^
9 -
c
^
\
r-
<-
<3
i
^J?
^
<J
^
s'
>
^
^)
o)
^
i
0
<^,
< <x
V*
ys
^
^
S
-+J
f.
a
'0
^^
<^1
0
*-y
^p
QJ\
^
^
0
J
^
0(
^
-s
C^r
^
^
Name:
10/ t/^ fc>^
//l5/^C^-''8/Y/
Solving One-Step Equations
Addition and Subtraction
Balance both sides of the equation by using inverse operations to get the variable alone
and find its value.
x + 4 =12
examples:
-4
x
d- 7 =10
-4
7
.I
.
+7
d = 17
=8
* Be sure to make
the same change
to both sides of the
equa/ sign.
Solve each equation to find the value of the variable.
1. 25=y+ 20
2. /(r+22
4. ^ -21= 6
5. , 7-9=7
6. ^3-14=6
7. 18= c + 5
8. 2 = e -9
9. ^+8=13
10. cV+10 =24
n. 2+c7 =n
12. /r+17 =30
^
d^
37
3. 14=x+11
Super Teacher Worksheets - www. superteacherworteheefe. com
Name:
^01\/
^
n<;j^c^®rv
Solving One-Step Equations
Multiplication and Division
Balance both sides of the equation by using inverse operations; to get the variable alone
and find its value.
examples:
3x = 18
T~
T
(4) TT = 5 (4}
4
*Be sure to make
the same change
to both sides of the
x = 6
V = 20
equa/ sign.
Solve each equation to find the value of the variable.
1. 2e=4
2. 24=6o
3. 5c=50
4. -^-=1
-=f
«. ^=25
7. 32=4c/
«. i-
9. 7y=42
10. f=8
11. 108=9,-
12. 15, =30
y~
Super Teacher Worksheets - www.superteacherwortaheefs.com
3
5. 6.4: Problem Solving Using Equations
(<
Using variables, write mathematica^exgne§sions for the following.
Use different variables for eacl^^lnession^
1. A number:
2. A number tripled:
3. A number is decreased by seven:
4. Three larger than a number:
5. Eighteen increased by a number:
6. A number subtracted by another number:
7. Three times a number:
8. A number is divided by 15:
9. A number less than twelve:
10. Three consecutive numbers:
^ * Solve for "the number" in th^'quation.
Translate these sentences into efluatjons.
11. Ten less than triple a number is twenty-one.
12. If a number is doubled the result is sixty.
13. Seven plus a number reduced by two gives you eighteen.
14. Three times a number is sixty-three. _;
15. Increase the product of two and a number by 4 to obtain 56.
16. The sum of nine times a number and five is one hundred eighty-five.
17. A number divided by six is twenty-one. _;
18. Double a number plus five is seventy-five. _;
19. You get ten when subtracting sixteen from twice a number.
20. If a number is tripled and then reduced by nine, the result is sixty-six.
l\
TIPS4RM: Grade 7: Unit 5 -Solving Equations
22
Name
8.4 Writing and Reading Equations
MATHPOWERT
pp. 238-239
Choose the correct equation from the box below.
Write eachof thefollowing in words.
1. Two added to a number is eight.
12. x- 7= 14
2. A number dividedby seven is four.
13.
3. A number decreased by three is eleven.
4. Five subtracted from a number is nine.
z
5
2
14. 4x
28
15. x+ 9= 26
5. Thirteen added to a number is eighteen.
Write an equation for eachof thefollowing
6. A number multiplied by four is sixteen.
16. The length of theparking lot divided by
fifteen is three meh-es.
17. Eight times the number of shidents is 216. &
'"..'
x
3= 11
4z
x
16
7
=4
18. Mia's age 7 years from now will be 21.
x + 2 =8
p + 13 =
18
x - 4
=7
y -5= 9
19. Fiffy-five kilometres less than a distance is
one thousand kilometres.
Write an equationfor eachstatement.,
7. A number multiplied by 6 is 18.
20. The number of pages in a book decreased
by 12 is 470.
8. A number decreased by 3 is 4.
21. When Raj reads 5 more pages, he will be
on page 65.
9. A number divided by 2 is 9.
22. Write and solve an equation for each of
the following.
10. A number decreased by 5 is 11.
a) The height of a figure is 5 cm more than
the base. The base is 7 cm.
11. Sixteen divided by a number is 4.
b) Omar scored 4 times as many goals as
Brent. Omar scored 36 goals.
82
Copyright © 1996 McGraw-Hill Ryerson Limited
?-
*-^
--_I
Name
<»».
7. 1
Writing Equations
MATHPOWERT :
Verbaldescriptions ofcertainrelationships canbeexpressed asequations.
Circle thecorrect equationfor eachsentence.
15. Four less than a number is negative three.
1. A number increased by four is ten.
^_ 4 = 10
4x = 10
x+ 4 = 10
16. Four times a negative number is negahve
sucteen.
2. Sam'sagedividedby three is five.
1=3
3a=5
i=5
3. Three times Mane's money isequal to $9.45.
3m = 9.45
3 + ". = 9.45 ^ = 9.45
Writeanequationforeachstatement\'QOI^ ^5
17. The initial letters for the numbers one to
ten contain six more consonants than vowels.
4. A number decreasedby twelve iseighteen.
18= 12 y+ 12= 18 y- 12= 18
18. Two consecutive integers total thirty-five.
5. Janis4 cm taller thanAhmed. Thesum of
their heights is 156 cm.
h+4=156 h+4+h=156 4h+h=156
3
19. Pierre has $45 more in his bank account
thaninhispocket. Pierrehasa totalof$105.
Writeanequationforeachsentence.iS^^ SO ^6. A number increased by six is twenty.
G±^^Q-
^
20. The area of Lake Superior is 4. 4 times the
area of Lake Ontario. The sum of the areas is
103 000 km2.
7. A number multiplied by four is sixteen.
8. Sevenless than a number is five.
21. The flying distance from Toronto to
Reginais4 times the flying distance from
Toronto to Montreal. The sum of these
9. The square of a number is thirty-six.
distances is 2535 km.
10. The product of a number and hvo is thirty.
22. Thelongest openCanadianbridgeis in
Quebec. It is 277 m longer than the longest
11. Ten decreased by a number is six.
coveredbridgelocated'inNewBrunswick.
The sum of the lengths of these bridges is
1059 m.
12. One-fifth of a number is six.
23. The number of moons orbiting Saturn is
13. Six less than a number is twenty-two.
18. This is 9 times the number of moons
orbiting Mars.
14. A number dividedby six is seven.
77
lib
Copyright© 1995McGraw-Hill RyersonLimited
Al^£-(:-ks
-r
'^nod^l !
/»
^^
c-
\u-*-
x -5-- -^3
Y -I ^ 0
x+3^ 5
^ -3 ^ -SL
x +4 '- -3
x+ I r
7
p
^p
^t^e^aic Pcoccss ~ Inverse O^tra-h^s
'VS^ 40ur
your t^orfc!"
^-3--.3
CD X+-r1^c!
C^cL
cKecL
3^= 19
^c,
^3
n
C. ^c^
a^cit
Process
x
-^
-V
^
Name:
{One-Step Equations: Integers)-
Mixed Operations
Level 1: 51
Solve each equation.
D
10=z+6
2)
3)
q-12=1
4) 18=y
8y = 48
5) ^=7
6)
n=m-4
7)
t-19=2
8)
1 + s =3
9)
24 = 4c
10)
^=9
Printahlp Wnrkshppts (S) www.mathwnrkshppts4kids.rnm
;0
Name:
-(One-Step Equations: Integers^
Solve each equation.
1)
x+9=12
2)
s-1=10
3)
3=z-n
4)
5 +y = 7
5)
8= 2 + q
6)
6 = n -4
7)
r-2=5
8)
6= m + 6
9)
p+ 7 = 8
10)
4+a=13
Printahlp Wnrkshppts 0 www. mathwnrk<;hppt<;4kid<;. rom
Add/Sub Level1:S1
Name:
-(bne-Step Equations:Integers)Solve each equation.
y._
1)
3x=36
2) ^=3
3)
5p = 25
4) 14=-|
5) ^
6)
24 = 6c
7) A=1
n~
8)
8u = 40
9) 10=^
10)
7z=7
Printahlp Wnrkshppts (a) www.m?ithwnrk<;hppts4kiri<;.rnm
_Myj/Div
Level!: St
Score:
Name:
{bne-StepEquations- Integers}
Add/Sub: St
1) Natalie buysorganicalmonds priced at $77from the grocerystore. Howmuch did
she pay the cashier, if she received $23 in change?
2)
Lara and Mae participated in a quiz contest. They scored 23 points in all. IfLara
scored 9 points, how many points did Mae score?
3)
John was gifted a pack ofcrayons. He gave 13 crayons to his friend Rhea and was
left with 11 crayons. How many crayons did the pack contain?
4)
Smith and his friends are gaming online on a popular website. An hour later,
6 friends go offline. Fiveofthem continue playing. How many ofthem were
gaming online initially?
5)
Trevor takes up a test at school and completes it in an hour. The test has two
sections. If he takes 35 minutes to complete the first section, how much time does
he have left to complete the second section?
13
Printahlp Math Wnrl«;hppt<; t& www mathwnrk<;hppt<;4kiri<; mm
Score:
ie:
-(One-Step Equations- IntegersY
1)
Mul/Div:S1
Jamie paid the rent well past the due date for the months of April, May and June.
As a result, he had been charged a total of $75 as late fee. How much did he pay as
late fee per month?
2)
The kindergarten section of Lehigh Valley has 12 classrooms. If each classroom
can accomodate 15 kids, how many kids can the kindergarten section accomodate
in all?
3)
Juan sells raffle tickets at a charity event for $6 each. How many tickets does he
have to sell to make $114?
4)
Melanie works as a nanny and is paid $ 14 per hour. If she puts in 40 hours of work
in 7 days, how much does she earn in a week?
5)
The non-fiction section of the Montgomery County Library has 17 racks. Ifeach rack
holds 528 books, what is the total collection of non-fiction books in the library?
H
Score:
e:
-(One-StepEquations- Integers^
Mul/Div:S2
1)
If Bob has 35 nickels in his piggy bank, how many cents does he have in all?
2)
Kelly buys four cardigans of the same price from an apparel store. How much will
she be billed, if each cardigan costs $79?
3)
Susan, Lillian, John and Polly participated in an Easter egg hunt. At the end of the
hunt, 96 eggs were shared equally among them. How many Easter eggs did each
of them receive?
4)
Sam is seven times as old as Tim. If Sam is 42 years old, how old is Tim?
5)
The San Joseteam won a baseball tournament and the prize money was shared
among the nine players. Ifeach player received $500, what wasthe total prize
money?
15
.
^^^ One-step equations - iword problenas
One-step word problems - combined
2) Last week Mark ran 31 miles more than
1) Last week Daniel ran 6 miles more than
Jasmine. Daniel ran 24 miles. How many
Jack. Mark ran 46 miles. How many miles
miles did Jasmine mn?
did Jack run?
A*
0
^y^JLtLA
x
spcxn..
-^0
y ^ ^ ^ ^4
>c -^
^
Y -- \^
^ r^Si^
1^
^'
3) Heather wants to buy a comic book that
costs $3. How much change does she
receive if she gives the cashier $5?
K -=
5) Krystal won 55 lollipops playing the bean
bagtoss. After giving some awayshe only
has 37 remaining. How many did she give
away?
£k x -
7) Chelseawas 76 years old thirteen years ago.
4) Cody is cooking a cake. The recipe calls for
5 cups of flour. He accidentally put in 8
cups. How many extra cups did he put in?
2^^-
6) Arjun ran 19 miles less than Brenda last
week. Arjun ran 14 miles. How many miles
did Brenda run?
^ -=-
'^v^o-r
v^
How old is she now?
x^
\ r^e
K ^
^' CKr ^ ^^> I ^
(_£i. v ^v^' l
v/ ^Jr;Y« ^^o\^^
-e
You may use this math worksheet as long as you help someone learn math. -> MATHX. NET <-
8) A recipe for cupcakes calls for 4 cups of
flour. Leaaccidentallyput in 10cups. How
9) Jill paid $4 for a sandwich. She now has
$25. With how much money did she start?
many extra cups did she put in?
10) In twelve years Huong will be 58 years old.
How old is she now?
11
11) A recipe for a cake calls for 10 cups of
sugar. Micaela has already put in 2 cups.
How many more cups does she need to put
in?
12) Paul and his best fhend found some money
in anenvelope. They split the money
evenly, each getting $21 . How much money
did they find?
13) Howmanyboxes ofenvelopes can you buy
14) A recipe for muffins calls for 8 cups of
sugar. Jimmy has already put in 5 cups.
How many more cups does he need to put
in?
15) At a restaurant, Perry andhis five friends
decidedto dividethe bill evenly. If each
person paid $14 then what was the total bill?
with $27 if one box costs $3?
You may use this math worksheet as long as you help someone learn math. -> MATHX.NET <-
16) Norachai spent $63 on nine colored markers.
How much did each marker cost?
18) Last week Scott ran 27 miles more than Lea.
Scott ran 46 miles. How many miles did
17) Kali is cooking cookies. The recipe calls for
10 cups of flour. She has already put in 4
cups. How many more cups does she need
to put in?
19) Nine workers are hired to harvest potatoes
from a field. Each is given a plot which is
11x10 feet in size. What is the total area of
the field?
Lea mn?
20) Kayla won 50 pieces of gum playing
horseshoes at her school's game night.
Later, she gave one to each of her friends.
She only has 21 remaining. How many did
she give away?
21) Nine workers are hired to seed a field by
hand. Each is given a plot which is 6x10
feet in size. What is the total area of the
field?
22) Kim wants to buy pants for $63. She gives
the cashier $70. What is her change?
You may use this math worksheet as long as you help someone learn math. -> MATHX. NET <-
/z
23) Five workers are hired to seed a field by
hand. Each is given a plot which is 7x12
24) How many packs of batteries can you buy
with $9 if one pack costs $3?
feet in size. What is the total area of the
field?
25) Paulboughtthree toy cars for a total of $21.
Howmuch did eachtoy car cost?
26) Kim and 6 of her fnends went out to eat.
27) Marywon 65 lollipops playingbasketball at
the county fair. At school she gave one to
every student in her math class. She only
has 49 remaining. How many did she give
28) Darryl was 26 years old fifteen years ago.
They decidedto split the bill evenly. Each
person paid $10. What was the total bill?
How old is he now?
away?
29) Jasmine paid $7 for a salad. She now has
$7. How much money did she have before
buyingthe salad?
lci
30) After paying $2 for a pizza,Ndibahas $34.
Howmuch money did he havebefore
buyingthe pizza?
You may use this math worksheet as long as you help someone learn math. -> MATHX. NET <-