# SSAT Upper Level Math : Rational Numbers

## Example Questions

### Example Question #1 : How To Find The Ratio Of A Fraction

A smoothie is made up of  pineapple juice and  mango juice; the rest is orange juice. What is the ratio of orange juice to pineapple juice?

Explanation:

First, find out how much of the smoothie is orange juice.

Since we want the ratio of orange juice to pineapple juice, we want to set up the fractions like this:

Now, divide these fractions.

### Example Question #2 : How To Find The Ratio Of A Fraction

A bakery sells three different types of cookies.  of the cookies sold are chocolate chip,  sold are oatmeal raisin, and the rest sold are sugar cookies. What is the ratio of sugar cookies to oatmeal raisin cookies that the bakery sells?

Explanation:

First, find the fraction of sugar cookies that are sold.

Since we want the ratio of sugar cookies to oatmeal raisin cookies:

Now, multiply and simplify the resulting fraction.

### Example Question #3 : How To Find The Ratio Of A Fraction

What number can be filled in the blank to make the two ratios equivalent?

________

Explanation:

Set up a proportion statement:

Rewrite:

### Example Question #63 : 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?

199:1

200:1

1:200

1:199

1:199

Explanation:

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

### Example Question #64 : 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 #65 : Proportion / Ratio / Rate

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 #66 : Proportion / Ratio / Rate

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?

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 #1 : How To Express A Fraction As A Ratio

Express  as a ratio.

Explanation:

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

### Example Question #2 : 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?

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 #3 : 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?