SSAT Upper Level Math : How to express a fraction as a ratio

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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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:

1:199

1:200

199:1

200:1

Correct answer:

1:199

Explanation:

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

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

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 #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?

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 .

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

Express  as a ratio.

Possible Answers:

Correct answer:

Explanation:

Ratios take the form of numerator:deminator when in colon form.

Example Question #4 : How To Express A Fraction As A Ratio

In a biology class,  students are freshmen,  students are sophomores, and  students are juniors. What is the ratio of sophomores to freshmen in the class?

Possible Answers:

Correct answer:

Explanation:

The ratio of sophomores to freshmen in the class can be expressed by the fraction .

Now, simplify this fraction.

That fraction can also be expressed as .

Example Question #5 : How To Express A Fraction As A Ratio

In a music class of  students,  students play the clarinet,  students play the violin,  students play the oboe, and the rest play the piano. What is the ratio of piano players to oboe players in the class?

Possible Answers:

Correct answer:

Explanation:

First, find out how many piano players there are in the class.

Now, we can express the ratio of piano players to oboe players as the following fraction:

The fraction can also be expressed by .

Example Question #101 : Number Concepts And Operations

In a garden with  plants,  are tulips,  are daisies,  are roses, and the rest are bluebonnets. What is the ratio of bluebonnets to tulips in this garden?

Possible Answers:

Correct answer:

Explanation:

First, find the number of bluebonnets in the garden.

The ratio of bluebonnets to tulips can be expressed as a fraction:

The fraction can also be expressed as the ratio .

Example Question #102 : Number Concepts And Operations

Express  as a ratio.

Possible Answers:

Correct answer:

Explanation:

In the colon form of a ratio, the fraction becomes numerator:denominator.

Example Question #6 : How To Express A Fraction As A Ratio

A smoothie is made with  cups of apple juice,  cup of mango juice,  cups of orange juice, and  cups of blueberry juice. What is the ratio of the amount of orange juice to the amount of blueberry juice?

Possible Answers:

Correct answer:

Explanation:

The ratio of orange juice to blueberry juice can be expressed as a fraction:

That fraction can also be expressed as .

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