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