# ACT Math : Fractions and Percentage

## Example Questions

### Example Question #1 : Fractions

is equivalent to what percentage?

4.5%

5.5%

55%

15%

45%

55%

Explanation:

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 And Percentage

Write   as a percent

Explanation:

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 #7 : 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?

Explanation:

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.

Explanation:

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.

Explanation:

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 And Percentage

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

Between 700 and 800

Between 600 and 700

Between 300 and 400

Between 500 and 600

Between 400 and 500

Between 300 and 400

Explanation:

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.

### Example Question #1391 : Act Math

is  of  and  of ; all are positive integers. Give the smallest possible value of .

Explanation:

is  of  and  of , so

,

so .

so

must be divisible by 5, so the least possible value is 5 itself.

### Example Question #1392 : Act Math

is  of . Which of the following expressions is equal to ?

None of the other responses gives a correct answer.

Explanation:

is  of , so

### Example Question #1393 : Act Math

.

is  of , which is 80% of . What percent of  is ?

The correct answer is not given among the other responses.

The correct answer is not given among the other responses.

Explanation:

is 80% of , so .

Consequently,

is  of , so

Consequently, .

, so

is 800% of . This is not one of the choices.

### Example Question #1 : Fractions And Percentage

is  of

is what percent of  ?

The correct answer is not given among the other responses.

Explanation:

is  of , so

,

so

and

The question can be rewritten as

is what percent of  ?