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1. Multiply
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Learning
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Mini-Lecture
3.3exponential
Mini-Lecture
Evaluate exponential
expressions
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2.
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ng Objectives:
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3.3
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Mini-Lecture
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3.3
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fractions.
Mini-Lecture3.3
3.3
fractional
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uire
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1a) 1/63;
1b)48.
1/6; 1c) 5/9; 1d) -7; 1e) 3; 1f) 0;
-3/50; 71h)
*+ 5/9;
Michelle
Michelle
bike?
:multiplying.
1a)
1/63; 1b) 1/6; 1c)
1d)3 -7;bike?
1e)
3; 1f) 0; 1g) -3/50; 1h) –2/35; 2a) !; 2b)7 1/81; 2c) -8/125; 2d)
gng
Notes:
Notes:
1/49;
3b) 1;1b)
3c)1/6;
–19/45;
3d) 1d)
10/51;
3e)
2/3;
1f) 0;undef;
1g) -27/4;
3h) 0; 2a)
4a) !;
-4/27,
*+3a) 21/20;
2
Answers:
1a)
1/63;
1c)
5/9;
-7;
1e)
3;
1f)
1g)
-3/50;
1h)
–2/35;
2b) -3/4;
1/81; 2c) -8/125; 2d)
)When
21/20;dividing,
3b)
1; the
3c)
–19/45;
10/51;
3e)
2/3;-27;
1f)by
undef;
1g)Michelle
-27/4;
3h)bikes
0; 4a)
-4/27,
c)and
A3d)
bike
trail
is3c)
27
miles
long.
of1g)
the-3/4;
trail.
How
many
miles
did-8/125; 2d)
students
take
time
rewrite
the
problem
changing
the
2by -3/50;
encourage
students
take
the
time
and
rewrite
the3;division
problem
changing
the3h)
division
4b)
-25/63,
-9/7;
5a)
16;
5b)
5c)
18.
Answers:
1a)
1/63;
1b)
1/6;
1c)
5/9;
1d)
-7;
1e)
1f)
0;
1g)
1h)
–2/35;
2a)
!;
2b)
1/81;
2c)
1/49;
3a)
21/20;
3b)
1;
–19/45;
3d)
10/51;
3e)
2/3;
1f)
undef;
-27/4;
0;
4a)
-4/27,
Teaching
Teaching
Notes:
Notes:
Encourage
students
to
divide
out
common
factors
in
the
numerator
and
denominator
before
3of the trail.
c)
A bike
trail
isstudents
27 miles
long.
How many miles-3/4;
did
Encourage
to
divide
common
factors
in “simplifying”
theMichelle
numeratorbikes
and denominator
before
63,
-9/7; 5a)students
5b)reciprocal.
-27;
5c) out
18.
nd
multiply
by16;
the
Many
begin
and
symbol
to
multiplication
and
multiply
by
the
reciprocal.
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students
begin
“simplifying”
and
1/49;
21/20;
3b)trail
1; 3c)
10/51;
3e) 2/3; 1f)
undef;
3h) 0; How
4a) -4/27,
4b) 3a)
-25/63,
-9/7;
5a)
16;
5b)
-27;3d)
5c)
18. Michelle
3 2/31g)
13.
A bike
is –19/45;
27 miles
long.
bikes
of -27/4;
the trail.
many-3/4;
miles did
multiplying.
multiplying. M-18
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bike?
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©out
2007
Pearson
Education,
as Pearson
Prentice
Hall before
*+-25/63,
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students
to
to
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in publishing
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denominator
denominator
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eciprocal.
4b) by
-9/7;
5a)
16;
5b)
-27;
5c)
18.
forget
to
multiply
reciprocal.
Copyright
©
2007
Pearson
Education,
Inc.,
publishing
as
Pearson
Prentice
Hall
Michelle
bike?
Michelle
bike?
When
students
take
the
byInc.,
changing
the
division
Whendividing,
dividing,encourage
encourage
students
takethe
thetime
timeand
and©rewrite
rewrite
theproblem
problem
changing
division
M-18
Copyright
2007 Pearson
Education,by
publishing the
as Pearson
Prentice Hall
multiplying.
multiplying.
Teaching
Notes:
ymbol
totomultiplication
and
multiply
by
reciprocal.
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and
M-18
symbol
multiplication
and
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bythe
the
reciprocal.
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andPrentice
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1d)
1e)
3;1/6;
1f)*+
0;*+1g)
-3/50;
1h)1e)
–2/35;
2a)
2b)
1/81;
2c)
-8/125;
2d)
Teaching
Notes:
When
When
dividing,
dividing,
encourage
students
take
take
the
the
time
time
and
and
rewrite
the2c)
the
problem
problem
by
changing
changing
division
division
:orget
1a) -7;
1/63;
1b)
1c)
5/9;
1d)
-7;
3;encourage
1f)
0;!;1g)
-3/50;
1h)
–2/35;
2a)
!;
2b)rewrite
1/81;
-8/125;by
2d)
to
multiply
by
the
reciprocal.
forget
to
multiply
by
the
reciprocal.
*+
Encourage
students
to
divide
out
common
factors
in
the
numerator
and
denominator
before andand
d)
10/51;
3e)
2/3;
1f)
undef;
1g)
-27/4;
3h)
0;
4a)
-4/27,
-3/4;
symbol
symbol
to to
multiplication
multiplication
and
multiply
multiply
byby
the
the
reciprocal.
Many
Many
students
students
begin
begin
“simplifying”
“simplifying”
) 21/20; 3b) 1; 3c) –19/45;
3d) 10/51;
3e) 2/3; 1f) and
undef;
1g) -27/4;
3h)
0;reciprocal.
4a) -4/27,
-3/4;
*+ Encourage
students
to by
divide
out common factors in the numerator and denominator before
c) 18.
multiplying.
63,
-9/7; 5a) 16; 5b) -27;
5c) to
18.to
forget
forget
multiply
multiply
by
thethe
reciprocal.
reciprocal.
5/9;
1d)
-7;
1e)
3;3; 1f)
0;0; 1g)
-3/50;
1h)
2a)
!;
2b)
-8/125;
2d)
multiplying.
:1a)
1a)1/63;
1/63;1b)
1b)1/6;
1/6;1c)
1c)
5/9;
1d)
-7;
1e)
1f)
1g)
-3/50;take
1h)–2/35;
–2/35;
2a)
!;rewrite
2b) 1/81;
1/81;
2c)
-8/125;by
2d)changing the division
*+
dividing, encourage students
the time
and
the2c)
problem
*+ *+When
1;
3c)
–19/45;
3d)
10/51;
3e)
2/3;
1f)
undef;
1g)
-27/4;
3h)
0;
4a)
-4/27,
-3/4;
t)21/20;
©21/20;
20073b)
Pearson
Education,
Inc.,
publishing
as
Pearson
Prentice
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3b) 1; 3c)
–19/45;
3d)
10/51;
3e)
2/3;
1f)
undef;
1g)
-27/4;
3h)
0;
4a)
-4/27,
-3/4;
Copyright
©
2007
Pearson
Education,
Inc.,
publishing
as
Pearson
Prentice
Hall
*+
When
dividing,
encourage
students
take
the
time
and
rewrite
the
problem
by
changing
the
division
symbol
to
multiplication
and
multiply
by
reciprocal.
Many
students
begin
and 2d)2d)
Answers:
Answers:
1a)
1a)
1/63;
1/63;
1b)1b)
1/6;
1/6;
1c)1c)
5/9;
5/9;
1d)
1d)
-7;-7;
1e)1e)
3; the
3;
1f)1f)
0; 0;
1g)1g)
-3/50;
-3/50;
1h)1h)
–2/35;
–2/35;
2a)2a)
!; !;
2b)“simplifying”
2b)
1/81;
1/81;
2c)2c)
-8/125;
-8/125;
3,
5b)
-27;
5c)
18.
63,-9/7;
-9/7;5a)
5a)16;
16;
5b)
-27;
5c)
18.
symbol
to
multiplication
and
multiply
by
the
reciprocal.
Many
students
begin
“simplifying”
1/49;
1/49;
3a)3a)
21/20;
21/20;
3b)
1; 1;
3c)3c)
–19/45;
3d)3d)
10/51;
10/51;
3e)3e)
2/3;2/3;
1f)1f)
undef;
undef;
1g)1g)
-27/4;
-27/4;
3h)3h)
0; 0;
4a)4a)
-4/27,
-4/27,
-3/4;
-3/4; and
forget
to3b)
multiply
by–19/45;
the reciprocal.
forget
to-9/7;
multiply
by
the
reciprocal.
4b)4b)
-25/63,
-25/63,
-9/7;
5a)5a)
16;16;
5b)5b)
-27;
-27;
5c)Inc.,
5c)
18.
18.
Copyright
publishing
*+
Copyright©©2007
2007Pearson
PearsonEducation,
Education,Inc.,
publishingas
asPearson
PearsonPrentice
PrenticeHall
Hall
*+
Answers:
1a) 1/63; 1b) 1/6; 1c) 5/9; 1d) -7; 1e) 3; 1f) 0; 1g) -3/50; 1h) –2/35; 2a) !; 2b) 1/81; 2c) -8/125; 2d)
M-18
M-18
Copyright
Copyright
© 2007
©
Pearson
Education,
Education,
Inc.,
Inc.,
publishing
publishing
as Pearson
as Pearson
Prentice
Prentice
HallHall
Answers:
1/63;3b)
1b)1;1/6;
5/9;
1d)
-7;2007
1e)Pearson
3; 2/3;
1f)
0;
-3/50;
1h)
–2/35;
2a)
2b)
1/81;
2c) -8/125; 2d)
1/49; 3a)1a)
21/20;
3c) 1c)
–19/45;
3d)
10/51;
3e)
1f)1g)
undef;
1g)
-27/4;
3h)
0; !;
4a)
-4/27,
-3/4;