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Why is the expression $(((30 / 2) / 2) / 2)$ same as $30 / 2^3$ [on hold]

-1

$begingroup$

Why is the expression $$(((30 / 2) / 2) / 2)$$ same as $$30 / 2^3$$

arithmetic

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edited Apr 7 at 17:23

Asaf Karagila♦

308k33441775

asked Apr 7 at 11:11

Michael MuntaMichael Munta

111112

$endgroup$

put on hold as off-topic by Servaes, Saad, Adrian Keister, Jyrki Lahtonen, Leucippus yesterday

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Servaes, Saad, Adrian Keister, Jyrki Lahtonen, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  A parenthesis is missing?
  $endgroup$
  – Dr. Sonnhard Graubner
  Apr 7 at 11:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes! It is correct
  $endgroup$
  – HAMIDINE SOUMARE
  Apr 7 at 11:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $30/2=15$, $15/2=7.5$, $7.5/2=3.75$. Then $30/2^3=30/8=3.75$.
  $endgroup$
  – thesmallprint
  Apr 7 at 11:47
  

  
  
  
  

add a comment | 

-1

$begingroup$

Why is the expression $$(((30 / 2) / 2) / 2)$$ same as $$30 / 2^3$$

arithmetic

share|cite|improve this question

edited Apr 7 at 17:23

Asaf Karagila♦

308k33441775

asked Apr 7 at 11:11

Michael MuntaMichael Munta

111112

$endgroup$

put on hold as off-topic by Servaes, Saad, Adrian Keister, Jyrki Lahtonen, Leucippus yesterday

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Servaes, Saad, Adrian Keister, Jyrki Lahtonen, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  A parenthesis is missing?
  $endgroup$
  – Dr. Sonnhard Graubner
  Apr 7 at 11:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes! It is correct
  $endgroup$
  – HAMIDINE SOUMARE
  Apr 7 at 11:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $30/2=15$, $15/2=7.5$, $7.5/2=3.75$. Then $30/2^3=30/8=3.75$.
  $endgroup$
  – thesmallprint
  Apr 7 at 11:47
  

  
  
  
  

add a comment | 

$begingroup$

Why is the expression $$(((30 / 2) / 2) / 2)$$ same as $$30 / 2^3$$

arithmetic

share|cite|improve this question

edited Apr 7 at 17:23

Asaf Karagila♦

308k33441775

asked Apr 7 at 11:11

Michael MuntaMichael Munta

111112

$endgroup$

share|cite|improve this question

edited Apr 7 at 17:23

Asaf Karagila♦

308k33441775

asked Apr 7 at 11:11

Michael MuntaMichael Munta

111112

share|cite|improve this question

edited Apr 7 at 17:23

Asaf Karagila♦

308k33441775

asked Apr 7 at 11:11

Michael MuntaMichael Munta

111112

edited Apr 7 at 17:23

Asaf Karagila♦

308k33441775

edited Apr 7 at 17:23

Asaf Karagila♦

308k33441775

asked Apr 7 at 11:11

Michael MuntaMichael Munta

111112

asked Apr 7 at 11:11

Michael MuntaMichael Munta

111112

3 Answers
3

active

oldest

votes

1

$begingroup$

Note that

$$beginalign colorblue(30/2)/2 &= frac302times frac12\
&=colorteal frac302^2
endalign.$$

Hence
$$beginalign
(colorblue(30/2)/2)/2 &= colortealleft(frac302^2right)bigg/2\
&= frac302^2times frac12\
&= frac302^3.
endalign$$

share|cite|improve this answer

edited Apr 7 at 11:27

answered Apr 7 at 11:22

Minus One-TwelfthMinus One-Twelfth

3,388413

$endgroup$

add a comment | 

3

$begingroup$

Recall:

$(30/2)=30cdot dfrac12;$

$((30/2)/2)=(30cdot dfrac12)cdot dfrac12;$

$(30/2)/2)/2=$

$((30 cdot dfrac12)cdot dfrac12)cdot dfrac12= 30 cdot (dfrac12)^3= dfrac302^3$

Used: Associative law of multiplication.

share|cite|improve this answer

edited Apr 7 at 13:37

answered Apr 7 at 12:06

Peter SzilasPeter Szilas

11.9k2822

$endgroup$

add a comment | 

2

$begingroup$

$$30div2div2div2=frac302div2div2$$
$$=frac302^2div2$$
$$=frac302^3$$

share|cite|improve this answer

answered Apr 7 at 11:21

Peter ForemanPeter Foreman

6,9401318

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Looking at this as a multiplication by a fraction is the only way to prove it?
  $endgroup$
  – Michael Munta
  Apr 7 at 11:25
  

  
  
  
  

add a comment | 

1

$begingroup$

Note that

$$beginalign colorblue(30/2)/2 &= frac302times frac12\
&=colorteal frac302^2
endalign.$$

Hence
$$beginalign
(colorblue(30/2)/2)/2 &= colortealleft(frac302^2right)bigg/2\
&= frac302^2times frac12\
&= frac302^3.
endalign$$

share|cite|improve this answer

edited Apr 7 at 11:27

answered Apr 7 at 11:22

Minus One-TwelfthMinus One-Twelfth

3,388413

$endgroup$

add a comment | 

1

$begingroup$

Note that

$$beginalign colorblue(30/2)/2 &= frac302times frac12\
&=colorteal frac302^2
endalign.$$

Hence
$$beginalign
(colorblue(30/2)/2)/2 &= colortealleft(frac302^2right)bigg/2\
&= frac302^2times frac12\
&= frac302^3.
endalign$$

share|cite|improve this answer

edited Apr 7 at 11:27

answered Apr 7 at 11:22

Minus One-TwelfthMinus One-Twelfth

3,388413

$endgroup$

add a comment | 

$begingroup$

Note that

$$beginalign colorblue(30/2)/2 &= frac302times frac12\
&=colorteal frac302^2
endalign.$$

Hence
$$beginalign
(colorblue(30/2)/2)/2 &= colortealleft(frac302^2right)bigg/2\
&= frac302^2times frac12\
&= frac302^3.
endalign$$

share|cite|improve this answer

edited Apr 7 at 11:27

answered Apr 7 at 11:22

Minus One-TwelfthMinus One-Twelfth

3,388413

$endgroup$

share|cite|improve this answer

edited Apr 7 at 11:27

answered Apr 7 at 11:22

Minus One-TwelfthMinus One-Twelfth

3,388413

answered Apr 7 at 11:22

Minus One-TwelfthMinus One-Twelfth

3,388413

answered Apr 7 at 11:22

Minus One-TwelfthMinus One-Twelfth

3,388413

3

$begingroup$

Recall:

$(30/2)=30cdot dfrac12;$

$((30/2)/2)=(30cdot dfrac12)cdot dfrac12;$

$(30/2)/2)/2=$

$((30 cdot dfrac12)cdot dfrac12)cdot dfrac12= 30 cdot (dfrac12)^3= dfrac302^3$

Used: Associative law of multiplication.

share|cite|improve this answer

edited Apr 7 at 13:37

answered Apr 7 at 12:06

Peter SzilasPeter Szilas

11.9k2822

$endgroup$

add a comment | 

3

$begingroup$

Recall:

$(30/2)=30cdot dfrac12;$

$((30/2)/2)=(30cdot dfrac12)cdot dfrac12;$

$(30/2)/2)/2=$

$((30 cdot dfrac12)cdot dfrac12)cdot dfrac12= 30 cdot (dfrac12)^3= dfrac302^3$

Used: Associative law of multiplication.

share|cite|improve this answer

edited Apr 7 at 13:37

answered Apr 7 at 12:06

Peter SzilasPeter Szilas

11.9k2822

$endgroup$

add a comment | 

$begingroup$

Recall:

$(30/2)=30cdot dfrac12;$

$((30/2)/2)=(30cdot dfrac12)cdot dfrac12;$

$(30/2)/2)/2=$

$((30 cdot dfrac12)cdot dfrac12)cdot dfrac12= 30 cdot (dfrac12)^3= dfrac302^3$

Used: Associative law of multiplication.

share|cite|improve this answer

edited Apr 7 at 13:37

answered Apr 7 at 12:06

Peter SzilasPeter Szilas

11.9k2822

$endgroup$

share|cite|improve this answer

edited Apr 7 at 13:37

answered Apr 7 at 12:06

Peter SzilasPeter Szilas

11.9k2822

answered Apr 7 at 12:06

Peter SzilasPeter Szilas

11.9k2822

answered Apr 7 at 12:06

Peter SzilasPeter Szilas

11.9k2822

2

$begingroup$

$$30div2div2div2=frac302div2div2$$
$$=frac302^2div2$$
$$=frac302^3$$

share|cite|improve this answer

answered Apr 7 at 11:21

Peter ForemanPeter Foreman

6,9401318

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Looking at this as a multiplication by a fraction is the only way to prove it?
  $endgroup$
  – Michael Munta
  Apr 7 at 11:25
  

  
  
  
  

add a comment | 

2

$begingroup$

$$30div2div2div2=frac302div2div2$$
$$=frac302^2div2$$
$$=frac302^3$$

share|cite|improve this answer

answered Apr 7 at 11:21

Peter ForemanPeter Foreman

6,9401318

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Looking at this as a multiplication by a fraction is the only way to prove it?
  $endgroup$
  – Michael Munta
  Apr 7 at 11:25
  

  
  
  
  

add a comment | 

$begingroup$

$$30div2div2div2=frac302div2div2$$
$$=frac302^2div2$$
$$=frac302^3$$

share|cite|improve this answer

answered Apr 7 at 11:21

Peter ForemanPeter Foreman

6,9401318

$endgroup$

share|cite|improve this answer

answered Apr 7 at 11:21

Peter ForemanPeter Foreman

6,9401318

answered Apr 7 at 11:21

Peter ForemanPeter Foreman

6,9401318

answered Apr 7 at 11:21

Peter ForemanPeter Foreman

6,9401318