = + 40+ 40

Positive x PositvePositive x Positve

(+7) x (-6)(+7) x (-6)= = - 42- 42

Positve x NegativePositve x Negative

(-4) x (-3) (-4) x (-3) = + 12= + 12

Negative x NegativeNegative x Negative

(-8) x (+9)(-8) x (+9)= - 72= - 72

Negative x PositiveNegative x Positive

(-4) x (-2) x (-3)(-4) x (-2) x (-3)= = - 24- 24

Odd number of NegativesOdd number of Negatives

(-1) x (-9) x (-3) x (-2)(-1) x (-9) x (-3) x (-2)= = + 54+ 54

Even number of NegativesEven number of Negatives= = PositivePositive

Page 10: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

Multiplying Rational Multiplying Rational NumbersNumbers

Use the Use the SAME RULESSAME RULES for Rational for Rational numbers as you did for numbers as you did for IntegersIntegers..

multiply the two numerators and the multiply the two numerators and the two denominatorstwo denominators. .

REMEMBERREMEMBER: If there are negative signs : If there are negative signs to place them in the numerator.to place them in the numerator.

Page 11: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLESEXAMPLES

35

x

x =35

25

-3 4

-4 7

-3 8

x

=

=

Page 12: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLESEXAMPLES

35

x

x =35

25

-3 4

-4 7

-3 8

x

=

=

925

POSITIVE x POSITIVE = POSITIVE

Page 13: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLESEXAMPLES

35

x

x =35

25

-3 4

-4 7

-3 8

x

=

=

925

-6 20

POSITIVE x NEGATIVE = NEGATIVE

Page 14: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

EXAMPLESEXAMPLES

35

x

x =35

25

-3 4

-4 7

-3 8

x

=

=

925

-6 20

1256

NEGATIVE x NEGATIVE = POSITIVE

Page 15: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

MORE EXAMPLESMORE EXAMPLES

-4-5

x

x =-3 6

25

-3 4

-2 3

-3 4

x

=

=

2

-3-2

x

Page 16: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

MORE EXAMPLESMORE EXAMPLES

-4-5

x

x =-3 6

25

-3 4

-2 3

-3 4

x

=

=

2

-3-2

x

-12 30

Page 17: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

MORE EXAMPLESMORE EXAMPLES

-4-5

x

x =-3 6

25

-3 4

-2 3

-3 4

x

=

=

2

-3-2

x

-12 30

= -2 5

ODD ODD Number of Negatives Number of Negatives = Negative= Negative

Reduced to LOWEST Reduced to LOWEST TERMSTERMS

Page 18: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

MORE EXAMPLESMORE EXAMPLES

-4-5

x

x =-3 6

25

-3 4

-2 3

-3 4

x

=

=

2

-3-2

x

-2 5

12 5

-3 4

x =

CHANGE MIXED TO AN IMPROPER FRACTION

Page 19: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

MORE EXAMPLESMORE EXAMPLES

-4-5

x

x =-3 6

25

-3 4

-2 3

-3 4

x

=

=

2

-3-2

x

-2 5

12 5

-3 4

x = -36 20

=

Page 20: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

MORE EXAMPLESMORE EXAMPLES

-4-5

x

x =-3 6

25

-3 4

-2 3

-3 4

x

=

=

2

-3-2

x

-2 5

12 5

-3 4

x = -36 20

= 45

-1

Positive x Negative = NegativePositive x Negative = Negative

Change back to mixed and Change back to mixed and reduce fractionreduce fraction

Page 21: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

MORE EXAMPLESMORE EXAMPLES

-4-5

x

x =-3 6

25

-3 4

-2 3

-3 4

x

=

=

2

-3-2

x

-2 5

45

-1

1824

Page 22: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

MORE EXAMPLESMORE EXAMPLES

-4-5

x

x =-3 6

25

-3 4

-2 3

-3 4

x

=

=

2

-3-2

x

-2 5

45

-1

1824

= 34

Reduce to LOWEST Reduce to LOWEST TERMSTERMS

EVENEVEN Number of Negatives = Positive Number of Negatives = Positive

Page 23: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

TRY THESETRY THESE

-4 5

x 37

-5 8

3-7

-2-4

16

37

x x

x -1

=

=

=

Page 24: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

TRY THESETRY THESE

-4 5

x 37

-5 8

3-7

-2-4

16

37

x x

x -1

=

=

=

-12 35

Page 25: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

TRY THESETRY THESE

-4 5

x 37

-5 8

3-7

-2-4

16

37

x x

x -1

=

=

=

-12 35

30224

= 15112

Page 26: MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

TRY THESETRY THESE

-4 5

x 37

-5 8

3-7

-2-4

16

37

x x

x -1

=

=

=

-12 35

30224

= 15112

16

x -10 7

= -10 42

= -521