1/3 of Joy's total score is equal to 5/6 of Peter's total score. Find the ratio of Joy's total score to Peter's total score.
(Answer in simplest form)
(Answer in simplest form)
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I find it helps to start with an assumed score, if we give Joy a perfect 100 then a third of her score, 33.3333....... is 5/6 of Peter's which means that Peter's is found by dividing by 5 and multiplying by 6. So, Peter's is 40, which means that the ratio, if J:P, is 5:2 in simplest form.
Edit: The answer is NOT 2/5, since a smaller portion of Joy's score is equal to a larger portion of Peter's. That dictates that Joy must have a larger overall score, so the ratio CANNOT be below 1.
Edit:
>>>Edit: The answer is 2:5, not 5:2. The math above can prove this. Besides, 1/3 is smaller than 5/6. 1/3 is equal to 2/6, which is less than 5/6 because 2 is less than 5.
Point-by-point:
"The math above can prove this" - Actually the answerer directly below me has demonstrated this, what you have shown is that you can divide one fraction by another but you have not placed the fractions correctly as divisor and dividend.
"Besides, 1/3 is smaller than 5/6" - exactly opposite the point you are trying to make, if a small part of a set is the same size as a part of another set that is large compared to that second set, then the initial set MUST be larger. Think of a giant compared to a person, his toe will be as large as my torso, though his toe is (for simplicity's sake) 1% of his mass while my torso is 30% of mine. Who's bigger? The giant of course.
"1/3 is equal to 2/6, which is less than 5/6 because 2 is less than 5." - We're talking about fractions of DIFFERENT sets here, that is your mistake.
Edit: Sorry for getting worked up, I didn't mean to sound inappropriately offensive - I am too used to debating rather stubborn individuals on, say, global warming, so that mindset might have carried. My apologies.
Edit: The answer is NOT 2/5, since a smaller portion of Joy's score is equal to a larger portion of Peter's. That dictates that Joy must have a larger overall score, so the ratio CANNOT be below 1.
Edit:
>>>Edit: The answer is 2:5, not 5:2. The math above can prove this. Besides, 1/3 is smaller than 5/6. 1/3 is equal to 2/6, which is less than 5/6 because 2 is less than 5.
Point-by-point:
"The math above can prove this" - Actually the answerer directly below me has demonstrated this, what you have shown is that you can divide one fraction by another but you have not placed the fractions correctly as divisor and dividend.
"Besides, 1/3 is smaller than 5/6" - exactly opposite the point you are trying to make, if a small part of a set is the same size as a part of another set that is large compared to that second set, then the initial set MUST be larger. Think of a giant compared to a person, his toe will be as large as my torso, though his toe is (for simplicity's sake) 1% of his mass while my torso is 30% of mine. Who's bigger? The giant of course.
"1/3 is equal to 2/6, which is less than 5/6 because 2 is less than 5." - We're talking about fractions of DIFFERENT sets here, that is your mistake.
Edit: Sorry for getting worked up, I didn't mean to sound inappropriately offensive - I am too used to debating rather stubborn individuals on, say, global warming, so that mindset might have carried. My apologies.