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Math Problems
Grade 6
Ratios and rates: word problems
Aliyah jog in
5
5
5
hours?
\newline
write
10
10
10
pages of his novel in
4
4
4
hours. At this rate, how many
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Vivi is a drummer for a band. She burns
756
756
756
calories while drumming for
3
3
3
hours. She burns the same number of calories each hour. How many calories does Vivi burn per hour?
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Skylar is a lifeguard at a swimming pool. Last week, they worked
3
3
4
3\frac{3}{4}
3
4
3
equal-length shifts, because rain closed the pool early one day. Those shifts totaled
11
1
4
11\frac{1}{4}
11
4
1
hours of work. Skylar is a lifeguard at a swimming pool. Last week, they worked equal-length shifts, because rain closed. Skylar is a lifeguard at a swimming pool. Last week, they worked equal-length shifts, because rain closed the pool early one day. Those shifts totaled hours of work he pool early one day. Those shifts totaled hours of work.
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The ratio of the side length of a square to the square's perimeter is always
1
1
1
to
4
4
4
. Peter drew a square with a perimeter of
28
28
28
inches.
\newline
What is the side length of the square Peter drew?
\newline
_
_
_
_
\_\_\_\_
____
inches
\newline
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When Cara drives to work, it takes her
30
30
30
minutes to drive
15
15
15
miles. On her days off, she likes to drive to her favorite donut shop. It takes Cara
6
6
6
minutes to drive to The Dreamy Donut Shop at the same rate.
\newline
How many miles away is The Dreamy Donut Shop?
\newline
____ miles
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Hugo sells handmade key chains online. Yesterday, he made
6
6
6
keychains in
30
30
30
minutes. Hugo wants to make
9
9
9
keychains today.
\newline
If Hugo works at the same rate today, how long will it take him to make the keychains?
\newline
____ minutes
\newline
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The book fair is this week, and there's a special deal for teachers. For every
5
5
5
hardcover books a teacher buys, he or she can get
2
2
2
paperback books for free. Ms. Baldwin is buying
35
35
35
hardcover books for her classroom library.
\newline
How many paperback books will Ms. Baldwin get for free?
\newline
____ paperback books
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Monica makes tomato sauce with the plants she grows in her garden. She uses
3
3
3
basil leaves in her sauce for every
8
8
8
tomatoes. She is making a big batch of sauce with
32
32
32
tomatoes from her garden.
\newline
How many basil leaves should Monica use in her sauce?
\newline
____ basil leaves
\newline
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Rick's chore list shows that he is responsible for washing the dishes after dinner this week. Last night, he washed
4
4
4
plates in
2
2
2
minutes. Tonight, his grandparents are coming to dinner, and Rick will wash
6
6
6
plates.
\newline
If he washes plates at the same rate, how many minutes will it take Rick to wash the plates tonight?
\newline
____ minutes
\newline
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Britney just got a new video game for her birthday. Yesterday, she played for
27
27
27
minutes and beat
3
3
3
levels. Today, her parents said she can play for
45
45
45
minutes.
\newline
If she beats levels at the same rate, how many levels should Britney beat today?
\newline
____ levels
\newline
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Xavier loves to make waffles for breakfast. Normally, it takes him
9
9
9
minutes to make
3
3
3
waffles. He had some friends sleep over last night, and he wants to make
10
10
10
waffles this morning.
\newline
If the waffles cook at the same rate, how many minutes will it take Xavier to make the waffles this morning?
\newline
_
_
_
\_\_\_
___
minutes
\newline
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Michael's mom loves Bright Scents candles. A
4
4
4
-inch candle will burn for
8
8
8
hours. Michael bought his mom a
10
10
10
-inch candle for Mother's Day.
\newline
If Bright Scents candles all burn at the same rate, how many hours will the
10
10
10
-inch candle burn?
\newline
____ hours
\newline
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Liz is taking guitar lessons and practices every night. Yesterday, she played a total of
40
40
40
chords in
8
8
8
minutes. Today, she will play chords for
5
5
5
minutes.
\newline
If she plays at the same rate, how many chords will Liz play today?
\newline
____ chords
\newline
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Mini Sweets bake shop is running a special on cupcakes. For every
10
10
10
cupcakes purchased,
3
3
3
free cupcakes are added to the order. Edna is getting treats for her class party. She bought
30
30
30
cupcakes.
\newline
How many free cupcakes will be added to Edna's order?
\newline
____ free cupcakes
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Bobby likes to hike the trails near his house. On Saturday, he spent
4
4
4
hours hiking
8
8
8
miles. On Sunday, he plans to hike
12
12
12
miles.
\newline
If he hikes at the same rate, how many hours will he spend hiking on Sunday?
\newline
____ hours
\newline
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Mr. Thompson drew a rectangle on the chalkboard with a length to width ratio of
5
5
5
to
2
2
2
. He asked students to draw a rectangle with the same ratio of length to width in their journals. Audrey plans to draw a rectangle with a width of
6
6
6
centimeters.
\newline
What length should Audrey's rectangle have?
\newline
____ centimeters
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For history class, Joe spent
2
2
2
hours writing a
4
4
4
-page report on ancient Egypt. This weekend, he needs to write a
12
12
12
-page report on the Roman Empire.
\newline
If he writes at the same rate, how long will it take Joe to write his report?
\newline
_
_
_
\_\_\_
___
hours
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On weekday mornings, it takes Leo
12
12
12
minutes to bike
2
2
2
miles to his school. This Saturday, Leo will bike to the park to meet his friends. The park is
5
5
5
miles away from Leo's house.
\newline
If he bikes at the same rate, how many minutes will it take Leo to get to the park?
\newline
____ minutes
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The best drink at the Smoothie Shack is the Berry Blaster. It takes
3
3
3
cups of strawberries to make
2
2
2
Berry Blasters. The Smoothie Shack only has
15
15
15
cups of strawberries left.
\newline
How many Berry Blasters can the Smoothie Shack make?
\newline
____ Berry Blasters
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At soccer practice, Hassan warms up by kicking balls at the goal. Yesterday, Hassan made
24
24
24
goals in
3
3
3
minutes. Today, he only spent
2
2
2
minutes kicking balls at the goal.
\newline
If Hassan made goals at the same rate, how many goals did he make today?
\newline
____ goals
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Adele and her best friend, Valentina, want to rent a canoe to explore the lake by their campsite. The Boat Bunker charges
27
27
27
$
\$
$
for
3
3
3
hours. Oar City charges
45
45
45
$
\$
$
for
9
9
9
hours. Which store has the better value?
\newline
Choices:
\newline
(A)Boat Bunker
\newline
(B)Oar City
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Initially, there are
4
×
1
0
3
4 \times 10^{3}
4
×
1
0
3
bacteria in a container. It is given that the number of bacteria will be doubled after every
20
20
20
minutes. If the container is left alone for
6
6
6
hours, find the number of bacteria in the container, (Express the answer in scientific notation correct to
3
3
3
significant figures.)
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Heather is a cashier. She can ring up
12
12
12
customers in
9
9
9
minutes.
\newline
At this rate, how many minutes does it take her to ring up
4
4
4
customers?
\newline
□
\square
□
minutes
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Deshawn and Tyriq can weed their garden in
30
30
30
minutes together. Alone, it takes Tyriq
75
75
75
minutes to weed the garden.
\newline
How long does it take Deshawn to weed the garden alone?
\newline
□
\square
□
minutes
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Jerry is a judge. He hears
5
5
5
cases every
2
(
3
)
8
\frac{2(3)}{8}
8
2
(
3
)
hours. Jerry hears cases at a constant rate.
\newline
How many cases does he hear per hour?
\newline
□
\square
□
cases per hour
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Maria looked through her Grandma's famous
10
10
10
-page recipe book. One page had free recipes, the next nine pages had six recipes each. How many recipes in all did Maria find in her Grandma's recipe book?
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Miss McDonald's Farm has two barns. One Barn houses five groups of
11
11
11
chickens, and the other barn houses
12
12
12
pigs. How many animals are there all together in the barns?
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To train for an upcoming race hannah ran
1
1
1
mile each day for
3
3
3
days. Then she ran
2
2
2
miles each day for
4
4
4
days. How many miles did she run altogether over
7
7
7
days
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Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold
50
50
50
cards, which was
5
%
5 \%
5%
of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
\newline
Answer:
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Nevaeh and Mason are adding chocolate chips to a batch of pre-made cookie dough to make chocolate chip cookies. Nevaeh mixes
4
4
4
cups of dough with
5
5
5
quarter-cups of chocolate chips and Mason mixes
4
4
4
cups of dough with
1
1
1
quarter-cup of chocolate chips. Whose cookies will be doughier?
\newline
Nevaeh's cookies will be doughier.
\newline
Mason's cookies will be doughier.
\newline
The two sets of cookies will be equally doughy.
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Shandra practices the piano
392
392
392
minutes in
2
2
2
weeks. Assuming she practices the same amount every week, how many minutes would she practice in
5
5
5
weeks?
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Mia hired a moving company. The company charged
$
500
\$ 500
$500
for its services, and Mis gives the movers a
16
%
16 \%
16%
tip.
\newline
How much does Mia tip the movers?
\newline
$
\$
$
_________
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According to a
2018
2018
2018
Gallup poll of adults around the world,
15
%
15\%
15%
of respondents said they would like to move permanently to another country if they had the opportunity. If the poll results are representative of the approximately
5
5
5
billion adults in the world, approximately how many adults world wide would like to move permanently to another country if they had the opportunity?
\newline
Choose
1
1
1
answer:
\newline
(A)
75
75
75
million
\newline
(B)
300
300
300
million
\newline
(C)
750
750
750
million
\newline
(D)
1.5
1.5
1.5
billion
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Naoya read a book cover to cover in a single session, at a rate of
55
55
55
pages per hour. After reading for
4
4
4
hours, he had
330
330
330
pages left to read.
\newline
How long is the book?
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Levi can shovel the driveway in
3
3
3
hours, but if his sister Mariah helps it would take
2
2
2
.
5
5
5
hours. How long would it take Mariah to shovel the driveway alone?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
hours
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Ai Mi practices the piano
1064
1064
1064
minutes in
4
4
4
weeks. Assuming she practices the same amount every week, how many minutes would she practice in
3
3
3
weeks?
\newline
Answer: minutes
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Jayden practices the piano
896
896
896
minutes in
4
4
4
weeks. Assuming he practices the same amount every week, how many minutes would he practice in
5
5
5
weeks?
\newline
Answer: minutes
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Emily practices the piano
595
595
595
minutes in
5
5
5
weeks. Assuming she practices the same amount every week, how many minutes would she practice in
4
4
4
weeks?
\newline
Answer: minutes
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Melanie practices the piano
1435
1435
1435
minutes in
5
5
5
weeks. Assuming she practices the same amount every week, how many minutes would she practice in
4
4
4
weeks?
\newline
Answer: minutes
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Mr. Hansraj wants to find the least number of boxes to be added to get a perfect square. He already has
7924
7924
7924
boxes with him. How many more boxes are required?
\newline
(
A
)
819
(A)819
(
A
)
819
\newline
(
B
)
412
(B)412
(
B
)
412
\newline
(
C
)
419
(C)419
(
C
)
419
\newline
(
D
)
176
(D)176
(
D
)
176
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