Download 7th Grade Algebra - Wyckoff School District

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EisenhowerMiddleSchool
MathematicsSummerPacket
Entering7thGradeAlgebra
The following is a review of important topics in 6tr grade that will be neededfor 7th
grade Algebra. Do not use a calculator. It is very important that you have mastered
working with decimals,fractions,integers,expressionsand equationsfor next year.
Mastery in these areaswill set you up for successnext year.
A lot of learningis lost in the summer,and every problem doesnot need to be
completed.Make sure you can do a few on eachpage.Thesetopicswill come up
again and again next year.
Completionof the packet is optional, and the packet will not be collectedby your
teacher next vear.
Period
Name
Date
with DecimalsR eviewWorksheet
Operations
Findeachsumor difference.
t. 36.t2+ 5.793
4. 42.75- 26.36
7. 5.002- 4.3
2. 8.9+ 2.14+ 7.1
3 . 3 . 6+ 5 . 2 7+ 8 . 9 3
5. 53.85- 16.47
5. 56.89- 48.91
8. 15.26+ 13.29+ 38.96
9.46.21.+ 53.942
Findeachproductor quotient.
10. O.9Lc 2.7
1 1 . 4 . 6 ( 3 .e )
12. 17.3X L5.23
13. 2.112.6
L4. 36.78+ 2.4
15.
.
Period
N a me
Date
16. 2.33(3.s51
L7. 12.1sX 19
18. 8.7X 0.4s
le. 0.78J0.16614
zo. 7s.o4+s.s
21.0.85F:0tr
22.Aliciapaid51.32for a bagof pinto beans.The beanscostS.SSper lb. How muchdid the
bagof pinto beansweigh?
23. Ninaand 3 friendsate lunchat a cafe.Theydecidedto splitthe bill evenly.Thetotal bill
was 517.84.How muchwas eachperson'sshare?
each.How muchdoesa bookof 50 stampscost?
24. Postage
stampscostSO.SZ
edding,Subtracting,Multiplyin& and Dividingwith Mixed Numbers
.)
numbers
it is oftennecessar5rto
change
themixednumbertom
Whenworkingwithmixed
you
go
process
Then
frastion.
can
through
the
rsual
accordingtotheoperationyou ar€
improper
your
check
answer
it
is
in
simplest
Always
to
be
sure
form.
doing.
, , +*, ?r:
z . f + 11 :
3. zL+si-:
4 . 6 3 - z l=
t.,!:4+:
6. 8g - s?:
7. q?xr1 :
8. n!
g. t9 x s!:
lo. n! -ll :
48
ll. ro?+
t2. 5Z* 1! :
E7
10 8
89
l0
t2
35
3
41:
7
5s
xll :
53
83
Solvethe following problemsaccordingto the way mixednumbersare conputed.
13. Ifarestaranttras z! cherrvoies,+l- alplepies,and
remainingafter
|otabhreberrypie
4
dinneronenight, howmanypiesareleft?
14. If Lisa has? of herhomeworkp.ages
of thatamountdone,
doneandJenniferhasonly
-8I
company.Shewants to apply it equally
15. Denisehasro] shares
to placewith ap'hone
3-
among 4 of the companiesshe has read about. If she doesthis, how many
shares will she have with each company?
g
ffi$Effi
i,
ConvertingFractions& Decimals(C)
Fraction
Instructions:Fill in the blanks of eachrow.
Decimal
Percent(Vo)
7
8
7:8
0.625
8
9
Ratio
62.5
0.888
60
3: 5
T:4
20
0.5
9
10
0.s55
3:4
MATH-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS.COM MATH
and Negative Numbers
andnegativenumbersarealsocalledintegers.They are equidistantaparton the
line. For every positivenumberthereis an opposite,a negativenumber. These
carrya sign. This is the negativesign O anda positive sign (+). When a number
with no sign, it is consideredto be positive.Sometimesusing a numberline is helpful
working with integers.
theoppositeterm.
2.
-14:
3.
- 1 0:
4.
6.
89:
7.
-56:
8 . - 1 6 5:
30:
addingor subtractingwith integers,it is importantto pay attentionto the signs.
t2. -1,5-7 :
-4+3:
10. 5*9:
r 1. 8 + ( - 10) :
12+ 1-t1:
14. 3 + 1-8;:
1s. c10)+ (-14):
2 + (-11):
17. 6-(-181:
18. 7 + 1-3;:
1 9 .6 *8 :
e + (-13):
2r. (-14)*5:
22. 9+1-8;:
2 3 . - 4 + 9:
whatyou know aboutintegers,solvethe following by filling in the missingnumber.
-4+
-3
25.
- ( 8 ): - 1 8
28. 20 + (-7):
26. -15+
:-11
29. 16+ -
: 12
Muttiplying and Dividing Positive and NegativeNumbers
Multiplication:
Multiplying a negativenumberwith a positivenumbergivesa negativeproduct.
Multiplying a positivenumberwith a positivenumbergivesa positiveproduct.
Multiplying a negativenumberwith a negativenumbergivesa positivenumber.
Solve:
1. (-8)(e): _
2. 5 (-01:
z:
3. (-r+)
4. ( - 2 )+:
5. (e)G4): _
6. (-7)(7):
7. (-7) (-10):
8.e (-8):
e. G3)(8): _
10. (5) G5):
11.6 (-2):
t2.rr (-2)
13. (4) (-s):_
14. 4 (6): -
ls. e (-121:
16.15(-2):
Division:
A positive numberdividedby a negativenumbergivesa negativequotient.
A negativenumberdivided by a positivenumbergivesa negativequotient.
A poiitive numberdividedby a positivenumbergivesa positivequotient.
Solve:
17. 56 + (-8):
1 8. (a5)+ (-5) :
19.
( - 1 4 )+ 2:
20. (-2r) + 3 :
2t.
-49+-7:
22.
40 + (-8) :
23. (-32) + 8 :
24. 60+ (-s):
25.
72 + (-8):
26. If John getson the elevatoron the seventhfloor and goestwo floors up, then goesthree;
ii
floors down, andthen rides two floors up again,what floor is he at now?
If Mary getson the elevatorin the basementandthen goesthree floors up, andtwo
down, at which floor is shenow?
PERIOD
DATE
StudyGuideandlntervention
Variablesand ExPressions
(w,the letters{
Write Mathematical Expressiohs In thg algebraic expression,
numbers
Ii algebra, a variable is-used to represent unspecified
and ur are called
above because
""ri"uu"
Any letter .utr U" used Is a variable. The letters 4 and w are used
;;ri"*.
( and w are
(w,
expression
In
the
width.
a\d
tf." h6t f"itltr oftfr" words length
tft"y
called"r"factors, and the result is called the product'
an algebraic expression for each verbal expression.
b. the difference of a number squared and 8
a. four more than a number z
The expres sion dffirence of implies subtraction'
The words more tltan imply addition'
the difference of a number squared and 8
four more than a number n
n 2 -8
4* n
The algebraic exPression is n2 - 8.
The algebraic exPression is 4 * n'
write
a.3a
3a:3'3
:81
write
Evaluate each exPression.
b. five cubed
Cubed means raised to the third power'
3 ' 3 U s e 3 a s a fa c to r4 t i mes.
53 :
MultiPlY.
an algebraic
5'
5'
: L25
5
U se5asafactor3ti mes'
Multiply.
expression for each verbal expression.
o
1. a number decreasedbY 8
2. a number divided bY 8
3. a number squared
4. four times a number
5. a number divided bY 6
6. a number multiPlied bY 37
7. the sum of 9 and a number
8. 3 less than 5 times a number
€
=.
o
@
6o
=
€
-=
3.
6'
9. twice the sum of 1-5and a number
1"0.one-half the square of b
o
=
t
:
11. 7 more than the product of 6 and a number
P
6'
lr
12. 30 increased by 3 times the square of a number
Evaluate
each exPression.
13. 52
L4.33
15. 104
L6.L22
17. 83
18. 28
Chapter1
GlencoeAlgebra1
PERIOD
DATE_
StudyGuideandlntervention
Order of Operations
EvalUate RatiOnal ExpfeSSiOIlS Numericalexpressionsoften containmorethan one
, operation.To evaluatethem, use the rules for order of operationsshownbelow.
insidegroupingsymbols.
Evaluateexpressions
Evaluateall powersand/ordivisionfromleftto right.
Do all multiplication
fromleftto right.
Do all additionand/orsubtraction
Step 1
Order of
I Step 2
OperationsI Step3
Step 4
Evaluate each expression.
Evaluate each expression.
a . 7 *2 ' 4 ' 4
7+2' 4- 4=rr;:
:11
; ^ Hi,:'nT:.
a. 3[2 + (12 + 3)21
3[2 + (12 + 3)21 :
Subtract4 trom15.
b. 3(2) + 4(2 + 6)
3(2) + 4(2 + 6) : 3(2) + 4(8) Add2and6.
:
'oiutoe12by 3.
B(2 + 42)
: 3(2 + 16) Find4 squared.
: 3(18)
Add2 and16.
: 54
3 and18.
Multiply
6 + 32
3+23
n .ffi
,
Multiplyleftto
right.
:3 8
Add 6 and 32
3+23 : 3+8
-F.s
Vz-4
:-
\'
11
42.3
Evaluatepowerin numerator.
Add3 and8 in the numerator.
11
16.3
powerin denominator
Evaluate
11
48
Multiply.
I:E
. -N
]E
:(,
=
i
F
6
o
F
Evaluate each expression.
1.(8-4).2
2. (L 2 + 4 ). 6
3.10+2.3
4.10 + 8. 1
5. 1 5 -L 2 + 4
^
o'
To4
7 . 1 2 ( 2 0 - t7 )-3 .6
8. 2 4 + 3 . 2 -3 2
9.82+ ( 2.$+2
o
:E
.:
=
15+60
I
,3
o
o
_9
0
'tr
,t
tQ2
l O . 8 2 + B*22 .7 _ 2 0 +E
11.ffi
1 3 . 2 5 0+ [5(3'7 + 4 )]
t+'
9,(9\ - L
L2.:+:-.-;
6:+
d
.-
4(52)- 4'g
Lo'[email protected]+D
2. 42 - 8+2
1sJ 21.2
trz-a
tz.7offi
15.
4.32-3.2
3.5
c2
ts',rffi
q.2
Glencoe Algebra 1
PERIOD
Study Guideand lntervention ftontinued)
The Distributive ProPertY
of
EXpfeSSiOnS A term is a number, a variable, o1 a product or_q_uotient
Simplify
with
.ro*betr-and variables. Like terms are terms that contain the same variables,
corresponding variables having the same powers. The Distributive Propert_y.and prop.erties
of equaliti", iut be used to simplify expressiong:-h expression is in simplest form if it is
repliced by an equivalent expression with no like terms or parentheses.
4(a2 + 8,o,b\' ab.
+'ab)
4(a2
-,:i: ::;[**
- =iY,iii;r
:;:il
Simplify
: 4a2 + LLab
Substitution
each expression. If not possible, write simplified.
Simplify
L.tAa - a
2.3x * 6x
3.3r - 1
4.L29- 109+1
5. -2x - 12
6.4x2*3x*7
7.20a+l%a -8
8.3x2 + 2x2
9. -6r + 3x2 + l0x2
Lo.2p* in
11.10r y- 4( xy+ xy)
L 3 ; 3 r - 2 x-2Y +2Y
L4.xy
I.2.2lc + 18c + 31b - 3b
Zxy
L5.t2a- LZb+ t2c
L7 . 2 - ! - 6 x * x 2
L8. hc2 + 3x2 + 2x
-
L6.4x + f,Oox - 20y)
'l
E
@E
GlencoeAlgebra1
NAME
DATE-
PERIOD
Study Guideand lntervention pontinued)
Commutativeand AssociativeProperties
S!rypllfy Expressiohs TheCommutative
andAssociative
Propertiescanbeusedalong
with other properties when evaluating and simplifying expressions.
Simplifu 8(y + 2x\ + 7y.
8 0 + 2 x ) + 7y
: 8y + LGx + 7y
: 8y * 7y + 16x
: (8 + 7)y+ L6x
Distributive
Property
(+)
Commutative
property
Distriburive
: Lly l- LGx
Substitution
The simplified expression is 15y * 16*.
Simplify
each expression.
1.4x* 3v* r
2 .3a* 4 b + a
3 . 8 rs * 2 rs 2 + 7 rs
4 . 3 a 2 + 4 b +Lo a z
5.6(x + y) + 2(2x+ y)
6.6n * 2(4n + 5)
7 . 6 ( a + b ) +a+3b
8.5 ( 2 x + 3 y ) + 6 ( y + r )
9.5( 0.3*+0.1y) +0. 2x
to.3*+ @* r or * f
\[rite
an algebraic
!!. z2+.9x2* t"' *
**'
L2.6(2x + 4y) + 2(x + 9)
expression for each verbal expression. Then simplify.
13. twice the sum of y and z is increased by y
14. four times the product of r andy decreasedby 2xy
15. the product of five and the square of a, increased by the sum of eight, a2, and,4
16. three times the sum of r and y increased by twice the sum of * and y
Chapter1
@
GlencoeAlgebraI
Equations
ion is an algebraicalgorithmthat is usedto solvefor an unknownvalue or variable.
an equals(:) sign in an equation.Thereis not one in an expression;therefore,
may be solved,not just simplified. Answerscouldbe wholenumbers,negative
or rationalnumbers.
following equations.
x+ 1: 15
2.
- 2 + 4 x:1 3
3.
8 x + ( - 4 ) : 12
+ 4x -- 45
5.
8x-(2+31:11
6.
7 x+ 2 - 3 x:18
8.
( 6 x+ 2 ) + 7 x: 4 l
9.
(10x)(2x): 40
1 2+3x -9x : - 1 8
11.
(8x +3)+( 4 x + 2 ) : 1 7
1 3 . 4 2 : - l4 p
1 4 x+ 3 :- 4 x- 6
1 4 . 7 5 :- 5 ( a +5)
17 (x - 2) : -34
63: 9(2-a)
16.
-54:3 (2 + 5m)
17.
- x -15: -15
19.
1 8+ 4 .5 p : 6 p + 1 2
20. -3k+19:ft+2
BrideePublishing
ReproductionProhibited.
Math 7 NO CALCULATORS
Name
Add, Subtract,Multiply, Divide RationalNumbers
@ 2012 K u t a S o f t w a r e L L C .
All r ig h ts r e se r ve d .
Date
Period
Evaluate each expression.
1) (-7)+ (-q) + t
D (4)+s-(-z)
3) (-r)- (-+)- (-:)
4) ( - 1)- 4+ 6
Find eachproduct.
s) 7 . -6 . 6
6) - 10.- 9._1
t ) -t . 6.- 8
8) -3 .2.-6
, -:-i
*,-i:
Find eachquotient.
ll ) 7 + - 1
tZ\ 6+3
1 3 ) -6 +6
14) -45 +9
t s)-?5 +i
7
rct -z! +f
55
d
Evaluate eachexpression.
rD (-6.3)- (-t.qe)
18)(-3.4)-l.s
l e);(+ )
zor
(-r+).i
21) (-3 0 - 1 0 )+-4 +-s -z
2 2 )s.8 + 2 - ( - 0 - - s)
Evaluate each using the values given.
2 3 ) n -(* * r ) ;
usem=2 ,and,n =-3
4 : u s e d = 3 "a nd b=-4
z sl
' 6'
ZT @)b - 2); usem = 5, and.p - -5
29)(-6)(m-r,);os"
*=-1,and,n=-+
2 4 ) a b z ; u s ed = -3 , a n d . b --4
26) ( c) ( a- D) ;use
a= 4,b= 2,and' c= - Z
2S
, -4
' 4)+ - h ; u s eh = - 6 , a n dj=
30)x +x+y;use-tr=-l,und
y=+
46
@