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Math Problems
Grade 6
Convert between percents, fractions, and decimals: word problems
Erica plays trombone in the marching band. She has
75
%
75\%
75%
of her music for this year's show memorized so far.
\newline
Write
75
%
75\%
75%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
75
%
75\%
75%
as a decimal.
\newline
____
\newline
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About
30
%
30\%
30%
of the earth's surface is covered in land.
\newline
Write
30
%
30\%
30%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
30
%
30\%
30%
as a decimal.
\newline
____
\newline
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Krysta needs
1
2
\frac{1}{2}
2
1
of a teaspoon of vanilla for her cookie recipe.
\newline
Write
1
2
\frac{1}{2}
2
1
of a teaspoon as a decimal.
\newline
_
_
_
\_\_\_
___
teaspoons
\newline
\newline
Write
1
2
\frac{1}{2}
2
1
of a teaspoon as a percent.
\newline
_
_
_
%
\_\_\_\%
___%
of a teaspoon
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Mitchell has finished writing
60
%
60\%
60%
of his essay for history class.
\newline
Write
60
%
60\%
60%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
60
%
60\%
60%
as a decimal.
\newline
____
\newline
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Michelle's grandmother gave her an antique necklace that has gone up in value by
35
%
35\%
35%
from when it was new.
\newline
Write
35
%
35\%
35%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
35
%
35\%
35%
as a decimal.
\newline
____
\newline
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Erik used
3
4
\frac{3}{4}
4
3
of a yard of ribbon to make himself a new lanyard for school.
\newline
Write
3
4
\frac{3}{4}
4
3
of a yard as a decimal.
\newline
_
_
_
\_\_\_
___
yards
\newline
\newline
Write
3
4
\frac{3}{4}
4
3
of a yard as a percent.
\newline
_
_
_
\_\_\_%
___
of a yard
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Philip is shopping at a store where everything is on sale for
25
%
25\%
25%
off.
\newline
Write
25
%
25\%
25%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
25
%
25\%
25%
as a decimal.
\newline
____
\newline
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Brody earned a
72
%
72\%
72%
on his history final exam.
\newline
Write
72
%
72\%
72%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
72
%
72\%
72%
as a decimal.
\newline
____
\newline
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The value of Edgar's RV has depreciated
8
%
8\%
8%
since it was new.
\newline
Write
8
%
8\%
8%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
8
%
8\%
8%
as a decimal.
\newline
____
\newline
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Farmer Johnson plants soybeans in
28
%
28\%
28%
of his fields.
\newline
Write
28
%
28\%
28%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
28
%
28\%
28%
as a decimal.
\newline
____
\newline
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Christine reads the nutrition label on her cereal. She notices it gives her
15
%
15\%
15%
of her daily allowance of vitamin A.
\newline
Write
15
%
15\%
15%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
15
%
15\%
15%
as a decimal.
\newline
____
\newline
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Hanson's new house is
24
%
24\%
24%
larger than his old house.
\newline
Write
24
%
24\%
24%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
24
%
24\%
24%
as a decimal.
\newline
____
\newline
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Melissa earns
94
%
94\%
94%
on her science test.
\newline
Write
94
%
94\%
94%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
94
%
94\%
94%
as a decimal.
\newline
____
\newline
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Jayce checks his phone to see how much of the battery power is left. He sees there is
55
%
55\%
55%
left.
\newline
Write
55
%
55\%
55%
as a fraction in simplest form.
\newline
____
\newline
\newline
Write
55
%
55\%
55%
as a decimal.
\newline
____
\newline
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In the school band,
1
5
\frac{1}{5}
5
1
of the students play percussion instruments.
\newline
Write
1
5
\frac{1}{5}
5
1
as a decimal.
\newline
_
_
\_\_
__
\newline
\newline
Write
1
5
\frac{1}{5}
5
1
as a percent.
\newline
_
_
\_\_
__
%
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Diego is building a model car that is
1
20
\frac{1}{20}
20
1
the size of a normal car.
\newline
Write
1
20
\frac{1}{20}
20
1
as a decimal.
\newline
____
\newline
\newline
Write
1
20
\frac{1}{20}
20
1
as a percent.
\newline
____
%
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7
8
\frac{7}{8}
8
7
of the local science bowl contestants were competing for the first time, while
4
7
\frac{4}{7}
7
4
of the regional science bowl contestants were competing for the first time. Which science bowl had a greater fraction of first-time contestants?
\newline
Choices:
\newline
(A) local
\newline
(B) regional
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An international company has
24
,
700
24,700
24
,
700
employees in one country. If this represents
16.3
%
16.3\%
16.3%
of the company's employees, how many employees does it have in total?
\newline
Round your answer to the nearest whole number.
\newline
□
\square
□
employees
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A shelf contains only black, purple and orange pots of paint. The ratio of black pots of paint to purple pots of paint is
14
:
9
14: 9
14
:
9
. The ratio of purple pots of paint to orange pots of paint is
3
:
9
3: 9
3
:
9
.
\newline
Calculate the percentage of pots of paint that are orange.
\newline
________
%
\%
%
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The sales tax in your city is
8.8
%
8.8\%
8.8%
, and an item costs
$
63
\$63
$63
before tax.
\newline
How much tax would you pay on that item?
\newline
Round to the nearest hundredth or cent.
\newline
$
\$
$
□
\square
□
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Emilie Maguren Mathematics Standard Year
11
11
11
\newline
Revision for Half Yearly Examination
2024
2024
2024
- worksheet \#
01
01
01
\newline
(show all working)
\newline
1
1
1
. A necklace in Thailand costs
4419
4419
4419
baht after a VAT of
7
%
7 \%
7%
has been added. What was its original price, to the nearest baht?
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A Belgian key-cutter charges
€
3
€3
€3
, plus
€
0.57
€0.57
€0.57
in VAT, for every key cut. What percentage VAT is being charged?
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1
5
20
+
1
1
5
1 \frac{5}{20}+1 \frac{1}{5}
1
20
5
+
1
5
1
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Convert the fraction below into a decimal
\newline
11
40
\frac{11}{40}
40
11
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
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Convert the fraction below into a decimal
\newline
19
60
\frac{19}{60}
60
19
\newline
Edit the repeating and non-repeating part of the decimal:
\newline
0.
□
□
‾
0.\square\overline{\square}
0.
□
□
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155
155
155
.
1
1
1
is what percent of
352
352
352
? Round to the nearest thousandth.
\newline
Answer:
□
\square
□
%
\%
%
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The volume of a rectangular prism is
500
c
m
3
500 \mathrm{~cm}^{3}
500
cm
3
. Bob measures the sides to be
10.35
c
m
10.35 \mathrm{~cm}
10.35
cm
by
10.06
c
m
10.06 \mathrm{~cm}
10.06
cm
by
4.92
c
m
4.92 \mathrm{~cm}
4.92
cm
. In calculating the volume, what is the relative error, to the nearest thousandth.
\newline
Answer:
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Write
0.624
0.624
0.624
as a percent and as a simplified fraction.
\newline
62.4
%
62.4\%
62.4%
and
\newline
156
25
\frac{156}{25}
25
156
\newline
6.24
%
6.24\%
6.24%
and
\newline
624
1000
\frac{624}{1000}
1000
624
\newline
624
%
624\%
624%
and
\newline
78
125
\frac{78}{125}
125
78
\newline
62.4
%
62.4\%
62.4%
and
\newline
78
125
\frac{78}{125}
125
78
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An organization determined most of its sales only occurred after at least
4
4
4
contacts. However,
44
%
44\%
44%
of its salespeople gave up on a customer after the
1
st
1^{\text{st}}
1
st
contact didn't make a sale. Of the remaining salespeople,
40
%
40\%
40%
gave up after the
2
nd
2^{\text{nd}}
2
nd
contact. Finally,
41
%
41\%
41%
of the salespeople who made a
3
rd
3^{\text{rd}}
3
rd
contact gave up when that call did not make a sale. To the nearest percent, what percent of the original salespeople made
4
4
4
or more contacts if the first
3
3
3
contacts did not result in sales? (Round to the nearest percent. Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
44
%
44\%
44%
0
0
0
, enter
44
%
44\%
44%
1
1
1
.)
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