Mixing
Rounding a percentage to the nearest multiple of $frac{1}{n}$
$begingroup$
If I take a percentage like $60%$ I can easily round it to a multiple of $frac{1}{n}$ where $n=2$ like this...
$$60%doteq50%$$
$$50%=frac{1}{2}$$
...or where $n=3$ like this.
$$60%doteq 66%$$
$$66%doteq frac{2}{3}$$
But what if $n$ was a not-so-friendly number, like 43? How do I round $60%$ to the nearest multiple of a fraction like $frac{1}{43}$ without doing so much guessing and checking?
Is there a consistent method for rounding $k%$ to the nearest multiple of $frac{1}{n}$ with minimal use of the guess and check method?
fractions percentages
asked Jan 7 at 3:04
Diriector_DocDiriector_Doc
1207
$endgroup$
add a comment |
$begingroup$
If I take a percentage like $60%$ I can easily round it to a multiple of $frac{1}{n}$ where $n=2$ like this...
$$60%doteq50%$$
$$50%=frac{1}{2}$$
...or where $n=3$ like this.
$$60%doteq 66%$$
$$66%doteq frac{2}{3}$$
But what if $n$ was a not-so-friendly number, like 43? How do I round $60%$ to the nearest multiple of a fraction like $frac{1}{43}$ without doing so much guessing and checking?
Is there a consistent method for rounding $k%$ to the nearest multiple of $frac{1}{n}$ with minimal use of the guess and check method?
fractions percentages
asked Jan 7 at 3:04
Diriector_DocDiriector_Doc
1207
$endgroup$
add a comment |
$begingroup$
If I take a percentage like $60%$ I can easily round it to a multiple of $frac{1}{n}$ where $n=2$ like this...
$$60%doteq50%$$
$$50%=frac{1}{2}$$
...or where $n=3$ like this.
$$60%doteq 66%$$
$$66%doteq frac{2}{3}$$
But what if $n$ was a not-so-friendly number, like 43? How do I round $60%$ to the nearest multiple of a fraction like $frac{1}{43}$ without doing so much guessing and checking?
Is there a consistent method for rounding $k%$ to the nearest multiple of $frac{1}{n}$ with minimal use of the guess and check method?
fractions percentages
asked Jan 7 at 3:04
Diriector_DocDiriector_Doc
1207
$endgroup$
If I take a percentage like $60%$ I can easily round it to a multiple of $frac{1}{n}$ where $n=2$ like this...
$$60%doteq50%$$
$$50%=frac{1}{2}$$
...or where $n=3$ like this.
$$60%doteq 66%$$
$$66%doteq frac{2}{3}$$
But what if $n$ was a not-so-friendly number, like 43? How do I round $60%$ to the nearest multiple of a fraction like $frac{1}{43}$ without doing so much guessing and checking?
Is there a consistent method for rounding $k%$ to the nearest multiple of $frac{1}{n}$ with minimal use of the guess and check method?
fractions percentages
fractions percentages
asked Jan 7 at 3:04
Diriector_DocDiriector_Doc
1207
asked Jan 7 at 3:04
Diriector_DocDiriector_Doc
1207
asked Jan 7 at 3:04
Diriector_DocDiriector_Doc
1207
asked Jan 7 at 3:04
Diriector_DocDiriector_Doc
1207
asked Jan 7 at 3:04
Diriector_DocDiriector_Doc
1207
1207
add a comment |
add a comment |
3 Answers
3
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votes
$begingroup$
Let $m = text{round}left(dfrac{k cdot n}{100}right)$, i.e. compute $dfrac{k cdot n}{100}$ and round it to the nearest integer.
Then, the nearest multiple of $dfrac{1}{n}$ to $k%$ is $dfrac{m}{n}$.
This works since the following statements are equivalent:
$dfrac{m}{n}$ is the nearest multiple of $dfrac{1}{n}$ to $k%$
$dfrac{m-tfrac{1}{2}}{n} < dfrac{k}{100} le dfrac{m+tfrac{1}{2}}{n}$
$m-dfrac{1}{2} < dfrac{kn}{100} le m+dfrac{1}{2}$
$m$ is the nearest integer to $dfrac{kn}{100}$
answered Jan 7 at 3:12
JimmyK4542JimmyK4542
40.8k245105
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$begingroup$
Round $kn%$ to the nearest integer and that's your numerator!
eg $60%*43=25.8$ so $60%≈frac{26}{43}$.
answered Jan 7 at 3:13
timtfjtimtfj
1,706418
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add a comment |
$begingroup$
Find the nearest integer to $k%$ of $n$. In your example, we can say that 1 is the nearest integer to 60% of 2 i.e. 1.2 and 2 is the nearest integer to 60% of 3 i.e. 1.8.
Hope it helps:)
answered Jan 7 at 3:14
MartundMartund
1,573212
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add a comment |
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3 Answers
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3 Answers
3
active
oldest
votes
active
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active
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votes
$begingroup$
Let $m = text{round}left(dfrac{k cdot n}{100}right)$, i.e. compute $dfrac{k cdot n}{100}$ and round it to the nearest integer.
Then, the nearest multiple of $dfrac{1}{n}$ to $k%$ is $dfrac{m}{n}$.
This works since the following statements are equivalent:
$dfrac{m}{n}$ is the nearest multiple of $dfrac{1}{n}$ to $k%$
$dfrac{m-tfrac{1}{2}}{n} < dfrac{k}{100} le dfrac{m+tfrac{1}{2}}{n}$
$m-dfrac{1}{2} < dfrac{kn}{100} le m+dfrac{1}{2}$
$m$ is the nearest integer to $dfrac{kn}{100}$
answered Jan 7 at 3:12
JimmyK4542JimmyK4542
40.8k245105
$endgroup$
add a comment |
$begingroup$
Let $m = text{round}left(dfrac{k cdot n}{100}right)$, i.e. compute $dfrac{k cdot n}{100}$ and round it to the nearest integer.
Then, the nearest multiple of $dfrac{1}{n}$ to $k%$ is $dfrac{m}{n}$.
This works since the following statements are equivalent:
$dfrac{m}{n}$ is the nearest multiple of $dfrac{1}{n}$ to $k%$
$dfrac{m-tfrac{1}{2}}{n} < dfrac{k}{100} le dfrac{m+tfrac{1}{2}}{n}$
$m-dfrac{1}{2} < dfrac{kn}{100} le m+dfrac{1}{2}$
$m$ is the nearest integer to $dfrac{kn}{100}$
answered Jan 7 at 3:12
JimmyK4542JimmyK4542
40.8k245105
$endgroup$
add a comment |
$begingroup$
Let $m = text{round}left(dfrac{k cdot n}{100}right)$, i.e. compute $dfrac{k cdot n}{100}$ and round it to the nearest integer.
Then, the nearest multiple of $dfrac{1}{n}$ to $k%$ is $dfrac{m}{n}$.
This works since the following statements are equivalent:
$dfrac{m}{n}$ is the nearest multiple of $dfrac{1}{n}$ to $k%$
$dfrac{m-tfrac{1}{2}}{n} < dfrac{k}{100} le dfrac{m+tfrac{1}{2}}{n}$
$m-dfrac{1}{2} < dfrac{kn}{100} le m+dfrac{1}{2}$
$m$ is the nearest integer to $dfrac{kn}{100}$
answered Jan 7 at 3:12
JimmyK4542JimmyK4542
40.8k245105
$endgroup$
Let $m = text{round}left(dfrac{k cdot n}{100}right)$, i.e. compute $dfrac{k cdot n}{100}$ and round it to the nearest integer.
Then, the nearest multiple of $dfrac{1}{n}$ to $k%$ is $dfrac{m}{n}$.
This works since the following statements are equivalent:
$dfrac{m}{n}$ is the nearest multiple of $dfrac{1}{n}$ to $k%$
$dfrac{m-tfrac{1}{2}}{n} < dfrac{k}{100} le dfrac{m+tfrac{1}{2}}{n}$
$m-dfrac{1}{2} < dfrac{kn}{100} le m+dfrac{1}{2}$
$m$ is the nearest integer to $dfrac{kn}{100}$
answered Jan 7 at 3:12
JimmyK4542JimmyK4542
40.8k245105
answered Jan 7 at 3:12
JimmyK4542JimmyK4542
40.8k245105
answered Jan 7 at 3:12
JimmyK4542JimmyK4542
40.8k245105
answered Jan 7 at 3:12
JimmyK4542JimmyK4542
40.8k245105
40.8k245105
add a comment |
add a comment |
$begingroup$
Round $kn%$ to the nearest integer and that's your numerator!
eg $60%*43=25.8$ so $60%≈frac{26}{43}$.
answered Jan 7 at 3:13
timtfjtimtfj
1,706418
$endgroup$
add a comment |
$begingroup$
Round $kn%$ to the nearest integer and that's your numerator!
eg $60%*43=25.8$ so $60%≈frac{26}{43}$.
answered Jan 7 at 3:13
timtfjtimtfj
1,706418
$endgroup$
add a comment |
$begingroup$
Round $kn%$ to the nearest integer and that's your numerator!
eg $60%*43=25.8$ so $60%≈frac{26}{43}$.
answered Jan 7 at 3:13
timtfjtimtfj
1,706418
$endgroup$
Round $kn%$ to the nearest integer and that's your numerator!
eg $60%*43=25.8$ so $60%≈frac{26}{43}$.
answered Jan 7 at 3:13
timtfjtimtfj
1,706418
answered Jan 7 at 3:13
timtfjtimtfj
1,706418
answered Jan 7 at 3:13
timtfjtimtfj
1,706418
answered Jan 7 at 3:13
timtfjtimtfj
1,706418
1,706418
add a comment |
add a comment |
$begingroup$
Find the nearest integer to $k%$ of $n$. In your example, we can say that 1 is the nearest integer to 60% of 2 i.e. 1.2 and 2 is the nearest integer to 60% of 3 i.e. 1.8.
Hope it helps:)
answered Jan 7 at 3:14
MartundMartund
1,573212
$endgroup$
add a comment |
$begingroup$
Find the nearest integer to $k%$ of $n$. In your example, we can say that 1 is the nearest integer to 60% of 2 i.e. 1.2 and 2 is the nearest integer to 60% of 3 i.e. 1.8.
Hope it helps:)
answered Jan 7 at 3:14
MartundMartund
1,573212
$endgroup$
add a comment |
$begingroup$
Find the nearest integer to $k%$ of $n$. In your example, we can say that 1 is the nearest integer to 60% of 2 i.e. 1.2 and 2 is the nearest integer to 60% of 3 i.e. 1.8.
Hope it helps:)
answered Jan 7 at 3:14
MartundMartund
1,573212
$endgroup$
Find the nearest integer to $k%$ of $n$. In your example, we can say that 1 is the nearest integer to 60% of 2 i.e. 1.2 and 2 is the nearest integer to 60% of 3 i.e. 1.8.
Hope it helps:)
answered Jan 7 at 3:14
MartundMartund
1,573212
answered Jan 7 at 3:14
MartundMartund
1,573212
answered Jan 7 at 3:14
MartundMartund
1,573212
answered Jan 7 at 3:14
MartundMartund
1,573212
1,573212
add a comment |
add a comment |
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