d,nJJwei /1'iq
Name:
Date: _ _ _ __
Algebraic Expressions - Evaluating
Evaluate the following algebraic expression
for the given value(s).
Evaluate the following algebraic expression
for the given value(s).
n=-4
2(n+3),
2(-4+3)
abc 2 , a=-3, b=4, c=2, d=-6
(-3)· 4. 2 2
-i
-i
2 (-1)
(-J)o q o Jf
l
Evaluate the following algebraic expression
for the given value(s).
8w - 2v,
w =5 v =3
-12 °
8·5-2·3
-i ~
4
Evaluate the following algebraic expression
for the given value(s).
a 2 +d+cb,
a=-3, b=4, c=2, d=-6
tlo -G
34
2
(-3) +(-to);
Evaluate the following algebraic expression
for the given value(s).
3
4y +2,
'°f·3 t2J-::,
""'J.,
l
108 .. 2
q + -3 • 4
110
q ... -1J
.
J.
+2
Athletic trainers use the formula:
3(220- a)
.
----,where a 1s a person's age, to
5
find their minimum heart training rate. Find
Karen's minimum training heart rate is she
is 15 years old.
3(220-1;-)-9 3(2.os) _., G•5 _,,
5
2·4
-i
q +(-c,)~2·4
y=3
3
lf "ll
--i
Sheet # 04-01
Pre Algebra
5
8
@
J,
Evaluate the following algebraic expression
for the given value(s).
3a(l2-2d),
a=-3, b=4, c=2, d=-6
3 •(-3) ( 1a -~. (-<,))
J
ld~d
123
I~ +-I~
3-f 3J)
0
J4
-q ":i.4
Evaluate the following algebraic expression
for the given value(s).
be
a = 2, b = - 7, c = 4
( -:J) • 4 ~
J
-2 8 __, - ,4
2.
Evaluate the following algebraic expression
for the given value(s).
b 2 -(8+3c), a=2, b=-7, c=4
(-1)
2
- ( 8 .f- 3 ° q)
~
( -1-) l -
~ + 12
-~
"''o
J._
'itl - 20
Evaluate the following algebraic expression
for the given value(s).
b2
-
d +a,
c
a= -3, b = 4, c = 2, d
= -6
Tue funnula F = ( C x. ~} + 32 am. be
used 10 oomret't 1em.pen.rure.i in degrttA
Cekim m ~Fahrenheit.
2 ° 24 .J- 2 .. ,2
A.
36ft
B.
48fr
7lfr
@
J
48 +24
105
1,050
C)
D)
B)
36
.+
-/-c,zif
- G21
) @
4
degees
A Fahrenheit rhe:rm001~ re:ads
26
154
me
95 ~ W'hkh diows
tem~rature in ~es C)e'kius?
@
-I - 6211.
35oe
B. 63<>C
C. lB°C
o.
~ (-h24)
+ -624
(qs -32)~2=l-
q
1
\;.o
~
)C
5
2·03.:.C
Evaluate the expression to find the missing
values in the table.
6ill>
x
8
11
Evaluate a 2 - (a 2 - b 2) when a= -2 and
b=3. (-2)~-{€2)Z.-32)
j;!, 1
-i ""J, C) -9
@) 9
'f - q D) -1
22
(-i)~
4+5
q
x+ 2 •4
16
11-1-2·4 ? 1q
224-2·4? 30
Which expression completes the table?
Evaluate 2ac - b2 -:- c when a= -2, b = 4,
and c = -1.
A) 18
B) -18
j can be
~to convat ~pen.tures in
&h.renheit to d.~es Cels.i.w.
Evaluate x + (-624) for x =
I
3<0 +32
Tue fonnula C • (F - 32) x
C)
qo6)b
[Z-O •;J+s2
1,000
22
Evaluate 90 - k when k = -64.
164
68(>F
tf
= 7, and h = 15.
10·1·15
--i
1-0 o()
A)
@
C. '5TP
Evaluate lwh when l = 10, w
@
Fahrenheit?
8. 5-01:1p
D. 288fc
A)
A Gtlsiw dtttmom.eter reads 20 ~~.
Whida thGWS th~ tx:mpcrarnre in d~
©
D)
20
-12
t
??
8
25
9
= 2 .. g +q
27 :;:. 2°9 + q
29
10
a. t+ 14
b.
4t-1
@ 2t+9
d.
3t+ 1
-- d·lo+G
Name:
arwwet ~
Algebraic Expressions - Writing Expressions
Date: ------
Sheet # 04-02
PreAlgebra
Practice Problems:
Define a variable when necessary. Highlight each key word. Translate each verbal sentence
into a mathematical sentence.
seve~the quotient of p and q
twelve minus a number
..L -'t
ci
Algebraic expresston:_J_;l_-__,Qi------------
the quotient of a number and five
the product of two and a number plus six
n;5
2q + ~
Algebraic expression: _ _ _ _ _ _O,..,i(=---'-n-'-'-~-'5"-------
the product of r and x
six decreased by five multiplied by a number
~
three ~a number
Algebraic expression:
3+
n
Q(
the sum of six and twice a number
n 'f- 3
the difference of two and a number
Algebraic expression: _
-5q
G+lq
triple the difference of 5 and a number
3 (s -a)
___,J<.>.----'-q+------------
six ~twenty five percent of a number
one-half of a number
i______
Algebraic expression: _ _X-'-2_•-'-q+-__.O._..K,,.__ __
five times a number, increased by two
double a number, diminished by 17
5_Q_,__+_2___________
2.n-ll-
Algebraic expression: __
s i x @ a number
six times a number squared, increased by 3
Algebraic expression: _"'-q+----_..G.._____________
the sum of a number and seven
Eight feet~the height
b -8
Q-+-_+_1-___________
Algebraic expression: _ _
ten plus the product of x and y
Sarah worked eight more hours than Paida
'?+a
!O_+_x__,yi-----------
Algebraic expression: ___
twice a number a number decreased by six
Kumar made twice the number of goals as
Jacob.
2j
Algebraic expression: __L_Q_,__~__..b,____________
three more than five times a number
Algebraic expression:
3 +5q ()( 5Q+-3
Addison is three years younger than Nathan.
Algebraic expression: _
_.:....q_,__-_3~----------
If n sca:nd.s for the number, which blfS:t
represen.u the fullowlng phrase?
the sum efa number and t~Ji'llUktl by
Tell whether the statement below is
sometimes, always, or never true. Justify your
reasoning.
seven
@
A. n+I3
•. i+3
The expressions
D. 7 + (n
+ 3)
If n SwW for the ltUnlbet which OOt
reptesent$ the foUowing phrase?
eight~ by six ~imes a
A.
@
Sn- 6
8-6n
c.
Some~rtW s 1}
Sawu qum kt.
6n-8
D. 6-
an
3r~6
C 6-3r
~· 3r + 6
D. 6 + ,3r
Bonnie bough£ a prepaid cell phone with
400 min.mes of Cilllin:g time. Sin« then,
@
sh.e bas Ulred th.e phone for 20 minutes
each day. Wb.iro ap~on shOW'5:
DUMbe:t of nclnutes left on the cell phone
after d clap hilve p.:wed?
me
1.0J- 400
B.
204~
$19.99 per day
$0.17 per ml
®
c.
56 - 6
D. 5b + 6
A Web site charges $0.99 to download a game
and a $12.49 membership fee.
$0.17 per ml
t_rYt________
Algebraic expression: __5_0_-l-_._I
Part B Use the expression you made in Part A to find
the cost for driving 150 miles.
50 +-.Ii- ( l~o)
D. 400+2M
expre#lon tepte$enu Emma~:s age?
$50 fee
Part A Suppose you rent a car using Option 2. Write
an expression that gives the total cost inoollars for
driving m miles.
@400-20J
Emma is .5 years oldet ~ 6 times &n's
.age. Let h repteSmt &n's age. Which
A. 6b- 5
6.b+ 5
-/L
A car rental company's fees are shown.
Answer$
400
x and y {JJIJ
number
D~ hu ~3 .times the numbei
of mtnps in her oSllectll.o.n that Rafael bu
in hi~.. Lc:t r equal ~ nu.moo o.f namps
Ratte! hu. Wbkb "pre.ssion rep:remu:s
the number ofstamps Diana has?
A.
x - 3 and y - 3 represent the same value.
(n:+ 3) + 7
:J 5.)()
Part C Suppose you rent a car using Option 1. Write
an expression that gives the total cost in dollars to rent
a car for d days and m miles.
Algebraic expression:
/
q. qqd -f- o / 1 (}(
Part D Use the expression you made in Part C to find
the cost for renting a car for 2 days and driving 70
miles.
1q,qq(2) .f-. Fl-(lO)
Part A Write an expression that gives the total cost in
dollars to download any number of games.
Algebraic expression:
_---'-•-q'-q~g-...:..+--"-1_2_.4-=-q~-----
Part B Find the cost of downloading 6 games.
0 qq (b~ +-I 2 .. 4q
Answer$
51. 88
--'--'-------------
THROWBACK! Evaluate the expression for the
given values without the use of a calculator.
1
2
6 1 ,z=5
xz+y 1"f x= 3 ,y=-.
5
Answer $
J 8 .4 3
3-k'·5-1-(-b.1)2..
I~ ~ +
-w:·
c.'
~,Gt
3:}. 21
lb+ 31-2.1 ~
.
53
0
l. \
3t-. 2-I
tb.00
i I
~S·
~. l
3'. 6
3 =1-.:i.
o
~
dMwetl 1ff q
Name:
Date: _ _ _ __
Algebraic Expressions - Terminology
Sheet # 04-03
Pre Algebra
Olivia was asked to pick the algebraic
expression from the following choices.
Which expression is a trinomial?
@ x +2yz-3
B
I2 + 2( 4)( 5) - 3
c x + 2yz = 3
n x + 2yz < 3
2
A
4x 3
B
7x+l2
3x 3 +3x 2
C
@ 5x
3
+3x 2 -11
2
In the expression@x- 2 -t@:-2, 4 and 1 are
examples of which of the following?
2
A
A.
Olivia is a little confused as to which one to
pick. Explain which choice is the algebraic
expression and also explain why the others are
not.
~lqelxa1c
C Constants
Terms
@
Coefficients
D Factors
of \fa<ta\:ilt
Fill in the following chart:
h
I t1 .fYol\-1-
as \J(l(1abb
e)(0'f5Stofl _..,
Monomial
Coefficient
l0x 3
63
Which of these phrases best describes a
polynomial?
A A fraction whose numerator is greater
than its denominator
c
An algebraic expression containing
exactly one term
)(
3
I
r
I
NoV1e
G
3
Alyssa's teacher asks her to write an expression
that contains five terms, two exponents, and a
quotient. Alyssa writes the expression:
4x 3 -2x 2 +~-5
4
PART A Identify the terms, coefficients, and constants in
Alyssa's expression.
Terms:
A number that has more than two factors
@ An algebraic expression containing one
Exoonent
Base
lo
r
B
3tum.s
1)(3 . - 2..x 2,
4, 2 , •
;1
Coefficients:
1
I
-
f
7
J
~
-5
or more terms
Constants:
Which is the name of the expression shown
below?
2x 2 y-5x+3
A
term
B
equation
C
coefficient
-5
~-=:__~--~----~
PART B Does her expression satisfy all the requirements?
If not, describe a change she could make to create an
expression that meets all the requirements.
A Yes
@ polynomial
B
Which expression is a binomial?
2. +erm~
A
p2
@ 3w+l
B
3w
D 3p 2 +2p+2
C
No; she could change ~in her expression to x + 4
I
4 sha. woul6 lo&e her ~uohettt·
No; she could change 4x 3 in her expression to
4•x
@
3
mulhply1n9 1s +k Sam£~
No; she could add the term n to her expression.
rleech
a se ieJ M.
1
Name:~-------------­
Date: _ _ _ __
Algebraic Expressions - Combining Monomials
Pre Algebra
Sheet # 04-04
viit'::::rs~''"''i A school is collecting fruit during their "Go Healthy" campaign. Below you can see how
many apples and oranges two students donated to the cause.
A. How many apples did Bich Su donate? Haley?
Together?
'+
3
I
B.
Io
"'
How many oranges did Bich Su donate? Haley?
2,
1Together?
5
C.
;
What would be the issue of putting all the fruit in a
box and labeling the box with number 17?
Wou ld,d 11now how IY)Q<I~ ort.011
t how fY!llny apples.
Cosgrove, Maximus, and Patrick snagged some goodies after the pinata was opened at a
Halloween party.
The goodie bags all have the same amount of candy inside.
Write an expression to show how much candy each person has.
Let
)( + 4
X
= the
number of
candies in the bag.
3x+.2..
Write an expression to show how much candy was collected by them all.
_,_X_t_r:f______
Luis, David and Pelin work at a music store. Each week, Pelin works three more than
twice the number of hours that Luis works. David works two hours less than Luis.
works each
Let ~ =the number of hours Lui S
week.
Write an expression for each person's number of hours.
Luis
David
Place all the tiles in the space here.
Pelin
JR
81
[I]
II
i~
xx m
CTI
What does the space represent?
cd\ houvs
wo~ted b~ eoev-4 lM.t
Write an expression for the image.
x
x-J
3+ax
4x +-I
Name:
?laswei< 11.t 4
Date:
Algebraic Expressions - Combining Monomials
Which is equivalent to the
expression belmv? &-~ t :-1 bj + 5 r +- 3.:c
A.
@
C. 2y + 2z - 4
D. 2y + 2z + 4
-2y - 2z
-2y + 2z
Whkh is equival<:m to the
expression bdow?
qbt 1-b +_Sc +4 <:
9bt--5c+ 7b + 4c
d.. J
A.
-2b- c
C.
B.
-2b + 9c
@
l6b + 9c
16b- &
Which is equivalent to the
expression bclow?
2 Ol. + -8 .e +& -l -12
20z + 8 +
Simplify the expression below.
-4x$)
©
D
Sx
3x
-3x
-Sx
Simplify the expression:
3ab +Sb-tab+ 4ab +-2b
~-
Answer
I'
IOO.
12z- 4
B. la+ 4
C. 28z+ 4
b
.\-
3
"-
3~b +- 4a. b + -cb
b
5bt-2.b
Simplify the expression:
6a + Sa 2 +-3a +1a 2 +12
A./
-
,_..__.-..
(-Sz)t~;----J.
@
Sheet # 04-05
PreAlgebra
A
B
8y+-3z@+ 10y + 52@
-----
Answer -
-
5a. 2 +,~1a 7
ct
2a. 2.. ·+ 3 a. +1L G
\ 2.
t - 3a..
D. 28z-4
Simplify the expression:
Which is equivalent to
expression below?
i +-5kr-9 + 2k
th.e
- 5Kf 2 Yi
+I f -q
9x +:"5x 2 -t7 + 9x -i2x 2
~-==-
~+ -i
A. 3k + 8
C~
B. 3k - 8
@
-.3k + 8
-3k - 8
Whai: is rhe sum of the polynomials
modeled below? '
Answer
=.....--
-5x2+-2x"-
-+ X +I &x-1 q't
+-qx
+- - 1
2.
,
Which is equivalent to the
4a.. +- - a
expression below?
~+5tJ:+2
A.
I"-
lOa
B. Ila
""
~
+2
@
3a+7
D. 4a + 7
Simplify the expression below.
+
5g + 8 + b + 11 3g
A. .~i1 + 5x + 3
B. i-h'+l
C. i-x-1
@x2 +x+ l
!i9 + -:55
h_
tr-II
3
3
Simplify 4b tlb + 2h + 2h + 2h.
(f)
3
-=-
~I"--'
-=- ~
c.
6b + 3b
'fb3 +zb3
9b
6b3 - lb+ 4b -1b+-?.br2s
d.
9b
b.
Write a real-world situation for7.50y + 9.
I ma Ke t +~D
Ov'I
ktd
plus a..
'-lb- Jb
3
What is the perimeter of the figure in
simplest form?
11
1x+x-r2x
= -+·x
~-
3:1-
I -Q~
~
~
q-
~
2x+3
What is the perimeter of the figure in
simplest form?
3xf3x+x-1-><= &x
x+3
3+3+-2+-2
3:x-2
3x-2
--;].
G
+-4
=2
The cost of a game g with a 7% sales tax
can be represented by the
expression g + .07 g .
PART A Determine the cost of the game
after sales tax if the game costs $52. 2
S
52 +., O=J- 5L
5 J_ +- J. to1
;:_Q_L
0
s s. b ...,
.. 3/,lf,
ffl. OD
s s' '
'f
PART B Simplify the expression/g + .07 g .
{,0=1-5
Xf 3
What Is an expression for . e perimeter of
this rectangle~
PART C Use the simplified expression to
find the cost after sales tax of a $5~game.
J., Ot g
n2+5n+6
l.DJ{\.l)
n2
n24 ()2 .f
()2 .f
-
4
n2 = 4n 2
5,1 f 5n :::. /Oo
~ t-6 f''-/ f4 = ~
Answer
.1n t+t0n+4
Each side of an equilateral triangle
measures 3:l - 5 inches. What is: the
perimeter of this triangle?
3-KCT-5
3x2 -s
f,,V
- 5 +-s +-5 ::: - Is-
-ti
5 5. 61
i
5·i__
2.
It
~-2 ~ s 0
PART D What are some benefits of
evaluating the simplified version of
expressions in the real world?