### All ACT Math Resources

## Example Questions

### Example Question #84 : Fractions

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

1:199

1:200

**Correct answer:**

1:199

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:**

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?

**Possible Answers:**

**Correct answer:**

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 #1 : 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:**

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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