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Math Problems
Grade 6
Add, subtract, multiply, or divide two fractions
Maureen and Ashley own neighboring cornfields. Maureen harvested
4
4
4
acres of corn on Monday and Ashley harvested
5
8
\frac{5}{8}
8
5
of an acre. How many more acres did Maureen harvest than Ashley?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
_
\_\_\_\_
____
acres
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Divide.
\newline
2
4
9
2\frac{4}{9}
2
9
4
÷
\div
÷
1
7
9
1\frac{7}{9}
1
9
7
= _____
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Divide.
\newline
1
5
8
1\frac{5}{8}
1
8
5
÷
\div
÷
1
1
8
1\frac{1}{8}
1
8
1
= _____
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Divide.
\newline
3
3
4
3\frac{3}{4}
3
4
3
÷
\div
÷
2
1
2
2\frac{1}{2}
2
2
1
= _____
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Divide.
\newline
2
3
4
2\frac{3}{4}
2
4
3
÷
\div
÷
2
4
9
2\frac{4}{9}
2
9
4
= _____
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Divide.
\newline
1
1
2
1\frac{1}{2}
1
2
1
÷
\div
÷
1
1
4
1\frac{1}{4}
1
4
1
= _____
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Divide.
\newline
2
1
2
2\frac{1}{2}
2
2
1
÷
\div
÷
1
1
2
1\frac{1}{2}
1
2
1
= _____
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Divide.
\newline
2
1
3
2\frac{1}{3}
2
3
1
÷
\div
÷
3
1
9
3\frac{1}{9}
3
9
1
= _____
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Divide.
\newline
3
3
4
3\frac{3}{4}
3
4
3
÷
\div
÷
1
3
4
1\frac{3}{4}
1
4
3
= _____
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Divide.
\newline
1
2
3
÷
1
2
3
=
1\frac{2}{3} \div 1\frac{2}{3} =
1
3
2
÷
1
3
2
=
_____
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Solve for
a
a
a
:
2
a
+
3
5
\frac{2a +3}{5}
5
2
a
+
3
=
3
3
3
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In making macaroni and cheese, Porter used
1
2
\frac{1}{2}
2
1
of a cup of cheddar and
3
5
\frac{3}{5}
5
3
of a cup of parmesan. How much cheese did Porter use in all?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
\_\_\_
___
cups
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Laura, a pet store employee, wants to fit two fish tanks on one table. One fish tank is
2
1
8
2\frac{1}{8}
2
8
1
feet wide and the other fish tank is
1
1
1
foot wide. When placed next to each other, what is the total width of the two fish tanks?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
\_\_\_
___
feet
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Vince owns two dogs. Each day, one dog eats
1
7
10
1\frac{7}{10}
1
10
7
scoops of dog food and the other dog eats
1
1
2
1\frac{1}{2}
1
2
1
scoops. Together, how much dog food do the two dogs eat each day?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_
_
_
_
\_\_\_\_
____
scoops
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Last week, a chocolate shop sold
4
1
6
4\frac{1}{6}
4
6
1
ounces of white chocolate. It sold
4
1
2
4\frac{1}{2}
4
2
1
times as much milk chocolate as white chocolate. How many ounces of milk chocolate did the shop sell?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ ounces
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A biologist studied how cells grow by adding liquid protein to cell samples. She reported in her study that she divided
8
1
3
8\frac{1}{3}
8
3
1
ounces of liquid protein evenly among
3
3
3
cell samples. How much liquid protein did she give to each cell sample?
\newline
Write your answer as a fraction or as a whole or mixed number.
\newline
_____ ounces
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Divide.
\newline
1
2
\frac{1}{2}
2
1
÷
\div
÷
2
3
\frac{2}{3}
3
2
=
_
_
_
_
_
\_\_\_\_\_
_____
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Divide.
\newline
−
1
4
÷
−
1
3
=
-\frac{1}{4} \div -\frac{1}{3} =
−
4
1
÷
−
3
1
=
_____
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Divide.
\newline
1
8
\frac{1}{8}
8
1
÷
\div
÷
1
10
\frac{1}{10}
10
1
= _____
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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.
\newline
□
\square
□
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Sarah received
$
55
\$55
$55
for her birthday. 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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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
□
\square
□
balls
\text{balls}
balls
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The garden club earned
$
15
\$15
$15
per hour by weeding neighborhood gardens for
t
t
t
hours. A generous donor has agreed to double their earnings.
\newline
How much did the garden club earn in all?
\newline
Write your answer as an expression.
\newline
$
\$
$
◻
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7
7
7
divided
3
4
\frac{3}{4}
4
3
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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
$
\$
$
□
\square
□
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2
2
2
A group of
66
66
66
third graders and
14
14
14
adults are going on a field trip to the zoo in small buses. Each bus holds
10
10
10
people.
\newline
How many buses will be needed for the trip to the zoo?
\newline
A
10
10
10
\newline
B
8
8
8
\newline
C
70
70
70
\newline
D
9
9
9
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6
1
2
6 \frac{1}{2}
6
2
1
years is how many weeks?
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The garden club earned
15
$
$
15\$\$
15$$
\) per hour by weeding neighborhood gardens for
t
t
t
hours. A generous donor has agreed to double their earnings. How much did the garden club earn in all? Write your answer as an expression.
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1
7
9
DIVIDE BY
4
5
1 \frac{7}{9} \text{ DIVIDE BY } \frac{4}{5}
1
9
7
DIVIDE BY
5
4
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3
(
x
+
5
)
=
18
3(x+5)=18
3
(
x
+
5
)
=
18
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Evaluate.
8
÷
2
(
2
+
2
)
8 \div 2(2+2)
8
÷
2
(
2
+
2
)
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1
×
8
+
8
x
=
9
1 \times 8 + 8x = 9
1
×
8
+
8
x
=
9
Find
x
x
x
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Find
x
x
x
.
10
+
x
=
4
10+x=4
10
+
x
=
4
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To get ready for school, Traci spent
1
20
\frac{1}{20}
20
1
of an hour getting dressed and
1
10
\frac{1}{10}
10
1
of an hour doing her hair. What is the total amount of time she spent getting ready?
\newline
Give your answer in simplest form.
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10
+
10
=
10+10=
10
+
10
=
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Evaluate
x
x
x
.
3
(
x
+
1
)
2
=
108
3(x+1)^2=108
3
(
x
+
1
)
2
=
108
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Solve for
x
x
x
:
\newline
2
x
+
9
=
11
2x + 9 = 11
2
x
+
9
=
11
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Divide:
\newline
6
4
÷
9
15
=
\frac{6}{4}\div\frac{9}{15}=
4
6
÷
15
9
=
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Solve for x:
(
3
x
+
9
)
÷
2
=
(
1
x
+
4
)
÷
8
(3x+9) \div 2 = (1x+4) \div 8
(
3
x
+
9
)
÷
2
=
(
1
x
+
4
)
÷
8
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4
4
4
friends evenly divided up an
n
n
n
-slice pizza. One of the friends, Harris, ate
1
1
1
fewer slice than he received. How many slices of pizza did Harris eat? Write your answer as an expression.
\newline
slices of pizza
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Suppose a charity received a donation of
$
14.7
\$14.7
$14.7
million. If this represents
39
%
39\%
39%
of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
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Sicilia randomly selected
25
%
25\%
25%
of the Sound Sleep email subscribers and asked them how many hours of sleep they average each night. Of the subscribers surveyed,
16
16
16
average less than
6
6
6
hours of sleep each night. Based on the data, what is the most reasonable estimate of the number of Sound Sleep email subscribers who average less than
6
6
6
hours of sleep?
\newline
Choose
1
1
1
answer:
\newline
(A)
16
16
16
\newline
(B)
48
48
48
\newline
(C)
64
64
64
\newline
(D)
400
400
400
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1
+
3
x
−
4
=
2
1+ 3x - 4 = 2
1
+
3
x
−
4
=
2
Find
x
x
x
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2
y
+
5
=
7
2 y+5=7
2
y
+
5
=
7
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Solve the equation.
−
5
+
x
=
11
-5+x=11
−
5
+
x
=
11
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Solve for
x
x
x
.
2
x
+
3
=
2
2x+3 =2
2
x
+
3
=
2
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5
x
+
2
=
4
5x+2=4
5
x
+
2
=
4
. Find `x`
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Find `x`.
x
+
5
=
3
x + 5 = 3
x
+
5
=
3
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In a bag full of small balls,
1
4
\frac{1}{4}
4
1
of these balls are green,
1
8
\frac{1}{8}
8
1
are blue,
1
12
\frac{1}{12}
12
1
are yellow and the remaining
26
26
26
white. How many balls are blue?
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As a fraction in simplest terms, what would you multiply the first number by to get the second?
\newline
First number:
25
25
25
Second number:
24
24
24
\newline
25
⋅
□
=
24
25 \cdot \square=24
25
⋅
□
=
24
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