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Math Problems
Grade 6
Add, subtract, multiply, or divide two fractions
An unknown metal has been found and the following experimental results have been tabulated in below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that express volume as a function of the mass.
\newline
Round your answers to
3
3
3
decimal places
\newline
\begin{tabular}{|r|r|}
\newline
\hline grams & Volume in
m
t
\mathrm{mt}
mt
\\
\newline
\hline
18
18
18
&
141
141
141
.
3
3
3
\\
\newline
\hline
19
19
19
.
5
5
5
&
153
153
153
.
1
1
1
\\
\newline
\hline
21
21
21
&
168
168
168
.
1
1
1
\\
\newline
\hline
22
22
22
.
5
5
5
&
178
178
178
.
4
4
4
\\
\newline
\hline
24
24
24
&
184
184
184
.
6
6
6
\\
\newline
\hline
25
25
25
.
5
5
5
&
202
202
202
.
2
2
2
\\
\newline
\hline
27
27
27
&
214
214
214
.
1
1
1
\\
\newline
\hline
\newline
\end{tabular}
\newline
Volume
=
=
=
□
\square
□
x
+
x+
x
+
□
\square
□
where
x
x
x
is the grams of the unknown metal
\newline
Question Help:
\newline
Message instructor
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2
a
5
+
3
=
3
2a_{5}+3=3
2
a
5
+
3
=
3
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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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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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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
4
÷
−
1
3
=
-\frac{1}{4} \div -\frac{1}{3} =
−
4
1
÷
−
3
1
=
_____
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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
8
\frac{1}{8}
8
1
÷
\div
÷
1
10
\frac{1}{10}
10
1
= _____
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3
3
3
)
8
÷
7
4
)
≤
4
8 \div 7_{4)} \leq 4
8
÷
7
4
)
≤
4
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X
6
=
4
\frac{X}{6} = 4
6
X
=
4
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3
1
3
×
2
5
3 \frac{1}{3} \times \frac{2}{5}
3
3
1
×
5
2
equal
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How many pounds of candy that sells for
$
3.25
\$ 3.25
$3.25
per lb must be mixed with candy that sells for
$
2.75
\$ 2.75
$2.75
per lb to obtain
20
l
b
20 \mathrm{lb}
20
lb
of a mixture that should sell for
$
3.15
\$ 3.15
$3.15
per
l
b
\mathrm{lb}
lb
?
\newline
□
\square
□
Ib of
$
3.25
\$ 3.25
$3.25
-per-lb candy must be mixed with
□
\square
□
Ib of
$
2.75
\$ 2.75
$2.75
-per-lb candy. (Type integers or decimals.)
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How many pounds of candy that sells for
$
1.75
\$ 1.75
$1.75
per lb must be mixed with candy that sells for
$
1.25
\$ 1.25
$1.25
per
l
b
\mathrm{lb}
lb
to obtain
20
l
b
20 \mathrm{lb}
20
lb
of a mixture that should sell for
$
1.50
\$ 1.50
$1.50
per
l
b
\mathrm{lb}
lb
?
\newline
□
\square
□
lb of
$
1.75
\$ 1.75
$1.75
-per-lb candy must be mixed with
□
\square
□
lb of
$
1.25
\$ 1.25
$1.25
-per-lb candy.
\newline
(Type integers or decimals.)
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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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3
3
3
Write each number as a power of
5
5
5
.
\newline
a
0
0
0
.
2
2
2
\newline
b
25
25
25
\newline
c
0.04
\quad 0.04
0.04
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lines of symmetry?
\newline
4
4
4
\newline
0
0
0
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4
4
4
) Using the table above, what percentage of patients did not exercise
\newline
1
1
1
\newline
given that they did not catch a cold? Do not round your answer.
\newline
0.24
0.24
0.24
\newline
Use the table below to answer questions
5
5
5
-
7
7
7
.
\newline
5
5
5
) What percentage *
1
1
1
of those surveyed listen to pop music? Round to the nearest percent.
\newline
\begin{tabular}{|c|c|c|c|}
\newline
\hline & Vote Red & Vote Blue & Total \\
\newline
\hline Listen to Pop &
30
30
30
&
100
100
100
&
130
130
130
\\
\newline
\hline \begin{tabular}{c}
\newline
Listen to \\
\newline
Country
\newline
\end{tabular} &
90
90
90
&
5
5
5
&
95
95
95
\\
\newline
\hline Total &
120
120
120
&
105
105
105
&
?
?
?
\\
\newline
\hline
\newline
\end{tabular}
\newline
Your answer
\newline
6
6
6
) Using the table above, what percentage of students voted blue?
\newline
Round to the nearest whole percent.
\newline
Your answer
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B.E.S.T. EOC Geometry > Segments formed by intersecting chords wsiz
\newline
Find the value of
x
x
x
.
\newline
Write your answer as a whole number or a decimal.
\newline
x
=
x=
x
=
\newline
□
\square
□
\newline
Submit
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8
8
8
. A jeweler created a parallelogram-shaped pendant.
1
4
\frac{1}{4}
4
1
of the pendant is covered in emeralds,
1
6
\frac{1}{6}
6
1
of it is covered in rubies,
1
12
\frac{1}{12}
12
1
of it is covered in diamonds, and the rest of it is covered in sapphires. How many square centimeters of the pendant are covered in sapphires? Round to the nearest tenth.
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763
=
9
7 6 3=9
763
=
9
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First try was incorrect
\newline
Mr. Pewser counted the number of marbles in a bag.
\newline
Use the circle graph to answer the question below.
\newline
Total Marbles
\newline
What percentage (to the nearest tenth) of the marbles were not green?
\newline
symbol required
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5
×
7
=
5\times7=
5
×
7
=
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Get
24
24
24
from
23
23
23
22
22
22
1
1
1
1
1
1
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(
0.3
+
1.5
)
×
3
2
÷
5
2
(0.3+1.5) \times \frac{3}{2} \div \frac{5}{2}
(
0.3
+
1.5
)
×
2
3
÷
2
5
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7
7
7
divided
3
4
\frac{3}{4}
4
3
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6
6
6
divided
5
5
5
over
4
4
4
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1
1
1
.
1
/
2
×
5
/
6
÷
5
/
8
1 / 2 \times 5 / 6 \div 5 / 8
1/2
×
5/6
÷
5/8
\newline
2
2
2
.
2
1
2
×
1
3
+
1
/
6
2 \frac{1}{2} \times \frac{1}{3}+1 / 6
2
2
1
×
3
1
+
1/6
\newline
3
3
3
.
1
3
4
×
1
/
2
+
2
1
3
÷
1
1
4
1 \frac{3}{4} \times 1 / 2+2 \frac{1}{3} \div 1 \frac{1}{4}
1
4
3
×
1/2
+
2
3
1
÷
1
4
1
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A STORY OF RATIOS
\newline
Lesson
18
18
18
\newline
605
605
605
\newline
Anariesah
\newline
April
/
10
/
2024
/ 10 / 2024
/10/2024
\newline
Example
1
1
1
\newline
Fold the net used in the Opening Exercise to make a rectangular prism. Have the two faces with the largest area be the bases of the prism. Fill in the first row of the table below.
\newline
Examine the rectangular prism below. Complete the table.
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Name:
\qquad
5
5
5
−
4
-4
−
4
Additional Practice
1
1
1
.
2
−
4
2-4
2
−
4
Pairs of values on the coordinate plane.
\newline
2
2
2
.
\newline
3
3
3
. A store charges
$
140
\$ 140
$140
for every
10
10
10
bags of fertilizer a farmer buys.
\newline
a. Complete the table. Graph the values.
\newline
\begin{tabular}{|l|l|l|l|l|l|}
\newline
\hline \begin{tabular}{l}
\newline
Fertilizer \\
\newline
(bags)
\newline
\end{tabular} &
10
10
10
& \multicolumn{
2
2
2
}{|c|}{} \\
\newline
\hline Cost (s) &
140
140
140
&
30
30
30
&
40
40
40
&
70
70
70
\\
\newline
\hline
\newline
\end{tabular}
\newline
b. How much would a farmer pay for
50
50
50
bags of fertilizer? Explain.
\newline
4
4
4
. A car uses
5
5
5
gallons of gas for every
120
120
120
miles it travels.
\newline
a. Complete the table. Graph the values.
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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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(
0.654
+
1
)
∧
8
=
56
(0.654+1)^{\wedge} 8=56
(
0.654
+
1
)
∧
8
=
56
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6 rac{1}{2} ext{ years is how many weeks} ext{?}
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Trish and Jaz both bought a small cheescake. Trish ate
40
%
40\%
40%
of her cheesecake and Jaz ate
30
%
30\%
30%
of his cheesecake. Trish says that in total they ate
40
%
+
30
%
=
70
%
40\% + 30\% = 70\%
40%
+
30%
=
70%
of the cheesecakes. a. Can you explain what Trish has done wrong? b. What proportion of the cheesecakes did they actually eat? Give your answer as a percentage, fraction and decimal.
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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.
Get tutor help
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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Ruth is training for a half-marathon. On Saturday, she ran
3
3
3
miles in
34
34
34
.
5
5
5
minutes. On Sunday, she ran
2
2
2
.
5
5
5
miles in
28
28
28
minutes. How much faster, in minutes per mile, was her pace on Sunday than on Saturday?
\newline
Write your answer as a decimal or a whole number.
\newline
minutes per mile
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−
3
(
4
+
9
x
)
+
11
=
27
-3(4+9 x)+11=27
−
3
(
4
+
9
x
)
+
11
=
27
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Khan Academy
\newline
Donate
⌣
\smile
⌣
\newline
Quiz
3
3
3
\newline
Liam had
$
250
\$ 250
$250
. Then, he and his classmates bought a present for their teacher, evenly splitting the
$
p
\$ p
$
p
cost among the
24
24
24
of them.
\newline
How much money does Liam have left?
\newline
Write your answer as an expression.
\newline
$
\$
$
\newline
Report a problem
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1
×
6
=
4
(
−
2
+
4
)
1 \times 6=4(-2+4)
1
×
6
=
4
(
−
2
+
4
)
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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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work:
11
11
11
.
4
4
4
HW -
\newline
HW Score:
27.59
%
,
8
27.59 \%, 8
27.59%
,
8
of
29
29
29
\newline
Question
9
9
9
,
11
11
11
.
4
4
4
.
3
3
3
\newline
points
\newline
Points:
0
0
0
of
1
1
1
\newline
Save
\newline
The probability of rolling an even number on a
10
10
10
-sided die is
□
\square
□
.
\newline
(Type an integer or a simplified fraction.)
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Compare the rates to find which is the better value.
\newline
$
23
\$ 23
$23
for
4
4
4
burgers or
$
26
\$ 26
$26
for
5
5
5
burgers
\newline
The unit rate for
$
23
\$ 23
$23
for
4
4
4
burgers is
$
□
\$ \square
$
□
per burger. The unit rate for
$
26
\$ 26
$26
for
5
5
5
burgers is
$
□
\$ \square
$
□
per burger. So, is the better value.
\newline
(Type whole numbers or decimals.)
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1
2
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