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Math Problems
Grade 6
GCF and LCM: word problems
Will is decorating papers with a total of
45
45
45
heart stickers and
27
27
27
star stickers for the child he is babysitting. If he wants to make all the papers identical, with the same combination of heart and star stickers and no stickers left over, what is the greatest number of pages Will can decorate?
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Walter has two pieces of cable, one
16
16
16
feet long and the other
12
12
12
feet long. For a science project, he wants to cut them up to produce many pieces of cable that are all of the same length, with no cable left over. What is the greatest length, in feet, that he can make them?
\newline
_____ feet
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One day, Aiden and his friends had lunch while sitting at tables of
10
10
10
. Another day, they had lunch at tables of
5
5
5
. What is the smallest number of people that could be in the group?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
people
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Ashley has
18
18
18
commemorative plates and
12
12
12
commemorative spoons. She wants to display them in groups throughout her house, each with the same combination of plates and spoons, with none left over. What is the greatest number of groups Ashley can display?
\newline
_
_
_
_
_
_
_
_
_
\_\_\_\_\_\_\_\_\_
_________
groups
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At a dinner party with an equal number of adults and children, adults are seated at tables of exactly
8
8
8
and children are seated at tables of exactly
4
4
4
. What is the minimum number of children attending?
\newline
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
_______________
children
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Zane notices an identical number of two types of insects in his neighborhood: butterflies and fireflies. He always seems to observe butterflies in groups of
5
5
5
and fireflies in groups of
10
10
10
. What is the smallest number of butterflies that he could have seen?
\newline
_
_
_
_
_
_
_
_
_
\_\_\_\_\_\_\_\_\_
_________
butterflies
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At a local bakery, Edgar decorated
6
6
6
cakes at a time. Javier decorated
8
8
8
at a time. If they ended up decorating the same number of cakes by the end of the day, what is the smallest number of cakes that each must have decorated?
\newline
\newline
_____cakes
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For a Cinco de Mayo party, Myra is placing sets of chips and salsa throughout the house. She has
8
8
8
bags of chips and
20
20
20
jars of salsa, which she wants to distribute evenly with no bags of chips or jars of salsa left over. What is the greatest number of places Myra can put the chips and salsa?
\newline
_
_
_
\_\_\_
___
places
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Connor is making trail mix out of
6
6
6
bags of nuts and
9
9
9
bags of dried fruit. He wants each new portion of trail mix to be identical, containing the same combination of bags of nuts and bags of dried fruit, with no bags left over. What is the greatest number of portions of trail mix Connor can make?
\newline
_____ portions
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Kiera has two pieces of thread, one
15
15
15
feet long and the other
20
20
20
feet long. For a sewing project, she needs to cut them up to produce many pieces of thread that are all of the same length, with no thread left over. What is the greatest length, in feet, that she can make them?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
feet
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Cora is creating potpourri bowls using
18
18
18
bags of shredded bark and
12
12
12
bags of flower petals. If she wants to make all the potpourri bowls identical, containing the same number of bags of shredded bark and the same number of bags of flower petals, what is the greatest number of potpourri bowls Cora can create?
\newline
_
_
_
_
\_\_\_\_
____
bowls
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Mrs. Larson, the math teacher, has
12
12
12
logic puzzles and
18
18
18
visual puzzles that she wants to group into sets for students who finish their tests early. Mrs. Larson wants each set to be identical, containing the same combination of logic puzzles and visual puzzles, with no puzzles left over. What is the greatest number of sets she can create?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
sets
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Camilla is creating lollipop bouquets using
20
20
20
cherry lollipops and
15
15
15
orange lollipops. She wants each bouquet to be identical, with no lollipops left over. What is the greatest number of lollipop bouquets Camilla can create?
\newline
_____ bouquets
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Lena is putting together bags of groceries to donate to charity. She has
16
16
16
boxes of macaroni and cheese and
8
8
8
cans of vegetables. Lena wants to divide them up evenly, so that each bag has the same contents and no items are left over. What is the greatest number of bags of groceries Lena can put together?
\newline
_____bags
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Julian owns a business and assigns two of his employees their shifts. He assigns the first employee shifts in blocks of
3
3
3
hours, and he assigns the second worker shifts in blocks of
12
12
12
hours. If both workers must receive the same number of hours, what is the minimum number of hours each must be assigned?
\newline
_
_
_
_
_
_
_
\_\_\_\_\_\_\_
_______
hours
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Pike Vitamin Shop sold equal quantities of Vitamin A and Vitamin D supplements this morning, even though the Vitamin A supplements come in packs of
4
4
4
and the Vitamin D supplements in packs of
7
7
7
. What is the smallest number of each type that the store could have sold?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
supplements
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Candice wants to create snack bags for a trip she is going on. She has
12
12
12
granola bars and
9
9
9
pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Candice can make?
\newline
_
_
_
\_\_\_
___
bags
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Victoria has two pieces of thread, one
12
12
12
feet long and the other
8
8
8
feet long. For a sewing project, she needs to cut them up to produce many pieces of thread that are all of the same length, with no thread left over. What is the greatest length, in feet, that she can make them?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
feet
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Ian has
12
12
12
math books and
18
18
18
science books. If he wants to distribute them evenly among some bookshelves so that each bookshelf has the same combination of math and science books, with no books left over, what is the greatest number of bookshelves Ian can use?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
bookshelves
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Harold has just moved to a new town and wants to share plates of baked goods with his neighbors. He has
20
20
20
cookies and
10
10
10
brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates he can make to share?
\newline
_
_
_
_
_
_
_
\_\_\_\_\_\_\_
_______
plates
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Troy is a dental sales representative who wants to distribute
18
18
18
brochures and
12
12
12
pamphlets to local dental offices. He wants to deliver the same combination of brochures and pamphlets to each office, without having any materials left over. What is the greatest number of dental offices Troy can distribute materials to?
\newline
_____ offices
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Britney enjoys bird-watching and observed two types of birds traveling this season: ducks and seagulls. While the ducks traveled in flocks of
10
10
10
, the seagulls traveled in flocks of
12
12
12
. If Britney observed the same total number of ducks and seagulls, what is the smallest number of ducks that she could have observed?
\newline
_____ ducks
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Kenji and Ed are each assigned a paper for a class they share. Kenji decides to write
7
7
7
pages at a time while Ed decides to write
3
3
3
pages at a time. If they end up writing the same number of pages, what is the smallest number of pages that the papers could have had?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
pages
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Mrs. Strickland, the math teacher, has
18
18
18
logic puzzles and
9
9
9
visual puzzles that she wants to group into sets for students who finish their tests early. Mrs. Strickland wants each set to be identical, containing the same combination of logic puzzles and visual puzzles, with no puzzles left over. What is the greatest number of sets she can create?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
sets
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A
300
300
300
-acre farm produced
20
,
000
20,000
20
,
000
bushels of corn last year. What is the minimum rate of production, in bushels per acre, that is needed this year so the farm's two-year production total will be at least
49
,
100
49,100
49
,
100
bushels of corn?
\newline
◻
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Increases in elevation are recorded with positive numbers. Decreases in elevation are recorded with negative numbers.
\newline
A group of hikers is hiking down a mountain. After
4
4
4
hours they descended
600
600
600
meters. They descended the mountain at the same rate each hour.
\newline
What was the hiking group's change in elevation each hour?
\newline
____meters
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A town uses positive numbers to track increases in population and negative numbers to track decreases in population.
\newline
The population has decreased by
300
300
300
residents over the past
5
5
5
years. The same number of residents left each year.
\newline
What was the change in the town's population each year?
\newline
residents
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Amy records deposits as positive numbers and withdrawals as negative numbers in her bank book.
\newline
Amy loaned an equal amount of money to each of
5
5
5
people. She loaned a total of
$
100
\$ 100
$100
. She recorded each loan by writing each amount in her bank book.
\newline
What is the amount Amy recorded in her bank book for each loan?
\newline
$
\$
$
____
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An elementary school in Birmingham has
8
8
8
classes participating in field day. Each class has
24
24
24
students. The students are placed on teams of
6
6
6
to compete in each activity.
\newline
What is the minimum number of teams needed for every student to participate?
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Moussa and Nicole are adding chocolate chips to a batch of pre-made cookie dough to make chocolate chip cookies. Moussa mixes
4
4
4
cups of dough with
1
1
1
quarter-cup of chocolate chips and Nicole mixes
6
6
6
cups of dough with
1
1
1
quarter-cup of chocolate chips. Whose cookies will be more chocolaty?
\newline
Moussa's cookies will be more chocolaty.
\newline
Nicole's cookies will be more chocolaty.
\newline
The two sets of cookies will be equally chocolaty.
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Wyatt wants to buy a car. The maximum loan he can get from the bank is
$
16
,
465
\$ 16,465
$16
,
465
. If Wyatt has
$
2
,
035
\$ 2,035
$2
,
035
available to make a down payment, what is the highest valued car he can purchase?
\newline
Answer:
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Fawzia and her children went into a restaurant where they sell hamburgers for
$
6.50
\$ 6.50
$6.50
each and tacos for
$
4
\$ 4
$4
each. Fawzia has
$
80
\$ 80
$80
to spend and must buy a minimum of
15
15
15
hamburgers and tacos altogether. If Fawzia decided to buy
10
10
10
tacos, determine the maximum number of hamburgers that she could buy.
\newline
Answer:
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Lauren has some nickels and some dimes. She has no more than
21
21
21
coins worth no less than
$
1.35
\$ 1.35
$1.35
combined. If Lauren has
10
10
10
dimes, determine the minimum number of nickels that she could have.
\newline
Answer:
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Sadie and her children went into a grocery store where they sell peaches for
$
1.25
\$ 1.25
$1.25
each and mangos for
$
0.50
\$ 0.50
$0.50
each. Sadie has
$
9.50
\$ 9.50
$9.50
to spend and must buy no less than
13
13
13
peaches and mangos altogether. If Sadie decided to buy
4
4
4
mangos, determine all possible values for the number of peaches that she could buy.
\newline
Answer:
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A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. If the river forms one side of the corrals and
150
y
d
150 \mathrm{yd}
150
yd
of fencing is available, find the largest total area that can be enclosed.
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Francine uses
2
3
\frac{2}{3}
3
2
cup of pineapple juice for every
1
3
\frac{1}{3}
3
1
cup of orange juice to make a smoothie.
\newline
Enter the number of cups of pineapple juice Francine uses for
1
1
1
cup of orange juice.
\newline
□
\square
□
cups of pineapple juice
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Ben drinks tea at an incredible rate. He drinks
3
1
2
3 \frac{1}{2}
3
2
1
liters of tea every
2
3
\frac{2}{3}
3
2
of an hour. Ben drinks tea at a constant rate.
\newline
How many liters of tea does he drink in one hour?
\newline
liters
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Jerry is a judge. He hears
5
5
5
cases every
2
3
8
2 \frac{3}{8}
2
8
3
hours. Jerry hears cases at a constant rate.
\newline
How many cases does he hear per hour?
\newline
cases per hour
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Uncle Drew scored
28
28
28
points in
5
5
6
5 \frac{5}{6}
5
6
5
minutes during a game of basketball.
\newline
How many points did he average per minute during that
5
5
6
5 \frac{5}{6}
5
6
5
minutes?
\newline
points per minute
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Brian irons
2
9
\frac{2}{9}
9
2
of his shirt in
3
3
5
3 \frac{3}{5}
3
5
3
minutes. Brian irons at a constant rate.
\newline
At this rate, how much of his shirt does he iron each minute?
\newline
of his shirt
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In basketball, the number of points you score is given by
3
x
+
2
y
+
1
z
3 x+2 y+1 z
3
x
+
2
y
+
1
z
where
x
x
x
is threepointers,
y
y
y
is two-pointers, and
z
z
z
is free throws (one-pointers).
\newline
What is the total number of points scored by a player who makes
3
3
3
three-pointers,
5
5
5
two-pointers, and
6
6
6
free throws?
\newline
points
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Lupe's dogs love to hide bones. Bubba hid
5
5
5
bones, Barry hid
4
4
4
bones, Larry hid
13
13
13
bones, and Goby hid
10
10
10
bones.
\newline
Find the median number of bones. bones
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Bubba Bulldog and all of his dog friends love to hide bones! Bubba hid
4
4
4
bones, Barry hid
5
5
5
bones, Larry hid
10
10
10
bones, and Goby hid
13
13
13
bones.
\newline
Find the mean number of dog bones.
\newline
dog bones
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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
minutes
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Teresa is maintaining a camp fire. She can keep the fire burning for
4
4
4
hours with
6
6
6
logs. She wants to know how many logs
(
y
)
(y)
(
y
)
she needs to keep the fire burning for
18
18
18
hours. She assumes all logs are the same.
\newline
How many logs does Teresa need to maintain the fire for
18
18
18
hours?
\newline
logs
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Some friends are planning to make a neighborhood garden. The total area available for the garden is
210
\mathbf{2 1 0}
210
square meters, and they want this to be
1
1
3
1 \frac{1}{3}
1
3
1
times the area of the plant beds in the garden.
\newline
What should the area of the plant beds be?
\newline
square meters
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Tomas was able to fill
6
2
3
6 \frac{2}{3}
6
3
2
equalsized buckets with a total of
33
1
3
33 \frac{1}{3}
33
3
1
liters of paint.
\newline
How much paint was in each whole bucket?
\newline
liters
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Ben likes to go in the covered dome when he feels overexcited. The dome covers an area of
1
2
3
1 \frac{2}{3}
1
3
2
square meters, which is
5
840
\frac{5}{840}
840
5
of the total area of the playground.
\newline
What is the total area of the playground?
\newline
square meters
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Paolo helped in the community garden for
2
3
4
2 \frac{3}{4}
2
4
3
hours this week. That was
1
5
6
1 \frac{5}{6}
1
6
5
equal-length shifts, because Paolo stopped early one day when it started to rain.
\newline
How long is a single shift?
\newline
hours
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Carlos has
4
5
\frac{4}{5}
5
4
of a tank of fuel in his car. He uses
1
10
\frac{1}{10}
10
1
of a tank per day.
\newline
How many days will his fuel last?
\newline
days
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