# ACT Math : How to express a fraction as a ratio

## Example Questions

### Example Question #54 : Proportion / Ratio / Rate

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?

1:199

199:1

200:1

1:200

1:199

Explanation:

One remote is defective for every 199 non-defective remotes.

### Example Question #55 : Proportion / Ratio / Rate

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?

Explanation:

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 .

### Example Question #1 : How To Express A Fraction As A Ratio

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?

Explanation:

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 .

### Example Question #2 : How To Express A Fraction As A Ratio

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?