Fractions and Ratios

[mobenny]

Hi,

I recently took a MGMAT tests and I came across a problem that said:

The ratio of Student to Teachers is 16:1. There are a total of 510 students and teachers.

When I looked at the explanation it said that:

Students = 16/17 * 510
Teachers = 1/17 * 510

Please explain why they solve this problem this way.

Thanks!

[hisabness]

This is simply the rule. 16:1 is the number of students to teachers, which means there is 16 students and 1 teacher for a total of 17 people. So, the proportion of students in the class is 1/17, and the proportion of teachers is 16/17. You can also think about these as probabilities, i.e., out of the 17 people what is the probability of a selection a student - 1/17. Don't know how else to explain this, but you may want to check out this link:

http://mathforum.org/library/drmath/view/56706.html


Best.
[editor: this is an accurate explanation of the method for converting ratios to fractions, but the fractions have been given backwards. the 1/17 is teachers, and the 16/17 is students.]

[mobenny]

Thank you. But isnt it the other way around -- proportion of students is 16/17 and prop of teachers is 1/17?

Thanks!

[RonPurewal]

Thank you. But isnt it the other way around -- proportion of students is 16/17 and prop of teachers is 1/17?

Thanks!

that is correct. the above poster posted the correct rule for converting ratios to fractions, but merely posted backward.

basically:

if a ratio is A:B
then the fraction of the first part is A / (A + B)
and the fraction of the second part is B / (A + B)

that's the story.