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Math Problems
Grade 6
Convert between percents, fractions, and decimals: word problems
number has a
3
3
3
with a value that is
100
100
100
times greater than the va in
20.342
?
20.342 ?
20.342
?
\newline
173
173
173
\newline
423
423
423
.
06
06
06
\newline
36
36
36
.
25
25
25
\newline
307
307
307
.
18
18
18
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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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Secondary
→
\rightarrow
→
Number
→
\rightarrow
→
Ratio \& Proportion
\newline
227
227
227
b: Combine two ratios to determine what
\newline
Watch Worked Example
\newline
fraction or percentage of items are a particular type.
\newline
Q
1
1
1
\newline
Q
2
2
2
\newline
Q
3
3
3
\newline
Q
4
4
4
\newline
Q
5
5
5
\newline
Q
6
6
6
\newline
Q
7
7
7
\newline
Q
8
8
8
\newline
Q
9
9
9
\newline
Q
10
10
10
\newline
Q
11
11
11
\newline
Q
12
12
12
\newline
Q
13
13
13
\newline
Q
14
14
14
\newline
Q
15
15
15
\newline
Q
16
16
16
\newline
Q
17
17
17
\newline
Q
18
18
18
\newline
Q
19
19
19
\newline
Q
20
20
20
\newline
COMPLETION
\newline
40
%
40 \%
40%
\newline
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
□
\square
□
%
\%
%
□
\square
□
%
\%
%
\newline
Submit Answer
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sixth-grade students at Madison Middle School had a walkathon to raise money for th al hospital. Their principal tracked how much money each student raised. This box plot ows the results.
\newline
Money raised ($)\(\newline\)What percent of the students raised more than \(\newline\)\(\$40\) ?\(\newline\)◻ \(\newline\)%\(\newline\)Submit\(\newline\)Work it out\(\newline\)Not feeling ready yet? These can help:
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Owen answered a set of math and history Quiz Bowl questions. Owen correctly answered
72
%
72 \%
72%
of all the
200
200
200
questions. However, Owen answered
53.3
%
53.3 \%
53.3%
of the math questions correctly. If
45
%
45 \%
45%
of the questions were in math, what percent of history questions did Owen answer correctly?
\newline
21
%
21 \%
21%
\newline
(Round to the nearest percent. Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
11.2
%
11.2 \%
11.2%
, enter
11
11
11
.)
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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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103
103
103
A trail is
2
1
2
2 \frac{1}{2}
2
2
1
miles long. How many yards long is the trail?
\newline
A
3
,
520
1
2
3,520 \frac{1}{2}
3
,
520
2
1
yards
\newline
B
4
4
4
,
400
400
400
yards
\newline
Write
2
1
2
2 \frac{1}{2}
2
2
1
as a decimal.
\newline
C
3
3
3
,
420
420
420
yards
\newline
D
4
4
4
,
200
200
200
yards
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7
7
7
\newline
In the year
2000
2000
2000
, a house was valued at
$
80000
\$ 80000
$80000
In
2020
2020
2020
, the same house was valued at
$
280000
\$ 280000
$280000
\newline
Work out the value of the house in
2020
2020
2020
as a percentage of its value in
2000
2000
2000
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Polygon
H
H
H
is a scaled copy of Polygon
G
G
G
using a scale factor of
1
4
\frac{1}{4}
4
1
.
\newline
Polygon
H
H
H
's area is what fraction of Polygon
G
G
G
's area?
\newline
□
\square
□
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Jevon earns
1
2
%
\frac{1}{2}\%
2
1
%
per year on the money in his savings account. Which expression is not another way to write
1
2
%
\frac{1}{2}\%
2
1
%
?
\newline
E.
0.005
/
100
0.005/100
0.005/100
\newline
F.
0.5
/
100
0.5/100
0.5/100
\newline
G.
5
/
1000
5/1000
5/1000
\newline
H.
1
/
200
1/200
1/200
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Jevon earns
1
2
%
\frac{1}{2}\%
2
1
%
per year on the money in his savings account. Which expression is not another way to write
1
2
%
\frac{1}{2}\%
2
1
%
?
\newline
E.
0.005
/
100
0.005/100
0.005/100
\newline
F.
0.5
/
100
0.5/100
0.5/100
\newline
G.
5
/
1
,
000
5/1,000
5/1
,
000
\newline
H.
1
/
200
1/200
1/200
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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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Calouleting Consumer Discounts: Mastery Test
\newline
Subrik Test
\newline
Select be cornect answer.
\newline
Savings
\newline
= price
\newline
×
\times
×
discount percentage
\newline
How much will you save It you buy an bem lsatd at
\newline
$
7550
\$7550
$7550
at a
\newline
25
%
25\%
25%
dscount?
\newline
A.
$
1888
\$1888
$1888
\newline
B.
$
9500
\$9500
$9500
\newline
C.
$
5652
\$5652
$5652
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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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Wyatt put the
$
450
\$450
$450
she earned from her summer job into an account and will use it to pay for school expenses. She withdraws
10
%
10\%
10%
of the remaining balance each month to pay for part of her living expenses. Which of the following functions models the balance,
B
B
B
, of Wyatt's money (in dollars)
t
t
t
months after she started school?
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8
8
8
. A domino has a percentage and a fraction written on it.
\newline
\begin{tabular}{|l|l|}
\newline
\hline
30
%
30 \%
30%
&
1
2
\frac{1}{2}
2
1
\\
\newline
\hline
\newline
\end{tabular}
\newline
The dominoes are matched so that the fraction joins its equivalent percentage.
\newline
\begin{tabular}{|l|l|}
\newline
\hline
30
%
30 \%
30%
&
1
2
\frac{1}{2}
2
1
\\
\newline
\hline
\newline
\end{tabular}
\newline
\begin{tabular}{|l|l|}
\newline
\hline
50
%
50 \%
50%
&
3
5
\frac{3}{5}
5
3
\\
\newline
\hline
\newline
\end{tabular}
\newline
Four of the dominoes are joined
\newline
\begin{tabular}{|l|l|}
\newline
\hline
30
%
30 \%
30%
&
1
2
\frac{1}{2}
2
1
\\
\newline
\hline
\newline
\end{tabular}
\newline
\begin{tabular}{|l|l|}
\newline
\hline
50
%
50 \%
50%
&
3
5
\frac{3}{5}
5
3
\\
\newline
\hline
\newline
\end{tabular}
\newline
\begin{tabular}{|c|c|c|c|}
\newline
\hline & &
1
2
\frac{1}{2}
2
1
0
0
0
&
1
2
\frac{1}{2}
2
1
1
1
1
\\
\newline
\hline
\newline
\end{tabular}
\newline
Write in the percentage and fraction needed on the blank domino.
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Miss Shiva pours
2
3
5
ℓ
2 \frac{3}{5} \ell
2
5
3
ℓ
of fruit punch equally into
4
4
4
glasses.
\newline
(a) Find the amount of fruit punch in each glass. Give your answer as a fraction in its simplest form.
\newline
(b) She buys another
2
ℓ
2 \ell
2
ℓ
of fruit punch. How many more glasses containing the same amount of fruit punch as before can she fill at most?
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Miss Shiva pours
?
5
3
f
?_{5}^{3} f
?
5
3
f
of fruit punch equally inte
4
4
4
glasses.
\newline
(a) Find the amount of fruit punch in sach glass. Glve your answer as a fraction in its simplest form.
\newline
(b) She buys another
2
2
2
of frult punch. How many more glasses containing the same amount of fruit punch as belore can she fill at most?
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What is
\newline
0.6
32
‾
0.6\overline{32}
0.6
32
as a fraction? Move numbers to the blanks to complete the fraction.
\newline
□
79
\frac{\Box}{79}
79
□
\newline
□
125
\frac{\Box}{125}
125
□
\newline
□
313
\frac{\Box}{313}
313
□
\newline
□
457
\frac{\Box}{457}
457
□
\newline
□
495
\frac{\Box}{495}
495
□
\newline
□
632
\frac{\Box}{632}
632
□
\newline
□
999
\frac{\Box}{999}
999
□
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What is
0.6
62
‾
0.6 \overline{62}
0.6
62
as a fraction? Move numbers to the blanks to complete the fraction.
\newline
□
\square
□
\newline
79
79
79
\newline
125
125
125
\newline
313
313
313
\newline
457
457
457
\newline
495
495
495
\newline
632
632
632
\newline
999
999
999
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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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