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Math Problems
Grade 6
Divide fractions and mixed numbers
Johanna bought
12
12
12
items at the college bookstore. The items cost a total of
$
29.00
\$ 29.00
$29.00
. The pens cost
$
0.50
\$ 0.50
$0.50
each, the notebooks were
$
4.00
\$ 4.00
$4.00
each, and the highlighters cost
$
1.50
\$ 1.50
$1.50
each. She bought
4
4
4
more notebooks than highlighters. How many of each item did she buy?
\newline
Use a system of three linear equations to solve the problem.
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What is the value of
\newline
4
3
÷
2
3
4^{3}\div 2^{3}
4
3
÷
2
3
?
\newline
2
2
2
\newline
8
8
8
\newline
16
16
16
\newline
7
7
7
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A student has
10
10
10
blue pens,
5
5
5
red pens, and
7
7
7
black pens.
\newline
In how many ways can he select
5
5
5
pens if only the choice of colors matters.
\newline
Use the Counting Rules.
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15
15
15
. Higher Order Thinking A map of a highway has a scale of
2
2
2
inches equals
33
33
33
miles. The length of the highway on the map is
6
6
6
inches. There are
11
11
11
rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of
1
1
1
inch equals
30
30
30
miles. How far apart are the rest stops on the new map?
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rac{
1
1
1
}{
3
3
3
} imes
3
3
3
.
14
14
14
imes
10
10
10
imes
10
10
10
imes
24
24
24
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13
13
13
\newline
Naomi travels to an interview.
\newline
She travels by car for
1
3
\frac{1}{3}
3
1
of the journey.
\newline
She travels by train for
5
8
\frac{5}{8}
8
5
of the journey.
\newline
She walks for the remaining
500
m
500 \mathrm{~m}
500
m
of the journey.
\newline
Find the length of this journey in kilometres.
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1239
=
10
1 2 3 9 = 10
1239
=
10
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John has
3
4
\frac{3}{4}
4
3
of a pizza left, and he wants to share it equally with his two friends. If each friend gets the same amount, what fraction of the original pizza does each friend receive?
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622.51
÷
7
622.51 \div 7
622.51
÷
7
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Tyshawn volunteers on the weekend at the Central Library. As a school project, he decides to record how many people visit the library, and where they go. On Saturday,
454
454
454
people went to The Youth Wing,
331
331
331
people went to Social Issues, and
444
444
444
went to Fiction and Literature.
\newline
On Sunday, the library had
600
600
600
total visitors. Based on what Tyshawn had recorded on Saturday, about how many people should be expected to go to The Youth Wing? Round your answer to the nearest whole number.
\newline
Answer:
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4
4
4
. The table shows the amount it costs to rock climb at an indoor rock climbing facility, based on the number of hours. What is the rule to find the amount charged to rock climb for
x
x
x
hours? (Example
4
4
4
)
\newline
Identify Structure Determine how the next term in each sequence
\newline
\begin{tabular}{|c|c|}
\newline
\hline Time
(
x
)
(x)
(
x
)
& Amount (\$) \\\(\newline\)\hline \(1\) & \(13\) \\\(\newline\)\hline \(2\) & \(21\) \\\(\newline\)\hline \(3\) & \(29\) \\\(\newline\)\hline \(4\) & \(37\) \\\(\newline\)\hline \( 5 x \) & \( 45= \) \\\(\newline\)\hline\(\newline\)\end{tabular}\(\newline\)can be found. Then find the next two terms in the sequence.
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Audrey volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday,
380
380
380
people went to The Youth Wing,
320
320
320
people went to Social Issues, and
396
396
396
went to Fiction and Literature.
\newline
On Sunday, the library had
1000
1000
1000
total visitors. Based on what Audrey had recorded on Saturday, about how many people should be expected to go to Social Issues? Round your answer to the nearest whole number.
\newline
Answer:
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Without dividing, determine if
34
34
34
,
757
757
757
is divisible by
9
9
9
and explain how you know.
\newline
34
,
757
□
34,757 \square
34
,
757
□
divisible by
9
9
9
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÷
2
(
1
+
2
)
\div 2(1+2)
÷
2
(
1
+
2
)
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A large cheese pizza costs
18
18
18
$
\$
$
Each topping you add on costs
1.50
1.50
1.50
$
\$
$
. How much would it cost to get a large cheese pizza with
c
c
c
toppings added? Write your answer as an expression.
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In a random sample of a particular model of drone,
2.5
%
2.5\%
2.5%
of the drones have a manufacturing defect. At this rate, how many of
4000
4000
4000
drones of the same model will have a manufacturing defect?
\newline
Choose
1
1
1
answer:
\newline
A)
2.5
2.5
2.5
\newline
B)
25
25
25
\newline
C)
100
100
100
\newline
D)
1
,
000
1,000
1
,
000
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In a random sample of a particular model of drone,
2.5
%
2.5\%
2.5%
of the drones have a manufacturing defect. At this rate, how many of
4000
4000
4000
drones of the same model will have a manufacturing defect?
\newline
Choose
1
1
1
answer:
\newline
A)
2.5
2.5
2.5
\newline
B)
25
25
25
\newline
C)
100
100
100
\newline
D)
1
,
000
1,000
1
,
000
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Sarah received
$
55
\$ 55
$55
for her birthday.
\newline
She used some of that money to buy
3
3
3
shirts priced at
m
m
m
dollars each.
\newline
How much money does Sarah have left?
\newline
Write your answer as an expression.
\newline
$
\$
$
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Donald has
x
x
x
twenty-dollar bills and
1
1
1
ten-dollar bill.
\newline
How much money does Donald have?
\newline
Write your answer as an expression.
\newline
dollars
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Anna baked
3
3
3
batches of cookies with
c
c
c
cookies in each batch. She then ate
8
8
8
cookies!
\newline
How many cookies does Anna have left?
\newline
Write your answer as an expression.
\newline
cookies
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Grandma baked
96
96
96
cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received
c
c
c
fewer cookies than she would have received had all of the cookies been evenly divided among the
8
8
8
grandchildren.
\newline
How many cookies did Cindy receive?
\newline
Write your answer as an expression.
\newline
cookies
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Sergio has
p
p
p
paintings in his art collection. He and other local painting collectors agreed to donate a total of
48
48
48
paintings to the local museum. Each of the
12
12
12
collectors will donate the same number of paintings.
\newline
How many paintings will Sergio have in his art collection after his donation?
\newline
Write your answer as an expression.
\newline
paintings
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Sunny earns
$
12
\$ 12
$12
per hour delivering cakes. She worked for
x
x
x
hours this week. Unfortunately, she was charged
$
15
\$ 15
$15
for a late delivery on Tuesday.
\newline
How much money did Sunny earn this week?
\newline
Write your answer as an expression.
\newline
$
\$
$
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Jack had
3
3
3
bags of golf balls with
b
b
b
balls in each bag; then his friend gave him
6
6
6
more golf balls.
\newline
How many golf balls does Jack have now?
\newline
Write your answer as an expression.
\newline
balls
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Steve had
48
48
48
chocolates but decided to give
8
8
8
chocolates to each of his
f
f
f
coworkers.
\newline
How many chocolates does Steve have left?
\newline
Write your answer as an expression.
\newline
chocolates
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Hannah's school hosted a book donation. There are
150
150
150
students at her school, and they donated a total of
b
b
b
books! Hannah donated
3
3
3
times as many as the average number of books each student donated.
\newline
How many books did Hannah donate?
\newline
Write your answer as an expression.
\newline
books
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The Running Aces card team won
$
548
\$ 548
$548
playing in poker tournaments last year. The winnings were split evenly among the
p
p
p
players.
\newline
How much money did each player receive?
\newline
Write your answer as an expression.
\newline
$
\$
$
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A bathtub is filling with water at a rate of
60
60
60
liters per minute.
\newline
How many liters of water are in the bathtub after
t
t
t
minutes?
\newline
Write your answer as an expression.
\newline
liters
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Suzie paid a total of
$
324
\$ 324
$324
for
x
x
x
tickets to a rock festival.
\newline
How much did each ticket cost?
\newline
Write your answer as an expression.
\newline
$
\$
$
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Ben has
b
b
b
dollars. Cam has
7
7
7
fewer dollars than Ben.
\newline
How many dollars does Cam have?
\newline
Write your answer as an expression.
\newline
dollars
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Richard caught
f
f
f
fish two weeks ago and
32
32
32
fish last week.
\newline
How many fish has Richard caught these last two weeks combined?
\newline
Write your answer as an expression.
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Daniel gets a paycheck every
4
4
4
weeks. He works
x
x
x
hours each week.
\newline
How many hours does Daniel get paid for on each paycheck?
\newline
Write your answer as an expression.
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Janelle saved up
$
265
\$ 265
$265
, then she bought a sweater for
d
d
d
dollars.
\newline
How much money does Janelle have left?
\newline
Write your answer as an expression.
\newline
$
\$
$
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Nicholas used a
$
10
\$ 10
$10
bill to pay for a granola bar that only costs
p
p
p
dollars.
\newline
How much change did Nicholas receive from the cashier?
\newline
Write your answer as an expression.
\newline
$
\$
$
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Gretchen is setting up for a banquet. She has
300
300
300
chairs and needs to distribute them evenly among
t
t
t
tables.
\newline
How many chairs should she put at each table?
\newline
Write your answer as an expression.
\newline
chairs
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Camelle manages her soccer team. She needs to order
4
4
4
practice jerseys for each player. There are
y
y
y
players.
\newline
How many total practice jerseys does she need to order?
\newline
Write your answer as an expression.
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Michelle used a
$
20
\$ 20
$20
bill to pay for a notebook that only costs
p
p
p
dollars.
\newline
How much change did Michelle receive from the cashier?
\newline
Write your answer as an expression.
\newline
$
\$
$
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Sebastian has
12
12
12
more trophies than Megan. Megan has
t
t
t
trophies.
\newline
How many trophies does Sebastian have?
\newline
Write your answer as an expression.
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Annika biked
37
k
m
37 \mathrm{~km}
37
km
this morning and another
x
k
m
x \mathrm{~km}
x
km
in the evening.
\newline
How many kilometers did Annika bike today?
\newline
Write your answer as an expression.
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Marco's mom gave him
d
d
d
dollars for his allowance one week. He also earned
$
14.55
\$ 14.55
$14.55
for his newspaper route that week.
\newline
How much money does Marco have?
\newline
Write your answer as an expression.
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Phil received a prize of
x
x
x
dollars from a poker tournament. The tournament cost him
100
100
100
dollars to enter.
\newline
What were Phil's net winnings from the tournament?
\newline
Write your answer as an expression.
\newline
dollars
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Susie ran a race. She ran
5
5
5
miles an hour, and the race took her
t
t
t
hours to complete.
\newline
How long was the race?
\newline
Write your answer as an expression.
\newline
miles
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It takes
b
b
b
minutes for Sylvia's bathtub to fill with water.
\newline
How many minutes will it take to fill
3
3
3
same-size bathtubs?
\newline
Write your answer as an expression.
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Flannery used
30
30
30
lilies and
78
78
78
roses to create six identical flower arrangements.
\newline
Write an equation to describe the relationship between
l
l
l
, the number of lilies, and
r
r
r
, the number of roses. Do NOT use a mixed number.
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2
7
÷
6
=
\frac{2}{7} \div 6=
7
2
÷
6
=
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10
7
÷
4
=
\frac{10}{7} \div 4=
7
10
÷
4
=
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3
8
÷
4
=
\frac{3}{8} \div 4=
8
3
÷
4
=
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Evaluate.
\newline
7
6
÷
4
3
=
\frac{7}{6} \div \frac{4}{3}=
6
7
÷
3
4
=
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