What does the relationship between dividing percentages signify in this problem?
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The following is an example calculation from Wikipedia's page on Percentage:
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
$endgroup$
add a comment |
$begingroup$
The following is an example calculation from Wikipedia's page on Percentage:
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
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
The following is an example calculation from Wikipedia's page on Percentage:
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
$endgroup$
The following is an example calculation from Wikipedia's page on Percentage:
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
percentages
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
add a comment |
$begingroup$
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
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
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:
$frac{F_{FCS}}{F_{CS}} = frac{N_{FCS}}{N_S} div frac{N_{CS}}{N_S} = frac{N_{FCS}}{N_S} times frac{N_S}{N_{CS}} = frac{N_{FCS}}{N_{CS}} = mbox{Fraction of computer science students who are female}$
$endgroup$
add a comment |
$begingroup$
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 $${.03Sover .1S}={.03over.1}=30%$$
$endgroup$
$begingroup$
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
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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:
$frac{F_{FCS}}{F_{CS}} = frac{N_{FCS}}{N_S} div frac{N_{CS}}{N_S} = frac{N_{FCS}}{N_S} times frac{N_S}{N_{CS}} = frac{N_{FCS}}{N_{CS}} = mbox{Fraction of computer science students who are female}$
$endgroup$
add a comment |
$begingroup$
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:
$frac{F_{FCS}}{F_{CS}} = frac{N_{FCS}}{N_S} div frac{N_{CS}}{N_S} = frac{N_{FCS}}{N_S} times frac{N_S}{N_{CS}} = frac{N_{FCS}}{N_{CS}} = mbox{Fraction of computer science students who are female}$
$endgroup$
add a comment |
$begingroup$
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:
$frac{F_{FCS}}{F_{CS}} = frac{N_{FCS}}{N_S} div frac{N_{CS}}{N_S} = frac{N_{FCS}}{N_S} times frac{N_S}{N_{CS}} = frac{N_{FCS}}{N_{CS}} = mbox{Fraction of computer science students who are female}$
$endgroup$
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:
$frac{F_{FCS}}{F_{CS}} = frac{N_{FCS}}{N_S} div frac{N_{CS}}{N_S} = frac{N_{FCS}}{N_S} times frac{N_S}{N_{CS}} = frac{N_{FCS}}{N_{CS}} = mbox{Fraction of computer science students who are female}$
answered Jan 3 at 3:39
ConManConMan
7,6121324
7,6121324
add a comment |
add a comment |
$begingroup$
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 $${.03Sover .1S}={.03over.1}=30%$$
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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 $${.03Sover .1S}={.03over.1}=30%$$
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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 $${.03Sover .1S}={.03over.1}=30%$$
$endgroup$
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 $${.03Sover .1S}={.03over.1}=30%$$
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
add a comment |
$begingroup$
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
add a comment |
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$begingroup$
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