A proportion is just a numeric expression
setting two ratios equal to each other, for example
3/4 = 12/16, a/b = c/d, etc.
What are
the common ratio problems? Here is
an example. Suppose you go to a restaurant 5 times in a 30-day month. Assume
you go to a restaurant no more than 1 time a day, what is the ratio of
restaurant days to non-restaurant days in this month?
The answer
is not 5:30. Instead, you need to subtract your restaurant days from the total
days in the month to get non-restaurant days, which is the required second part
of your ratio. The answer is therefore 5:25 (or 5/25).
You can
further simplify the above ratio by crossing out the "common factors", and you will get
a ratio of 1:5 (or 1/5).
What are
the common proportion problems? Here
is an example.
In a math
class, the ratio of passing grades to failing grades is 7 to 5. How many of the
36 students failed the course?
In this
example, the ratio 7/5 tells us that for every 7 students with a passing grade,
5 students will have a failing grade. This means if we have a group of 12
students, 7 students would pass, and 5 students would fail. Now, since we have
36 students, the question is essentially asking how many students would fail in
a group of 36 students?
We can
assume the number of failing students in a group of 36 is X, and we will have a
proportion as below:
Now all we have to do is to solve the above proportion:
So the
answer is: of the 36 students in the class, 15 students got a failing grade.