An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A1 Glencoe Algebra 1
Chapter Resources
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Cha
pte
r 1
3
Gle
ncoe
Alg
ebra
1
B
efor
e yo
u b
egin
Ch
ap
ter
1
•
Rea
d ea
ch s
tate
men
t.
•
Dec
ide
wh
eth
er y
ou A
gree
(A
) or
Dis
agre
e (D
) w
ith
th
e st
atem
ent.
•
Wri
te A
or
D i
n t
he
firs
t co
lum
n O
R i
f yo
u a
re n
ot s
ure
wh
eth
er y
ou a
gree
or
disa
gree
, wri
te N
S (
Not
Su
re).
Aft
er y
ou c
omp
lete
Ch
ap
ter
1
•
Rer
ead
each
sta
tem
ent
and
com
plet
e th
e la
st c
olu
mn
by
ente
rin
g an
A o
r a
D.
•
Did
an
y of
you
r op
inio
ns
abou
t th
e st
atem
ents
ch
ange
fro
m t
he
firs
t co
lum
n?
•
For
th
ose
stat
emen
ts t
hat
you
mar
k w
ith
a D
, use
a p
iece
of
pape
r to
wri
te a
n
exam
ple
of w
hy
you
dis
agre
e.
1A
ntic
ipat
ion
Gui
deE
xp
ressio
ns,
Eq
uati
on
s,
an
d F
un
cti
on
s
Step
1
Step
2
ST
EP
1A
, D
, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1.
An
alg
ebra
ic e
xpre
ssio
n c
onta
ins
one
or m
ore
nu
mbe
rs,
vari
able
s, a
nd
arit
hm
etic
ope
rati
ons.
2.
Th
e ex
pres
sion
x4
mea
ns
x +
x +
x +
x.
3.
Acc
ordi
ng
to t
he
orde
r of
ope
rati
ons,
all
mu
ltip
lica
tion
an
d di
visi
on s
hou
ld b
e do
ne
befo
re a
nyt
hin
g el
se.
4.
Sin
ce 2
mak
es t
he
equ
atio
n 3
t -
1 =
5 t
rue,
{2}
is
the
solu
tion
se
t fo
r th
e eq
uat
ion
.
5.
Bec
ause
of
the
Ref
lexi
ve P
rope
rty
of E
qual
ity,
if
a +
b =
c t
hen
c
= a
+ b
.
6.
Th
e m
ult
ipli
cati
ve i
nve
rse
of 2
3 is
1 −
23
.
7.
Th
e D
istr
ibu
tive
Pro
pert
y st
ates
th
at a
(b +
c)
wil
l eq
ual
ab
+ c
.
8.
Th
e or
der
in w
hic
h y
ou a
dd o
r m
ult
iply
nu
mbe
rs d
oes
not
ch
ange
th
eir
sum
or
prod
uct
.
9.
Giv
en t
he
stat
emen
t if
it
is c
old
, Lis
a w
ill
not
go
to t
he
foot
ball
ga
me,
you
can
con
clu
de t
hat
it
is c
old
if L
isa
is n
ot a
t th
e ga
me.
10.
In t
he
coor
din
ate
plan
e, t
he
x-ax
is i
s h
oriz
onta
l an
d th
e y-
axis
is
ver
tica
l.
A D D A D A A DD D
001_
023_
ALG
1CR
MC
01_8
9049
5.in
dd3
5/9/
084:
19:3
2P
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 1-1
Cha
pte
r 1
5
Gle
ncoe
Alg
ebra
1
Wri
te V
erb
al E
xpre
ssio
ns
An
alg
ebra
ic e
xpre
ssio
n c
onsi
sts
of o
ne
or m
ore
nu
mbe
rs a
nd
vari
able
s al
ong
wit
h o
ne
or m
ore
arit
hm
etic
ope
rati
ons.
In
alg
ebra
, var
iab
les
are
sym
bols
use
d to
rep
rese
nt
un
spec
ifie
d n
um
bers
or
valu
es. A
ny
lett
er m
ay b
e u
sed
as a
va
riab
le.
W
rite
a v
erb
al e
xpre
ssio
n f
or e
ach
alg
ebra
ic e
xpre
ssio
n.
a. 6
n2
the
prod
uct
of
6 an
d n
squ
ared
b.
n3
- 1
2mth
e di
ffer
ence
of
n c
ube
d an
d tw
elve
tim
es m
Exer
cise
sW
rite
a v
erb
al e
xpre
ssio
n f
or e
ach
alg
ebra
ic e
xpre
ssio
n.
1. w
- 1
2.
1 −
3 a
3
3. 8
1 +
2x
4. 1
2d
5. 8
4 6.
62
7. 2
n2
+ 4
8.
a3
․ b
3
9. 2
x3 -
3
10.
6k3
−
5
11.
1 −
4 b
2 12
. 7n
5
13. 3
x +
4
14.
2 −
3 k
5
15. 3
b2 +
2a3
16
. 4(n
2 +
1)
1-1
Stud
y G
uide
and
Inte
rven
tion
Vari
ab
les a
nd
Exp
ressio
ns
Exam
ple
1–16.
Sam
ple
an
sw
ers
are
giv
en
.
on
e t
hir
d t
he c
ub
e o
f a
12 t
imes d
the s
qu
are
of
6
the s
um
of
4 a
nd
tw
ice
the s
qu
are
of
n
th
e d
iffe
ren
ce o
f tw
ice
a n
um
ber
cu
bed
an
d 3
th
e s
um
of
thre
e
tim
es a
nu
mb
er
an
d 4
3 t
imes b
sq
uare
d
plu
s 2
tim
es a
cu
bed
4 t
imes t
he s
um
o
f th
e s
qu
are
of
n a
nd
1
on
e l
ess t
han
w
eig
hty
-on
e i
ncre
ased
by t
wic
e x
eig
ht
to t
he f
ou
rth
po
wer
a c
ub
ed
tim
es b
cu
bed
6 t
imes t
he c
ub
e o
f k d
ivid
ed
by 5
two
-th
ird
s t
he f
ifth
po
wer
of
k
on
e-f
ou
rth
th
e s
qu
are
of
bseven
tim
es t
he f
ifth
po
wer
of
n
001_
023_
ALG
1CR
MC
01_8
9049
5.in
dd5
4/2/
0811
:51:
59A
M
Answers (Anticipation Guide and Lesson 1-1)
A01_A34_ALG1CRMC01_890495.indd A1A01_A34_ALG1CRMC01_890495.indd A1 5/10/08 1:49:22 AM5/10/08 1:49:22 AM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A2 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Cha
pte
r 1
6
Gle
ncoe
Alg
ebra
1
Wri
te A
lgre
bra
ic E
xpre
ssio
ns
Tra
nsl
atin
g ve
rbal
exp
ress
ion
s in
to a
lgeb
raic
ex
pres
sion
s is
an
im
port
ant
alge
brai
c sk
ill.
W
rite
an
alg
ebra
ic e
xpre
ssio
n f
or e
ach
ver
bal
exp
ress
ion
.
a. f
our
mor
e th
an a
nu
mb
er n
Th
e w
ords
mor
e th
an i
mpl
y ad
diti
on.
fou
r m
ore
than
a n
um
ber
n4
+ n
Th
e al
gebr
aic
expr
essi
on i
s 4
+ n
.
b.
the
dif
fere
nce
of
a n
um
ber
sq
uar
ed a
nd
8T
he e
xpre
ssio
n di
ffer
ence
of
impl
ies
subt
ract
ion.
the
diff
eren
ce o
f a
nu
mbe
r sq
uar
ed a
nd
8n
2 -
8T
he
alge
brai
c ex
pres
sion
is
n2
- 8
.
Exer
cise
sW
rite
an
alg
ebra
ic e
xpre
ssio
n f
or e
ach
ver
bal
exp
ress
ion
.
1. a
nu
mbe
r de
crea
sed
by 8
2. a
nu
mbe
r di
vide
d by
8
3. a
nu
mbe
r sq
uar
ed
4. f
our
tim
es a
nu
mbe
r
5. a
nu
mbe
r di
vide
d by
6
6. a
nu
mbe
r m
ult
ipli
ed b
y 37
7. t
he
sum
of
9 an
d a
nu
mbe
r
8. 3
les
s th
an 5
tim
es a
nu
mbe
r
9. t
wic
e th
e su
m o
f 15
an
d a
nu
mbe
r
10. o
ne-
hal
f th
e sq
uar
e of
b
11. 7
mor
e th
an t
he
prod
uct
of
6 an
d a
nu
mbe
r
12. 3
0 in
crea
sed
by 3
tim
es t
he
squ
are
of a
nu
mbe
r
1-1
Stud
y G
uide
and
Inte
rven
tion
(con
tin
ued
)
Vari
ab
les a
nd
Exp
ressio
ns
Exam
ple
b -
8
h
−
8
n2 4
n n
−
6
37n
9 +
n
5n
- 3
2(1
5 +
n)
1
−
2 b
2
6n
+ 7
30 +
3n
2
001_
023_
ALG
1CR
MC
01_8
9049
5.in
dd6
4/2/
0811
:52:
04A
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 1-1
Cha
pte
r 1
7
Gle
ncoe
Alg
ebra
1
Wri
te a
ver
bal
exp
ress
ion
for
eac
h a
lgeb
raic
exp
ress
ion
.
1. 9
a2 2.
52
3. c
+ 2
d
4. 4
- 5
h
5. 2
b2 6.
7x3
- 1
7. p
4 +
6r
8. 3
n2
- x
Wri
te a
n a
lgeb
raic
exp
ress
ion
for
eac
h v
erb
al e
xpre
ssio
n.
9. t
he
sum
of
a n
um
ber
and
10
10. 1
5 le
ss t
han
k
11. t
he
prod
uct
of
18 a
nd
q
12. 6
mor
e th
an t
wic
e m
13. 8
in
crea
sed
by t
hre
e ti
mes
a n
um
ber
14. t
he
diff
eren
ce o
f 17
an
d 5
tim
es a
nu
mbe
r
15. t
he
prod
uct
of
2 an
d th
e se
con
d po
wer
of
y
16. 9
les
s th
an g
to
the
fou
rth
pow
er
1-1
Skill
s Pr
acti
ceV
ari
ab
les a
nd
Exp
ressio
ns
x
+ 1
0
1
8q
8
+ 3
x
2
y2
t
he p
rod
uct
of
9 a
nd
a
5 s
qu
are
d
sq
uare
d
t
he s
um
of
c a
nd
tw
ice d
th
e d
iffe
ren
ce o
f 4 a
nd
5
ti
mes h
2
tim
es b
sq
uare
d
1 l
ess t
han
7 t
imes x
cu
bed
p
to
th
e f
ou
rth
po
wer
plu
s6 t
imes r
3
tim
es n
sq
uare
d
min
us x
k
- 1
5
2
m +
6
1
7 -
5x
g
4 -
9
001_
023_
ALG
1CR
MC
01_8
9049
5.in
dd7
5/9/
084:
19:5
6P
M
Answers (Lesson 1-1)
A01_A34_ALG1CRMC01_890495.indd A2A01_A34_ALG1CRMC01_890495.indd A2 5/9/08 7:11:02 PM5/9/08 7:11:02 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A4 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Cha
pte
r 1
10
G
lenc
oe A
lgeb
ra 1
To
oth
pic
k T
rian
gle
sV
aria
ble
expr
essi
ons
can
be
use
d to
rep
rese
nt
patt
ern
s an
d h
elp
solv
e pr
oble
ms.
Con
side
r th
e pr
oble
m o
f cr
eati
ng
tria
ngl
es o
ut
of t
ooth
pick
s sh
own
bel
ow. F
igu
re 3
Fig
ure
2F
igu
re 1
1. H
ow m
any
toot
hpi
cks
does
it
take
to
crea
te e
ach
fig
ure
?
2. H
ow m
any
toot
hpi
cks
does
it
take
to
mak
e u
p th
e pe
rim
eter
of
each
im
age?
3. S
ketc
h t
he
nex
t th
ree
figu
res
in t
he
patt
ern
.
Fig
ure
4F
igu
re 5
Fig
ure
6
4. C
onti
nu
e th
e pa
tter
n t
o co
mpl
ete
the
tabl
e.
5. L
et t
he
vari
able
n r
epre
sen
t th
e fi
gure
nu
mbe
r. W
rite
an
exp
ress
ion
th
at c
an b
e u
sed
to
fin
d th
e n
um
ber
of t
ooth
pick
s n
eede
d to
cre
ate
figu
re n
.
6. L
et t
he
vari
able
n r
epre
sen
t th
e fi
gure
nu
mbe
r. W
rite
an
exp
ress
ion
th
at c
an b
e u
sed
to
fin
d th
e n
um
ber
of t
ooth
pick
s in
th
e pe
rim
eter
of
figu
re n
.
1-1
Enri
chm
ent
Ima
ge
Nu
mb
er
12
34
56
78
91
0
Nu
mb
er
of
too
thp
ick
s3
57
Nu
mb
er
of
too
thp
ick
s i
n
Pe
rim
ete
r3
45
3;
5;
7
3;
4;
5
9
11
13
15
17
19 21
6
7
8
9
10
11
12
2n
+ 1
n +
2
001_
023_
ALG
1CR
MC
01_8
9049
5.in
dd10
4/2/
0811
:52:
25A
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 1-2
Cha
pte
r 1
11
G
lenc
oe A
lgeb
ra 1
Eval
uat
e N
um
eric
al E
xpre
ssio
ns
Nu
mer
ical
exp
ress
ion
s of
ten
con
tain
mor
e th
an
one
oper
atio
n. T
o ev
alu
ate
them
, use
th
e ru
les
for
orde
r of
ope
rati
ons
show
n b
elow
.
Ord
er
of
Op
era
tio
ns
Ste
p 1
E
va
lua
te e
xp
ressio
ns in
sid
e g
rou
pin
g s
ym
bo
ls.
Ste
p 2
E
va
lua
te a
ll p
ow
ers
.
Ste
p 3
D
o a
ll m
ultip
lica
tio
n a
nd
/or
div
isio
n f
rom
le
ft t
o r
igh
t.
Ste
p 4
D
o a
ll a
dd
itio
n a
nd
/or
su
btr
actio
n f
rom
le
ft t
o r
igh
t.
E
valu
ate
each
exp
ress
ion
.
a. 3
4 34 =
3 ․
3 ․
3 ․
3
Use 3
as a
facto
r 4 t
imes.
=
81
Multip
ly.
b.
63 63 =
6 ․
6 ․
6
Use 6
as a
facto
r 3 t
imes.
=
216
M
ultip
ly.
E
valu
ate
each
exp
ress
ion
.
a. 3
[2 +
(12
÷ 3
)2 ]3[
2 +
(12
÷ 3
)2 ] =
3(2
+ 4
2 ) D
ivid
e 1
2 b
y 3
.
=
3(2
+ 1
6) Fi
nd 4
square
d.
=
3(1
8)
Add 2
and 1
6.
=
54
Multip
ly 3
and 1
8.
b.
3 +
23
−
42 �
3
=
3
+ 8
−
42 ․ 3
E
valu
ate
pow
er
in n
um
era
tor.
=
11
−
42 ․ 3
A
dd 3
and 8
in t
he n
um
era
tor.
=
11
−
16 ․
3
Evalu
ate
pow
er
in d
enom
inato
r.
=
11
−
48
Multip
ly.
3 +
23
−
42 ․ 3
3
+ 2
3 −
42
․ 3
Exer
cise
sE
valu
ate
each
exp
ress
ion
.
1. 5
2 2.
33
3. 1
04
4. 1
22 5.
83
6. 2
8
7. (
8 -
4)
․ 2
8.
(12
+ 4
) ․ 6
9.
10
+ 8
․ 1
10. 1
5 -
12
÷ 4
11
. 12(
20 -
17)
- 3
․ 6
12
. 24
÷ 3
․ 2
- 3
2
13. 3
2 ÷
3 +
22
․ 7
- 2
0 ÷
5
14.
4 +
32
−
12 +
1
15. 2
50 ÷
[5(
3 ․ 7
+ 4
)]
16.
2 ․ 4
2 - 8
÷ 2
−
(5
+ 2
) ․
2
17
. 4(
52 ) -
4 ․
3
−
4(4
․ 5
+ 2
)
18.
52 -
3
−
20(3)
+ 2
(3)
1-2
Stud
y G
uide
and
Inte
rven
tion
Ord
er
of
Op
era
tio
ns
Exam
ple
1Ex
amp
le 2
896
12
18
27
2
1
−
3
25
27
10,0
00
144
512
256
18
7
1
21
001_
023_
ALG
1CR
MC
01_8
9049
5.in
dd11
4/2/
086:
32:1
0P
M
Answers (Lesson 1-1 and Lesson 1-2)
A01_A34_ALG1CRMC01_890495.indd A4A01_A34_ALG1CRMC01_890495.indd A4 5/9/08 7:11:13 PM5/9/08 7:11:13 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A5 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Cha
pte
r 1
12
G
lenc
oe A
lgeb
ra 1
Eval
uat
e A
lgeb
raic
Exp
ress
ion
s A
lgeb
raic
exp
ress
ion
s m
ay c
onta
in m
ore
than
on
e op
erat
ion
. Alg
ebra
ic e
xpre
ssio
ns
can
be
eval
uat
ed i
f th
e va
lues
of
the
vari
able
s ar
e kn
own
. F
irst
, rep
lace
th
e va
riab
les
wit
h t
hei
r va
lues
. Th
en u
se t
he
orde
r of
ope
rati
ons
to c
alcu
late
th
e va
lue
of t
he
resu
ltin
g n
um
eric
al e
xpre
ssio
n.
E
valu
ate
x3 +
5(y
- 3
) if
x =
2 a
nd
y =
12.
x3 +
5(y
- 3
) =
23
+ 5
(12
- 3
) R
epla
ce x
with 2
and y
with 1
2.
=
8 +
5(1
2 -
3)
Evalu
ate
23.
=
8 +
5(9
) S
ubtr
act
3 f
rom
12.
=
8 +
45
Multip
ly 5
and 9
.
=
53
Add 8
and 4
5.
Th
e so
luti
on i
s 53
.
Exer
cise
sE
valu
ate
each
exp
ress
ion
if
x =
2, y
= 3
, z =
4, a
= 4 −
5 ,
and
b =
3 −
5 .
1. x
+ 7
2.
3x
- 5
3.
x +
y2
4. x
3 +
y +
z2
5.
6a
+ 8
b
6. 2
3 -
(a
+ b
)
7.
y2 −
x2
8.
2xy
z +
5
9. x
(2y
+ 3
z)
10. (
10x)
2 +
100
a
11.
3xy
- 4
−
7x
12
. a2
+ 2
b
13.
z2 - y
2 −
x2
14
. 6xz
+ 5
xy
15.
(z -
y) 2
−
x
16.
25ab
+ y
−
xz
17.
5 a 2 b
−
y
18.
(z ÷
x)2
+ a
x
19. (
x −
z ) 2 +
( y −
z ) 2
20.
x +
z
−
y +
2z
21. (
z ÷
x
−
y )
+ (
y ÷
x −
z
)
1-2
Stud
y G
uide
and
Inte
rven
tion
(con
tin
ued
)
Ord
er
of
Op
era
tio
ns
Exam
ple 9
111
27
21 3
−
5
9
−
4
53
36
480
1 2
1
−
25
7
−
4
78
1
−
2
1 7
−
8
16
−
25
5 3
−
5
13
−
16
6
−
11
1 1
−
24
19 3
−
5
001_
023_
ALG
1CR
MC
01_8
9049
5.in
dd12
4/2/
0811
:52:
39A
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 1-2
Cha
pte
r 1
13
G
lenc
oe A
lgeb
ra 1
Eva
luat
e ea
ch e
xpre
ssio
n.
1. 8
2 2.
34
3. 5
3 4.
33
5. (
5 +
4)
� 7
6.
(9
- 2
) � 3
7. 4
+ 6
� 3
8.
12
+ 2
� 2
9. (
3 +
5)
� 5
+ 1
10
. 9 +
4(3
+ 1
)
11. 3
0 -
5 �
4 +
2
12. 1
0 +
2 �
6 +
4
13. 1
4 ÷
7 �
5 -
32
14
. 4[3
0 -
(10
- 2
) � 3
]
15. 5
+ [
30 -
(6
- 1
)2 ]
16. 2
[12
+ (
5 -
2)2 ]
Eva
luat
e ea
ch e
xpre
ssio
n i
f x
= 6
, y =
8, a
nd
z =
3.
17. x
y +
z
18. y
z -
x
19. 2
x +
3y
- z
20
. 2(x
+ z
) -
y
21. 5
z +
(y
- x
)
22. 5
x -
(y
+ 2
z)
23. x
2 +
y2
- 1
0z
24. z
3 +
(y2
- 4
x)
25.
y +
xz
−
2
26.
3y +
x2
−
z
1-2
Skill
s Pr
acti
ceO
rder
of
Op
era
tio
ns
63
21
22
16
41
25
12
26
124
10
42
51
18
33
10
17
16
70
67
13
20
64
81
125
27
001_
023_
ALG
1CR
MC
01_8
9049
5.in
dd13
5/9/
084:
20:3
7P
M
Answers (Lesson 1-2)
A01_A34_ALG1CRMC01_890495.indd A5A01_A34_ALG1CRMC01_890495.indd A5 5/9/08 7:11:18 PM5/9/08 7:11:18 PM
Co
pyrig
ht © G
lencoe/M
cGraw
-Hill, a d
ivision o
f The M
cGraw
-Hill C
om
panies, Inc.
PDF Pass
Chapter 1 A8 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Cha
pte
r 1
18
G
lenc
oe A
lgeb
ra 1
E
valu
ate
24 �
1 -
8 +
5(9
÷ 3
- 3
). N
ame
the
pro
per
ty u
sed
in
eac
h s
tep
.24
․ 1
- 8
+ 5
(9 ÷
3 -
3)
= 2
4 ․ 1
- 8
+ 5
(3 -
3)
Subs
titut
ion;
9 ÷
3 =
3
=
24
․ 1
- 8
+ 5
(0)
Subs
titut
ion;
3 -
3 =
0
=
24
- 8
+ 5
(0)
Mul
tiplic
ativ
e Id
entit
y; 2
4 ․ 1
= 2
4
=
24
- 8
+ 0
M
ultip
licat
ive
Prop
erty
of Z
ero;
5(0
) = 0
=
16
+ 0
Su
bstit
utio
n; 2
4 -
8 =
16
=
16
Ad
ditiv
e Id
entit
y; 1
6 +
0 =
16
Exer
cise
sE
valu
ate
each
exp
ress
ion
. Nam
e th
e p
rop
erty
use
d i
n e
ach
ste
p.
1. 2
[ 1 −
4 +
( 1 −
2 ) 2 ]
2. 1
5 ․ 1
- 9
+ 2
(15
÷ 3
- 5
)
3. 2
(3 ․
5 ․
1 -
14)
- 4
․ 1 −
4
4. 1
8 ․ 1
- 3
․ 2
+ 2
(6 ÷
3 -
2)
1-3
Stud
y G
uide
and
Inte
rven
tion
Pro
pert
ies o
f N
um
bers
Iden
tity
an
d E
qu
alit
y Pr
op
erti
es T
he
iden
tity
an
d eq
ual
ity
prop
erti
es i
n t
he
char
t be
low
can
hel
p yo
u s
olve
alg
ebra
ic e
quat
ion
s an
d ev
alu
ate
mat
hem
atic
al e
xpre
ssio
ns.
Ad
dit
ive
Id
en
tity
Fo
r a
ny n
um
be
r a,
a +
0 =
a.
Ad
dit
ive
In
ve
rse
Fo
r a
ny n
um
be
r a,
a +
(-
a) =
a.
Mu
ltip
lic
ati
ve
Id
en
tity
Fo
r a
ny n
um
be
r a,
a .
1 =
a.
Mu
ltip
lic
ati
ve
Pro
pe
rty
of
0F
or
an
y n
um
be
r a,
a .
0 =
0.
Mu
ltip
lic
ati
ve
In
ve
rse
Pro
pe
rty
Fo
r e
ve
ry n
um
be
r ,
a, b
≠ 0
, th
ere
is e
xa
ctly o
ne
nu
mb
er
b
−
a su
ch
th
at
a −
b .
b
−
a =1
.
Re
fle
xiv
e P
rop
ert
yF
or
an
y n
um
be
r a,
a =
a.
Sy
mm
etr
ic P
rop
ert
yF
or
an
y n
um
be
rs a
an
d b
, if a
= b
, th
en
b =
a.
Tra
ns
itiv
e P
rop
ert
yF
or
an
y n
um
be
rs a
, b
, a
nd
c,
if a
= b
an
d b
= c
, th
en
a =
c.
Su
bs
titu
tio
n P
rop
ert
yIf
a =
b,
the
n a
ma
y b
e r
ep
lace
d b
y b
in
an
y e
xp
ressio
n.
Exam
ple
= 2
(15 �
1 -
14)
- 4
� 1
−
4
Su
bst.
=
18
� 1
- 3
� 2
+ 2
(2 -
2)
Su
bst.
= 2
(15 -
14)
- 4
� 1
−
4
Mu
lt.
Iden
tity
=
18
� 1
- 3
� 2
+ 2
(0)
Su
bsti
tuti
on
= 2
(1)
- 4
� 1
−
4
Su
bsti
tuti
on
=
18
- 3
� 2
+ 2
(0)
Mu
lt.
Iden
tity
= 2
- 4
� 1
−
4
Mu
lt.
Iden
tity
=
18
- 6
+ 2
(0)
Su
bsti
tuti
on
= 2
- 1
M
ult
. In
vers
e
= 1
8 -
6 +
0 M
ult
. P
rop
. Z
ero
= 1
S
ub
sti
tuti
on
=
12 +
0
Su
bsti
tuti
on
= 1
2
Ad
d.
Iden
tity
=
2 (
1
−
4 +
1
−
4 )
S
ub
sti
tuti
on
=
15 �
1 -
9 +
2(5
- 5
) S
ub
sti
tuti
on
=
2 (
1
−
2 )
S
ub
sti
tuti
on
=
15 �
1 -
9 +
2(0
) S
ub
sti
tuti
on
=
1
Mu
lt.
Invers
e
= 1
5 �
1 -
9 +
0
Mu
lt.
Pro
p.
Zero
=
15
- 9
+ 0
Mu
lt.
Iden
tity
=
6 -
0
S
ub
sti
tuti
on
=
6
S
ub
sti
tuti
on
001_
023_
ALG
1CR
MC
01_8
9049
5.in
dd18
4/2/
0811
:53:
22A
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 1-3
Cha
pte
r 1
19
G
lenc
oe A
lgeb
ra 1
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Pro
pert
ies o
f N
um
bers
1-3
Co
mm
uta
tive
an
d A
sso
ciat
ive
Pro
per
ties
Th
e C
omm
uta
tive
an
d A
ssoc
iati
ve
Pro
pert
ies
can
be
use
d to
sim
plif
y ex
pres
sion
s. T
he
Com
mu
tati
ve P
rope
rtie
s st
ate
that
th
e or
der
in w
hic
h y
ou a
dd o
r m
ult
iply
nu
mbe
rs d
oes
not
ch
ange
th
eir
sum
or
prod
uct
. Th
e A
ssoc
iati
ve P
rope
rtie
s st
ate
that
th
e w
ay y
ou g
rou
p th
ree
or m
ore
nu
mbe
rs w
hen
add
ing
or
mu
ltip
lyin
g do
es n
ot c
han
ge t
hei
r su
m o
r pr
odu
ct.
Co
mm
uta
tiv
e P
rop
ert
ies
For a
ny n
umbe
rs a
and
b, a
+ b
= b
+ a
and
a ․
b =
b ․
a.
As
so
cia
tiv
e P
rop
ert
ies
For a
ny n
umbe
rs a
, b, a
nd c
, (a
+ b
) + c
= a
+ (b
+ c
) an
d (a
b)c
= a
(bc)
.
E
valu
ate
6 �
2 �
3 �
5
usi
ng
pro
per
ties
of
nu
mb
ers.
Nam
e th
e p
rop
erty
use
d i
n e
ach
ste
p.
6 ․ 2
․ 3
․ 5
= 6
․ 3
․ 2
․ 5
C
om
muta
tive P
ropert
y
=
(6
․ 3
)(2
․ 5
) A
ssocia
tive P
ropert
y
=
18 ․
10
Multip
ly.
=
180
Multip
ly.
Th
e pr
odu
ct i
s 18
0.
E
valu
ate
8.2
+ 2
.5 +
2.5
+ 1
.8 u
sin
g p
rop
erti
es o
f n
um
ber
s. N
ame
the
pro
per
ty u
sed
in
ea
ch s
tep
.8.
2 +
2.5
+ 2
.5 +
1.8
=
8.2
+ 1
.8 +
2.5
+ 2
.5
Com
muta
tive P
rop.
=
(8.
2 +
1.8
) +
(2.
5 +
2.5
) As
socia
tive P
rop.
=
10
+ 5
A
dd.
=
15
Add.
Th
e su
m i
s 15
.
Exer
cise
sE
valu
ate
each
exp
ress
ion
usi
ng
pro
per
ties
of
nu
mb
ers.
Nam
e th
e p
rop
erty
use
d i
n
each
ste
p.
1. 1
2 +
10
+ 8
+ 5
2.
16
+ 8
+ 2
2 +
12
3.
10
․ 7
․ 2
.5
4. 4
․ 8
․ 5
․ 3
5.
12
+ 2
0 +
10
+ 5
6.
26
+ 8
+ 4
+ 2
2
7. 3
1 −
2 +
4 +
2 1 −
2 +
3
8. 3 −
4 ․
12
․ 4
․ 2
9.
3.5
+ 2
.4 +
3.6
+ 4
.2
10. 4
1 −
2 +
5 +
1 −
2 +
3
11. 0
.5 ․
2.8
․ 4
12
. 2.5
+ 2
.4 +
2.5
+ 3
.6
13.
4 −
5 ․
18
․ 2
5 ․ 2 −
9
14. 3
2 ․ 1 −
5 ․
1 −
2 ․
10
15
. 1 −
4 ․
7 ․
16
․ 1 −
7
16. 3
.5 +
8 +
2.5
+ 2
17
. 18
․ 8
․ 1 −
2 ․
1 −
9
18. 3
−
4 ․ 1
0 ․ 1
6 ․ 1 −
2
Exam
ple
1Ex
amp
le 2
35
58
175
480
47
60
13
72
13.7
13
5.6
11
80
32
4
16
860
1–18.
An
sw
ers
will
vary
001_
023_
ALG
1CR
MC
01_8
9049
5.in
dd19
4/2/
088:
09:4
5P
M
Answers (Lesson 1-3)
A01_A34_ALG1CRMC01_890495.indd A8A01_A34_ALG1CRMC01_890495.indd A8 5/9/08 7:11:33 PM5/9/08 7:11:33 PM
An
swer
s
Co
pyr
ight
© G
lenc
oe/
McG
raw
-Hill
, a d
ivis
ion
of
The
McG
raw
-Hill
Co
mp
anie
s, In
c.
PDF Pass
Chapter 1 A11 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Cha
pte
r 1
24
G
lenc
oe A
lgeb
ra 1
Eval
uat
e Ex
pre
ssio
ns
Th
e D
istr
ibu
tive
Pro
pert
y ca
n b
e u
sed
to h
elp
eval
uat
e ex
pres
sion
s.
Dis
trib
uti
ve
Pro
pe
rty
For a
ny n
umbe
rs a
, b, a
nd c
, a(b
+ c
) = a
b +
ac
and
(b +
c)a
= b
a +
ca
and
a(b
- c
) = a
b -
ac
and
(b -
c)a
= b
a -
ca.
U
se t
he
Dis
trib
uti
ve P
rop
erty
to
rew
rite
6(8
+ 10
). T
hen
eva
luat
e.
6(8
+ 1
0) =
6 ․
8 +
6 ․
10
Dist
ribut
ive
Prop
erty
=
48
+ 6
0 M
ultip
ly.
=
108
Ad
d.
U
se t
he
Dis
trib
uti
ve P
rop
erty
to
rew
rite
-2(
3x2
+ 5
x +
1).
T
hen
sim
pli
fy.
-2(
3x2
+ 5
x +
1)
= -
2(3x
2 ) +
(-
2)(5
x) +
(-
2)(1
) Di
strib
utiv
e Pr
oper
ty
= -
6x2
+ (
-10
x) +
(-
2)
Mul
tiply
.
= -
6x2
- 1
0x -
2
Sim
plify
.
Exer
cise
sU
se t
he
Dis
trib
uti
ve P
rop
erty
to
rew
rite
eac
h e
xpre
ssio
n. T
hen
eva
luat
e.
1. 2
0(31
) 2.
12
� 4
1 −
2
3. 5
(311
)
4. 5
(4x
- 9
) 5.
3(8
- 2
x)
6. 1
2 (6
-1 − 2
x )
7. 1
2 (2
+ 1 −
2 x )
8.
1 −
4 (1
2 -
4t)
9.
3(2
x -
y)
10. 2
(3x
+ 2
y -
z)
11. (
x -
2)y
12
. 2(3
a -
2b
+ c
)
13.
1 −
4 (1
6x -
12y
+ 4
z)
14. (
2 -
3x
+ x
2 )3
15. -
2(2x
2 +
3x
+ 1
)
1-4
Stud
y G
uide
and
Inte
rven
tion
Th
e D
istr
ibu
tive P
rop
ert
y
Exam
ple
1
Exam
ple
2
20
x -
45
24 -
6x
72 -
6x
24 +
6x
3 -
t6x -
3y
6
x +
4y -
2z
xy -
2y
6a -
4b
+ 2
c
4
x -
3y +
z
6 -
9x +
3x
2
-4x
2 -
6x -
2
620
54
1555
024_
056_
ALG
1CR
MC
01_8
9049
5.in
dd24
4/2/
0811
:54:
03A
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 1-4
Cha
pte
r 1
25
G
lenc
oe A
lgeb
ra 1
Sim
plif
y Ex
pre
ssio
ns
A t
erm
is
a n
um
ber,
a v
aria
ble,
or
a pr
odu
ct o
r qu
otie
nt
of
nu
mbe
rs a
nd
vari
able
s. L
ike
term
s ar
e te
rms
that
con
tain
th
e sa
me
vari
able
s, w
ith
co
rres
pon
din
g va
riab
les
hav
ing
the
sam
e po
wer
s. T
he
Dis
trib
uti
ve P
rope
rty
and
prop
erti
es
of e
qual
itie
s ca
n b
e u
sed
to s
impl
ify
expr
essi
ons.
An
exp
ress
ion
is
in s
imp
lest
for
m i
f it
is
repl
aced
by
an e
qu
ival
ent
expr
essi
on w
ith
no
like
ter
ms
or p
aren
thes
es.
S
imp
lify
4(a
2 +
3a
b) -
ab.
4(a2
+ 3
ab)
- a
b =
4(a
2 +
3ab
) -
1ab
M
ultip
licative I
dentity
=
4a2
+ 1
2ab
- 1
ab
Dis
trib
utive P
ropert
y
=
4a2
+ (
12 -
1)a
b D
istr
ibutive P
ropert
y
=
4a2
+ 1
1ab
Substitu
tion
Exer
cise
sS
imp
lify
eac
h e
xpre
ssio
n. I
f n
ot p
ossi
ble
, wri
te s
imp
lifi
ed.
1. 1
2a -
a
2. 3
x +
6x
3.
3x
- 1
4. 2
0a +
12a
- 8
5.
3x2
+ 2
x2 6.
-6x
+ 3
x2 +
10x
2
7. 2
p +
1 −
2 q
8.
10x
y -
4(x
y +
xy)
9.
21a
+ 1
8a +
31b
- 3
b
10. 4
x +
1 −
4 (1
6x -
20y
) 11
. 2 -
1 -
6x
+ x
2 12
. 4x2
+ 3
x2 +
2x
Wri
te a
n a
lgeb
raic
exp
ress
ion
for
eac
h v
erb
al e
xpre
ssio
n. T
hen
sim
pli
fy,
ind
icat
ing
the
pro
per
ties
use
d.
13. s
ix t
imes
th
e di
ffer
ence
of
2a a
nd
b, i
ncr
ease
d by
4b
14. t
wo
tim
es t
he
sum
of
x sq
uar
ed a
nd
y sq
uar
ed, i
ncr
ease
d by
th
ree
tim
es t
he
sum
of
x sq
uar
ed a
nd
y sq
uar
ed
1-4
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nu
ed)
Th
e D
istr
ibu
tive P
rop
ert
y
Exam
ple
1
1a
9x
sim
plifi
ed
3
2a -
85x
2
6x +
13x
2
8
x -
5y
1 -
6x +
x2
7x
2 +
2x
s
imp
lifi
ed
2
xy
39a +
28b
2(x
2 +
y
2)
+ 3(x
2 +
y
2)
2x
2 +
2y
2 +
3x
2 +
3y
2
Dis
trib
uti
ve P
rop
ert
y
5x
2 +
5y
2
Su
bsti
tuti
on
= 6
(2a -
b)
+ 4b
= 1
2a -
6b
+
4b
D
istr
ibu
tive P
rop
ert
y
= 1
2a -
2b
S
ub
sti
tuti
on
024_
056_
ALG
1CR
MC
01_8
9049
5.in
dd25
4/2/
0811
:54:
07A
M
Answers (Lesson 1-4)
A01_A34_ALG1CRMC01_890495.indd A11A01_A34_ALG1CRMC01_890495.indd A11 5/9/08 7:11:47 PM5/9/08 7:11:47 PM
