### All ACT Math Resources

## Example Questions

### Example Question #1 : Fractions

Order the following fractions from least to greatest:

2/3, 3/4, 1/2

**Possible Answers:**

1/2, 2/3, 3/4

2/3, 3/4, 1/2

3/4, 2/3, 1/2

2/3, 1/2, 3/4

3/4, 1/2, 2/3

**Correct answer:**

1/2, 2/3, 3/4

1/2 is the least, then 2/3, then 3/4.

### Example Question #1 : Fractions

Place the following fractions in order from greatest to least.

**Possible Answers:**

**Correct answer:**

This question can be most easily answered by converting the fractions into decimals first.

### Example Question #2 : Fractions

Order the following fractions from least to greatest:

**Possible Answers:**

**Correct answer:**

The most generic process of ordering fractions that can apply to all questions begins with finding the common denominator between all fractions, preferably the least common denominator. In this question, the LCD is 40. Therefore the fractions become: . From this point, we can simply arrange the fractions based upon their numerators. This becomes: . The final step is to reduce the fractions to their original denominators, which becomes: .

If you are comfortable and competent in quickly converting fractions to decimals, then there is a quicker method than what is described above. Simply convert each fraction to a decimal, organize the decimals, and then convert the decimals back to fractions. In this question we can convert to . Then we can reorganize this to and convert back to .

When approaching this kind of problem, choose the method in which you are more comfortable working with. There is no sense in trying to save time by choosing a method that you are not comfortable with and increasing your risk of answering the question incorrectly.

### Example Question #2 : Ordering

Place the following fractions in increasing order:

.

**Possible Answers:**

**Correct answer:**

To put these fractions in increasing order it is important to compare them as decimals, since fractions can often be deceiving. .

Now that the value of each fraction is obvious we can sort then in increasing order:

### Example Question #1 : Fractions

is equivalent to what percentage?

**Possible Answers:**

4.5%

45%

15%

5.5%

55%

**Correct answer:**

55%

Divide the fraction out to get the decimal

5.5 / 10 = 0.55

To find the percentage, shift the decimal point two to the right = 55%

### Example Question #1 : Fractions

Write as a percent

**Possible Answers:**

**Correct answer:**

To find a percent from a fraction you can either divide the number on your calculator and multiply by 100:

or you can just multiply the numerator and denominator by the same number that makes the denominator equal to 100 (because a % is just #/100):

### Example Question #1 : Fractions

One half of a group of professors is made up of mathematicians, and one fourth of the remaining portion is made up of philosophers. The remaining portion is made up of sociologists. If there are professors in the room, how many are sociologists?

**Possible Answers:**

**Correct answer:**

To begin, remember with percentages that "of" means multiplication and "is" means "equals." Now, we know that one fourth of the remaining half are philosophers. This means that he philosophers really are:

So, there are sociologists as a percentage. This is:

Therefore, *of* the are sociologists, or:

are sociologists.

### Example Question #1 : Fractions

Convert the following fraction into a percent.

**Possible Answers:**

**Correct answer:**

To convert a fraction into a percent, make the denominator 100 and then the numerator will be the percent. Thus,

### Example Question #1 : Fractions

On a acre plot of land, there are acres in which deer live. What percentage of the land does this represent? Round to the nearest hundredth.

**Possible Answers:**

**Correct answer:**

For percentages, it is always easiest to translate into language that uses "is" and "of." "Is" means "equals" and "of" means "multiply." So, we have:

What percentage of is ? This is the same as:

Solving for , you get:

Now, as a percent, this is equal to:

Rounding to the nearest hundredth, you have .

### Example Question #1 : Fractions

is of , which is 35% of . All three are positive integers. In which range does the smallest possible value of fall?

**Possible Answers:**

Between 700 and 800

Between 500 and 600

Between 600 and 700

Between 300 and 400

Between 400 and 500

**Correct answer:**

Between 300 and 400

is 35% of , so .

is of , so .

Consequently,

The smallest integer can be is 240. If this happens,

Their sum is

The correct choice is that the sum is between 300 and 400.