What does the relationship between dividing percentages signify in this problem?












1












$begingroup$


The following is an example calculation from Wikipedia's page on Percentage:
enter image description here



I understand everything up to the point where 3% is divided by 10%. I cannot seem to understand why these two percentages are divided, why do we divide? I understand how we get 3% of all students are female computer science majors since we understand that 60% of all students are female and 5% of those females are computer science majors. However, I do not understand the reasoning behind 10% of all students being computer science majors and having to divide the 3% of female computer science majors from that. Can someone explain why we divide and what the reasoning behind the division is as it relates to the problem? Thanks!










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$endgroup$












  • $begingroup$
    We are told at the beginning that $10%$ of all students are computer science majors.
    $endgroup$
    – saulspatz
    Jan 3 at 3:37










  • $begingroup$
    Yes I just want to know why we divide and what it signifies.
    $endgroup$
    – Sphygmomanometer
    Jan 3 at 3:38
















1












$begingroup$


The following is an example calculation from Wikipedia's page on Percentage:
enter image description here



I understand everything up to the point where 3% is divided by 10%. I cannot seem to understand why these two percentages are divided, why do we divide? I understand how we get 3% of all students are female computer science majors since we understand that 60% of all students are female and 5% of those females are computer science majors. However, I do not understand the reasoning behind 10% of all students being computer science majors and having to divide the 3% of female computer science majors from that. Can someone explain why we divide and what the reasoning behind the division is as it relates to the problem? Thanks!










share|cite|improve this question









$endgroup$












  • $begingroup$
    We are told at the beginning that $10%$ of all students are computer science majors.
    $endgroup$
    – saulspatz
    Jan 3 at 3:37










  • $begingroup$
    Yes I just want to know why we divide and what it signifies.
    $endgroup$
    – Sphygmomanometer
    Jan 3 at 3:38














1












1








1





$begingroup$


The following is an example calculation from Wikipedia's page on Percentage:
enter image description here



I understand everything up to the point where 3% is divided by 10%. I cannot seem to understand why these two percentages are divided, why do we divide? I understand how we get 3% of all students are female computer science majors since we understand that 60% of all students are female and 5% of those females are computer science majors. However, I do not understand the reasoning behind 10% of all students being computer science majors and having to divide the 3% of female computer science majors from that. Can someone explain why we divide and what the reasoning behind the division is as it relates to the problem? Thanks!










share|cite|improve this question









$endgroup$




The following is an example calculation from Wikipedia's page on Percentage:
enter image description here



I understand everything up to the point where 3% is divided by 10%. I cannot seem to understand why these two percentages are divided, why do we divide? I understand how we get 3% of all students are female computer science majors since we understand that 60% of all students are female and 5% of those females are computer science majors. However, I do not understand the reasoning behind 10% of all students being computer science majors and having to divide the 3% of female computer science majors from that. Can someone explain why we divide and what the reasoning behind the division is as it relates to the problem? Thanks!







percentages






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share|cite|improve this question










asked Jan 3 at 3:32









SphygmomanometerSphygmomanometer

627




627












  • $begingroup$
    We are told at the beginning that $10%$ of all students are computer science majors.
    $endgroup$
    – saulspatz
    Jan 3 at 3:37










  • $begingroup$
    Yes I just want to know why we divide and what it signifies.
    $endgroup$
    – Sphygmomanometer
    Jan 3 at 3:38


















  • $begingroup$
    We are told at the beginning that $10%$ of all students are computer science majors.
    $endgroup$
    – saulspatz
    Jan 3 at 3:37










  • $begingroup$
    Yes I just want to know why we divide and what it signifies.
    $endgroup$
    – Sphygmomanometer
    Jan 3 at 3:38
















$begingroup$
We are told at the beginning that $10%$ of all students are computer science majors.
$endgroup$
– saulspatz
Jan 3 at 3:37




$begingroup$
We are told at the beginning that $10%$ of all students are computer science majors.
$endgroup$
– saulspatz
Jan 3 at 3:37












$begingroup$
Yes I just want to know why we divide and what it signifies.
$endgroup$
– Sphygmomanometer
Jan 3 at 3:38




$begingroup$
Yes I just want to know why we divide and what it signifies.
$endgroup$
– Sphygmomanometer
Jan 3 at 3:38










2 Answers
2






active

oldest

votes


















1












$begingroup$

Remember that a percentage is just a fraction written in a different way. For example, in this case:



$F_{CS} = mbox{Fraction of students who are computer science majors} = frac{mbox{Number of computer science majors}}{mbox{Number of students}} = frac{N_{CS}}{N_S}$



$F_{FCS} = mbox{Fraction of students who are female computer science majors} = frac{mbox{Number of female computer science majors}}{mbox{Number of students}} = frac{N_{FCS}}{N_S}$



Notice that both of these fractions have the same denominator. As a result, when we divide one fraction by the other, the common denominator vanishes:



$frac{F_{FCS}}{F_{CS}} = frac{N_{FCS}}{N_S} div frac{N_{CS}}{N_S} = frac{N_{FCS}}{N_S} times frac{N_S}{N_{CS}} = frac{N_{FCS}}{N_{CS}} = mbox{Fraction of computer science students who are female}$






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    Suppose there are $S$ students in all. Then we know that there are $.1S$ computer science majors and $.03S$ female computer science majors. The fraction of computer science majors who are fmeale is $${.03Sover .1S}={.03over.1}=30%$$






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      Ok I think I figured it out, the reason we divide is because the 10% is serving as the total right? We are looking for the percentage of computer science majors that are female, we get the percentage (3%) of female computer science majors from the total of female students and to find what percentage they occupy in regards to all the computer science majors (10%) we divide. The portion (3%) is divided by the total (10%). I know this seems really rudimentary and I just embarrassingly figured out the 10% is serving as the total. Is this explanation correct?
      $endgroup$
      – Sphygmomanometer
      Jan 3 at 3:46











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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1












    $begingroup$

    Remember that a percentage is just a fraction written in a different way. For example, in this case:



    $F_{CS} = mbox{Fraction of students who are computer science majors} = frac{mbox{Number of computer science majors}}{mbox{Number of students}} = frac{N_{CS}}{N_S}$



    $F_{FCS} = mbox{Fraction of students who are female computer science majors} = frac{mbox{Number of female computer science majors}}{mbox{Number of students}} = frac{N_{FCS}}{N_S}$



    Notice that both of these fractions have the same denominator. As a result, when we divide one fraction by the other, the common denominator vanishes:



    $frac{F_{FCS}}{F_{CS}} = frac{N_{FCS}}{N_S} div frac{N_{CS}}{N_S} = frac{N_{FCS}}{N_S} times frac{N_S}{N_{CS}} = frac{N_{FCS}}{N_{CS}} = mbox{Fraction of computer science students who are female}$






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      Remember that a percentage is just a fraction written in a different way. For example, in this case:



      $F_{CS} = mbox{Fraction of students who are computer science majors} = frac{mbox{Number of computer science majors}}{mbox{Number of students}} = frac{N_{CS}}{N_S}$



      $F_{FCS} = mbox{Fraction of students who are female computer science majors} = frac{mbox{Number of female computer science majors}}{mbox{Number of students}} = frac{N_{FCS}}{N_S}$



      Notice that both of these fractions have the same denominator. As a result, when we divide one fraction by the other, the common denominator vanishes:



      $frac{F_{FCS}}{F_{CS}} = frac{N_{FCS}}{N_S} div frac{N_{CS}}{N_S} = frac{N_{FCS}}{N_S} times frac{N_S}{N_{CS}} = frac{N_{FCS}}{N_{CS}} = mbox{Fraction of computer science students who are female}$






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        Remember that a percentage is just a fraction written in a different way. For example, in this case:



        $F_{CS} = mbox{Fraction of students who are computer science majors} = frac{mbox{Number of computer science majors}}{mbox{Number of students}} = frac{N_{CS}}{N_S}$



        $F_{FCS} = mbox{Fraction of students who are female computer science majors} = frac{mbox{Number of female computer science majors}}{mbox{Number of students}} = frac{N_{FCS}}{N_S}$



        Notice that both of these fractions have the same denominator. As a result, when we divide one fraction by the other, the common denominator vanishes:



        $frac{F_{FCS}}{F_{CS}} = frac{N_{FCS}}{N_S} div frac{N_{CS}}{N_S} = frac{N_{FCS}}{N_S} times frac{N_S}{N_{CS}} = frac{N_{FCS}}{N_{CS}} = mbox{Fraction of computer science students who are female}$






        share|cite|improve this answer









        $endgroup$



        Remember that a percentage is just a fraction written in a different way. For example, in this case:



        $F_{CS} = mbox{Fraction of students who are computer science majors} = frac{mbox{Number of computer science majors}}{mbox{Number of students}} = frac{N_{CS}}{N_S}$



        $F_{FCS} = mbox{Fraction of students who are female computer science majors} = frac{mbox{Number of female computer science majors}}{mbox{Number of students}} = frac{N_{FCS}}{N_S}$



        Notice that both of these fractions have the same denominator. As a result, when we divide one fraction by the other, the common denominator vanishes:



        $frac{F_{FCS}}{F_{CS}} = frac{N_{FCS}}{N_S} div frac{N_{CS}}{N_S} = frac{N_{FCS}}{N_S} times frac{N_S}{N_{CS}} = frac{N_{FCS}}{N_{CS}} = mbox{Fraction of computer science students who are female}$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 3 at 3:39









        ConManConMan

        7,6121324




        7,6121324























            1












            $begingroup$

            Suppose there are $S$ students in all. Then we know that there are $.1S$ computer science majors and $.03S$ female computer science majors. The fraction of computer science majors who are fmeale is $${.03Sover .1S}={.03over.1}=30%$$






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              Ok I think I figured it out, the reason we divide is because the 10% is serving as the total right? We are looking for the percentage of computer science majors that are female, we get the percentage (3%) of female computer science majors from the total of female students and to find what percentage they occupy in regards to all the computer science majors (10%) we divide. The portion (3%) is divided by the total (10%). I know this seems really rudimentary and I just embarrassingly figured out the 10% is serving as the total. Is this explanation correct?
              $endgroup$
              – Sphygmomanometer
              Jan 3 at 3:46
















            1












            $begingroup$

            Suppose there are $S$ students in all. Then we know that there are $.1S$ computer science majors and $.03S$ female computer science majors. The fraction of computer science majors who are fmeale is $${.03Sover .1S}={.03over.1}=30%$$






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              Ok I think I figured it out, the reason we divide is because the 10% is serving as the total right? We are looking for the percentage of computer science majors that are female, we get the percentage (3%) of female computer science majors from the total of female students and to find what percentage they occupy in regards to all the computer science majors (10%) we divide. The portion (3%) is divided by the total (10%). I know this seems really rudimentary and I just embarrassingly figured out the 10% is serving as the total. Is this explanation correct?
              $endgroup$
              – Sphygmomanometer
              Jan 3 at 3:46














            1












            1








            1





            $begingroup$

            Suppose there are $S$ students in all. Then we know that there are $.1S$ computer science majors and $.03S$ female computer science majors. The fraction of computer science majors who are fmeale is $${.03Sover .1S}={.03over.1}=30%$$






            share|cite|improve this answer









            $endgroup$



            Suppose there are $S$ students in all. Then we know that there are $.1S$ computer science majors and $.03S$ female computer science majors. The fraction of computer science majors who are fmeale is $${.03Sover .1S}={.03over.1}=30%$$







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Jan 3 at 3:42









            saulspatzsaulspatz

            14.2k21329




            14.2k21329












            • $begingroup$
              Ok I think I figured it out, the reason we divide is because the 10% is serving as the total right? We are looking for the percentage of computer science majors that are female, we get the percentage (3%) of female computer science majors from the total of female students and to find what percentage they occupy in regards to all the computer science majors (10%) we divide. The portion (3%) is divided by the total (10%). I know this seems really rudimentary and I just embarrassingly figured out the 10% is serving as the total. Is this explanation correct?
              $endgroup$
              – Sphygmomanometer
              Jan 3 at 3:46


















            • $begingroup$
              Ok I think I figured it out, the reason we divide is because the 10% is serving as the total right? We are looking for the percentage of computer science majors that are female, we get the percentage (3%) of female computer science majors from the total of female students and to find what percentage they occupy in regards to all the computer science majors (10%) we divide. The portion (3%) is divided by the total (10%). I know this seems really rudimentary and I just embarrassingly figured out the 10% is serving as the total. Is this explanation correct?
              $endgroup$
              – Sphygmomanometer
              Jan 3 at 3:46
















            $begingroup$
            Ok I think I figured it out, the reason we divide is because the 10% is serving as the total right? We are looking for the percentage of computer science majors that are female, we get the percentage (3%) of female computer science majors from the total of female students and to find what percentage they occupy in regards to all the computer science majors (10%) we divide. The portion (3%) is divided by the total (10%). I know this seems really rudimentary and I just embarrassingly figured out the 10% is serving as the total. Is this explanation correct?
            $endgroup$
            – Sphygmomanometer
            Jan 3 at 3:46




            $begingroup$
            Ok I think I figured it out, the reason we divide is because the 10% is serving as the total right? We are looking for the percentage of computer science majors that are female, we get the percentage (3%) of female computer science majors from the total of female students and to find what percentage they occupy in regards to all the computer science majors (10%) we divide. The portion (3%) is divided by the total (10%). I know this seems really rudimentary and I just embarrassingly figured out the 10% is serving as the total. Is this explanation correct?
            $endgroup$
            – Sphygmomanometer
            Jan 3 at 3:46


















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