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Math Problems
Grade 6
Add, subtract, multiply, or divide two fractions
'
8
2
÷
[
(
11
−
3
)
⋅
2
]
8^2 \div [(11 - 3) \cdot 2]
8
2
÷
[(
11
−
3
)
⋅
2
]
'
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Mr. and Mrs. Ryan are working together to wash all the windows in their house. The following equation can be used to find
h
h
h
, the number of hours it will take them to finish the job.
\newline
h
6
+
h
3
=
1
\frac{h}{6} + \frac{h}{3} = 1
6
h
+
3
h
=
1
\newline
How long will it take Mr. and Mrs. Ryan to wash all the windows?
\newline
Write your answer as a whole number or as a fraction or mixed number in lowest terms.
\newline
____ hours
\newline
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Hayley invited a friend over for dinner. She wants to make personal pies to serve for dessert. Hayley makes
1
1
5
1\frac{1}{5}
1
5
1
cups of dough to use for the crust and splits the dough evenly between
2
2
2
pies. How much dough does Hayley use for each pie? Use the model to help answer the question. Write your answer as a whole number, proper fraction, or mixed number.
\newline
____ cups
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Lisa is growing her own plants from seeds. She opens a
4
4
4
-kilogram bag of soil and begins to fill her pots. Each pot holds
1
1
3
1 \frac{1}{3}
1
3
1
kilograms of soil. How many pots does Lisa fill? Use the model to help answer the question. Write your answer as a whole number, proper fraction, or mixed number.
\newline
____ pots
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Divide.
\newline
1
3
÷
2
3
=
\frac{1}{3} \div \frac{2}{3} =
3
1
÷
3
2
=
____
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Divide.
\newline
1
3
÷
3
4
=
\frac{1}{3} \div \frac{3}{4} =
3
1
÷
4
3
=
____
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Divide.
\newline
1
2
÷
3
4
=
\frac{1}{2} \div \frac{3}{4} =
2
1
÷
4
3
=
____
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8
÷
1
4
5
8\div 1 \frac{4}{5}
8
÷
1
5
4
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Divide.
\newline
1
1
4
1\frac{1}{4}
1
4
1
÷
\div
÷
1
1
4
1\frac{1}{4}
1
4
1
= _____
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\newline
7
9
\frac{7}{9}
9
7
÷
\div
÷
1
5
9
1\frac{5}{9}
1
9
5
= _____
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Divide.
\newline
3
4
\frac{3}{4}
4
3
÷
\div
÷
1
3
4
1\frac{3}{4}
1
4
3
=
_
_
_
_
_
\_\_\_\_\_
_____
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Divide.
\newline
2
3
\frac{2}{3}
3
2
÷
\div
÷
1
1
3
1\frac{1}{3}
1
3
1
= _____
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Divide.
\newline
4
9
\frac{4}{9}
9
4
÷
\div
÷
1
1
9
1\frac{1}{9}
1
9
1
=
_
_
_
_
_
\_\_\_\_\_
_____
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Divide.
\newline
2
÷
1
7
9
=
2 \div 1\frac{7}{9} =
2
÷
1
9
7
=
_____
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\newline
1
2
\frac{1}{2}
2
1
÷
\div
÷
1
1
4
1\frac{1}{4}
1
4
1
=
_
_
_
_
_
\_\_\_\_\_
_____
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Reagan filled a bucket with
2
3
\frac{2}{3}
3
2
of a gallon of water. Later, she poured out
1
2
\frac{1}{2}
2
1
of a gallon of the water. How much water is left in the bucket?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ gallons
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The cattle at the Clark Farm are fed
7
3
10
7\frac{3}{10}
7
10
3
bales of hay each day. The horses are fed
3
4
\frac{3}{4}
4
3
as much hay as the cattle. How many bales of hay are the horses fed each day?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ bales of hay
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As part of a lesson on earthquakes, a science class is researching the movement of a nearby fault line. The fault line moved
5
12
\frac{5}{12}
12
5
of an inch during the past year and
1
4
\frac{1}{4}
4
1
of an inch the year before. How far did the fault line move in all?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ inches
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At the Lawrence Ski Resort, it snowed
4
11
12
4\frac{11}{12}
4
12
11
feet yesterday and
1
1
1
foot today. How much more did it snow yesterday than today?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ feet
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At Keith's Boutique,
5
12
\frac{5}{12}
12
5
of the pants are denim. Another
1
6
\frac{1}{6}
6
1
are khaki. What fraction of the pants are either denim or khaki?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
_
\_\_\_\_
____
of the pants
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While making pastries, a bakery used
3
4
\frac{3}{4}
4
3
of a bag of wheat flour and
5
8
\frac{5}{8}
8
5
of a bag of white flour. How many bags of flour did the bakery use in all?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
\_\_\_
___
bags
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While taking inventory at her pastry shop, Paula realizes that she had
8
8
8
boxes of baking powder yesterday, but the supply is now down to
1
2
6
1\frac{2}{6}
1
6
2
boxes. How much more baking powder did Paula have yesterday?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
\_\_\_
___
boxes
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Carter and his roommates ate
1
2
4
1\frac{2}{4}
1
4
2
pints of ice cream on Friday night and
2
1
3
2\frac{1}{3}
2
3
1
pints of ice cream on Saturday night. How many pints did they eat in all?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
\_\_\_
___
pints
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Divide.
\newline
4
1
2
÷
5
=
4\frac{1}{2} \div 5 =
4
2
1
÷
5
=
_____
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Divide.
\newline
2
÷
1
1
2
=
2 \div 1\frac{1}{2} =
2
÷
1
2
1
=
_____
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Divide.
\newline
1
5
6
1\frac{5}{6}
1
6
5
÷
\div
÷
1
1
6
1\frac{1}{6}
1
6
1
= _____
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Divide.
\newline
3
1
7
3\frac{1}{7}
3
7
1
÷
\div
÷
1
5
7
1\frac{5}{7}
1
7
5
= _____
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Divide.
\newline
2
÷
3
1
2
=
2 \div 3\frac{1}{2} =
2
÷
3
2
1
=
_____
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Multiply. Write your answer as a fraction or as a whole or mixed number.
\newline
10
×
4
5
=
10 \times \frac{4}{5} =
10
×
5
4
=
_____
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Subtract. Write your answer as a fraction or as a whole or mixed number.
\newline
12
2
5
−
7
1
5
=
12\frac{2}{5} - 7\frac{1}{5} =
12
5
2
−
7
5
1
=
_____
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Subtract. Write your answer as a fraction or as a whole or mixed number.
\newline
14
1
3
−
11
2
3
=
14\frac{1}{3} - 11\frac{2}{3} =
14
3
1
−
11
3
2
=
_____
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Jaden found an orange caterpillar and a green caterpillar in his backyard. The green caterpillar was
11
12
\frac{11}{12}
12
11
of an inch long and the orange caterpillar was
2
3
\frac{2}{3}
3
2
of an inch long. How much longer was the green caterpillar than the orange caterpillar?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
\_\_\_
___
inches
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In the morning, Isaiah drove to the store and used
2
3
\frac{2}{3}
3
2
of a gallon of gas. In the afternoon, he drove to the movie theater and used
5
12
\frac{5}{12}
12
5
of a gallon of gas. How much gas did Isaiah use in all?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ gallons
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Amelia and her sister went together to get haircuts. Amelia got
7
12
\frac{7}{12}
12
7
of an inch cut off and her sister got
1
4
\frac{1}{4}
4
1
of an inch cut off. Compared to her sister, how much more hair did Amelia get taken off?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
\_\_\_
___
inches
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While making desserts for a bake sale, Irma used
7
8
\frac{7}{8}
8
7
of a scoop of brown sugar as well as
3
4
\frac{3}{4}
4
3
of a scoop of white sugar. How much more brown sugar did Irma use?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
\_\_\_
___
scoops
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A spaceship traveled
1
12
\frac{1}{12}
12
1
of a light-year and stopped at a space station. Then it traveled
3
4
\frac{3}{4}
4
3
of a light-year further to a planet. How far did the spaceship travel in all?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ light-years
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Sidney is trying to fit two boxes into the trunk of her car. One box is
1
6
\frac{1}{6}
6
1
of a foot tall and the other is
7
12
\frac{7}{12}
12
7
of a foot tall. Stacked on top of each other, what is the combined height of the two boxes?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ feet
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Of the flags in David's Flag Shop,
7
12
\frac{7}{12}
12
7
are red and another
1
4
\frac{1}{4}
4
1
are white. What fraction of the flags are either red or white?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
_
\_\_\_\_
____
of the flags
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Gabrielle watched a beetle and a spider on the sidewalk. The beetle crawled
7
12
\frac{7}{12}
12
7
of a yard and the spider crawled
1
3
\frac{1}{3}
3
1
of a yard. How much farther did the beetle crawl than the spider?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
_
\_\_\_\_
____
yards
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At a pie-eating contest, Rita got through
11
12
\frac{11}{12}
12
11
of a pie before time was called; Aisha finished just
2
3
\frac{2}{3}
3
2
of a pie. How much more pie did Rita eat than Aisha?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ of a pie
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Scarlett has the deluxe version of the card game Mysterious Monsters of the Deep with
3
3
3
D images printed on the playing cards. She randomly selects one card from the deck, puts it back in the deck, and picks another card. She repeats this several times and gets
2
2
2
anglerfish,
3
3
3
vampire squids,
1
1
1
viperfish,
4
4
4
megamouth sharks, and
5
5
5
ghost fish.
\newline
Based on the data, what is the probability that the next card Scarlett selects will have an anglerfish on it?
\newline
Write your answer as a fraction or whole number.
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A water bottle holds
3
10
\frac{3}{10}
10
3
of a gallon of water. There are
14
5
\frac{14}{5}
5
14
gallons of water in a water tank. How many water bottles can be filled with the water in the tank?
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Subtract. Write your answer as a fraction or as a whole or mixed number.
\newline
14
2
3
−
10
1
3
=
14\frac{2}{3} - 10\frac{1}{3} =
14
3
2
−
10
3
1
=
_____
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Add. Write your answer as a fraction or as a whole or mixed number.
\newline
2
3
8
+
3
1
8
=
2\frac{3}{8} + 3\frac{1}{8} =
2
8
3
+
3
8
1
=
_____
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Divide.
\newline
1
4
÷
2
=
_
_
_
_
\frac{1}{4} \div 2 = \_\_\_\_
4
1
÷
2
=
____
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A cookie factory uses
1
8
\frac{1}{8}
8
1
of a barrel of oatmeal in each batch of cookies. The factory used
5
8
\frac{5}{8}
8
5
of a barrel of oatmeal yesterday. How many batches of cookies did the factory make?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ batches
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A pizza restaurant had
1
2
\frac{1}{2}
2
1
of a gallon of pizza sauce left at the end of the evening and divided it equally between
2
2
2
pizzas. How much sauce did they put on each pizza?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ gallons
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Danielle bought
3
5
6
3\frac{5}{6}
3
6
5
pounds of green grapes and
1
1
2
1\frac{1}{2}
1
2
1
pounds of red grapes. How much more did the green grapes weigh than the red grapes?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
_
\_\_\_\_
____
pounds
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Roxanne added
2
5
\frac{2}{5}
5
2
of a cup of yellow raisins and
7
7
10
7\frac{7}{10}
7
10
7
cups of black raisins to a batch of trail mix. How many cups of raisins did Roxanne add in all?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ cups
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A meteorologist recorded the rainfall in Westminster in two consecutive months. In the first month, there was
1
1
1
inch of rain. In the second month, there was
2
2
3
2\frac{2}{3}
2
3
2
inches of rain. What was the total amount of rainfall during the two months?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
\_\_\_
___
inches
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1
2
3
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