How to express a fraction as a ratio - ACT Math
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When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?
When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?
One remote is defective for every 199 non-defective remotes.
One remote is defective for every 199 non-defective remotes.
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On a desk, there are 
papers for every 
paper clips and 
papers for every 
greeting card. What is the ratio of paper clips to total items on the desk?
On a desk, there are
Begin by making your life easier: presume that there are 
papers on the desk. Immediately, we know that there are 
paper clips. Now, if there are 
papers, you know that there also must be 
greeting cards. Technically you figure this out by using the ratio:
By cross-multiplying you get:
Solving for 
, you clearly get 
.
(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)
Now, this means that our desk has on it:
papers
paper clips
greeting cards
Therefore, you have 
total items. Based on this, your ratio of paper clips to total items is:
, which is the same as 
.
Begin by making your life easier: presume that there are
By cross-multiplying you get:
Solving for
(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)
Now, this means that our desk has on it:
Therefore, you have
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In a garden, there are 
pansies, 
lilies, 
roses, and 
petunias. What is the ratio of petunias to the total number of flowers in the garden?
In a garden, there are
To begin, you need to do a simple addition to find the total number of flowers in the garden:
Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by 
. This is:
Next, reduce the fraction by dividing out the common 
from the numerator and the denominator:
This is the same as 
.
To begin, you need to do a simple addition to find the total number of flowers in the garden:
Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by
Next, reduce the fraction by dividing out the common
This is the same as
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In a classroom of 
students, each student takes a language class (and only one—nobody studies two languages). 
take Latin, 
take Greek, 
take Anglo-Saxon, and the rest take Old Norse. What is the ratio of students taking Old Norse to students taking Greek?
In a classroom of
To begin, you need to calculate how many students are taking Old Norse. This is:
Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:
Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of 
:
This is the same as 
.
To begin, you need to calculate how many students are taking Old Norse. This is:
Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:
Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of
This is the same as
Compare your answer with the correct one above