ACT Math : How to express a fraction as a ratio

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #3 : How To Express A Fraction As A Ratio

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?

Possible Answers:

199:1

200:1

1:200

1:199

Correct answer:

1:199

Explanation:

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

Example Question #1141 : Gre Quantitative Reasoning

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?

Possible Answers:

Correct answer:

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 #2 : 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?

Possible Answers:

Correct answer:

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 #3 : 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?

Possible Answers:

Correct answer:

Explanation:

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 .

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