Why is the expression $(((30 / 2) / 2) / 2)$ same as $30 / 2^3$ [on hold] The 2019 Stack Overflow Developer Survey Results Are InOrder of operations: problem evaluating an expressionExpression with last digits differentWhy exactly does the distributive property work?What values will make this expression realIs $frac5x3$ The Same As $frac53x$?How to evolve an expression with two denominatorsWhy diferent calculators give different values for same expression?magnitude of a root of complex expression plus complex expressionExpression for Change in temperatureWhy do addition and subtraction have the same precedence?

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



The 2019 Stack Overflow Developer Survey Results Are InOrder of operations: problem evaluating an expressionExpression with last digits differentWhy exactly does the distributive property work?What values will make this expression realIs $frac5x3$ The Same As $frac53x$?How to evolve an expression with two denominatorsWhy diferent calculators give different values for same expression?magnitude of a root of complex expression plus complex expressionExpression for Change in temperatureWhy do addition and subtraction have the same precedence?










-1












$begingroup$


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






arithmetic







share|cite|improve this question











$endgroup$



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















-1












$begingroup$


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






arithmetic







share|cite|improve this question











$endgroup$



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













-1












-1








-1





$begingroup$


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






arithmetic







share|cite|improve this question











$endgroup$




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






arithmetic




arithmetic






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Apr 7 at 17:23









Asaf Karagila♦

308k33441775




308k33441775










asked Apr 7 at 11:11









Michael MuntaMichael Munta

111113




111113




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.







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












  • 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







1




1




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




$begingroup$
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




$begingroup$
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




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










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











$endgroup$




















    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











    $endgroup$




















      2












      $begingroup$

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






      share|cite|improve this answer









      $endgroup$








      • 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

















      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      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











      $endgroup$

















        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











        $endgroup$















          1












          1








          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











          $endgroup$



          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














          share|cite|improve this answer



          share|cite|improve this answer








          edited Apr 7 at 11:27

























          answered Apr 7 at 11:22









          Minus One-TwelfthMinus One-Twelfth

          3,398413




          3,398413





















              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











              $endgroup$

















                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











                $endgroup$















                  3












                  3








                  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











                  $endgroup$



                  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














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Apr 7 at 13:37

























                  answered Apr 7 at 12:06









                  Peter SzilasPeter Szilas

                  12k2822




                  12k2822





















                      2












                      $begingroup$

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






                      share|cite|improve this answer









                      $endgroup$








                      • 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















                      2












                      $begingroup$

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






                      share|cite|improve this answer









                      $endgroup$








                      • 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













                      2












                      2








                      2





                      $begingroup$

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






                      share|cite|improve this answer









                      $endgroup$



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







                      share|cite|improve this answer












                      share|cite|improve this answer



                      share|cite|improve this answer










                      answered Apr 7 at 11:21









                      Peter ForemanPeter Foreman

                      7,0701318




                      7,0701318







                      • 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












                      • 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







                      2




                      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




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



                      -