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

MULTIPLYING MULTIPLYING RATIONAL NUMBERSRATIONAL NUMBERSLESSON 8LESSON 8

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.

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

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

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

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

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

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

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

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.

EXAMPLESEXAMPLES

35

x

x =35

25

-3 4

-4 7

-3 8

x

=

=

EXAMPLESEXAMPLES

35

x

x =35

25

-3 4

-4 7

-3 8

x

=

=

925

POSITIVE x POSITIVE = POSITIVE

EXAMPLESEXAMPLES

35

x

x =35

25

-3 4

-4 7

-3 8

x

=

=

925

-6 20

POSITIVE x NEGATIVE = NEGATIVE

EXAMPLESEXAMPLES

35

x

x =35

25

-3 4

-4 7

-3 8

x

=

=

925

-6 20

1256

NEGATIVE x NEGATIVE = POSITIVE

MORE EXAMPLESMORE EXAMPLES

-4-5

x

x =-3 6

25

-3 4

-2 3

-3 4

x

=

=

2

-3-2

x

MORE EXAMPLESMORE EXAMPLES

-4-5

x

x =-3 6

25

-3 4

-2 3

-3 4

x

=

=

2

-3-2

x

-12 30

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

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

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

=

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

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

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

TRY THESETRY THESE

-4 5

x 37

-5 8

3-7

-2-4

16

37

x x

x -1

=

=

=

TRY THESETRY THESE

-4 5

x 37

-5 8

3-7

-2-4

16

37

x x

x -1

=

=

=

-12 35

TRY THESETRY THESE

-4 5

x 37

-5 8

3-7

-2-4

16

37

x x

x -1

=

=

=

-12 35

30224

= 15112

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