### All GRE Math Resources

## Example Questions

### Example Question #1 : Fractions And Percentage

Choose the answer below which best expresses the following fraction as a percentage:

**Possible Answers:**

**Correct answer:**

To solve this problem, first convert the fraction into a decimal, by dividing one by eight:

Then you can convert the decimal into a percentage, by putting the first two digits in the tens and ones digit of the percent (respectively), and any ensuing digits after a decimal for the percentage. Or in otherwords multiply the decimal by 100:

### Example Question #2 : Fractions And Percentage

Choose the answer which best expresses the following fraction as a percentage, to the nearest tenth of a percent:

**Possible Answers:**

%

%

%

%

%

**Correct answer:**

%

To solve this problem, first you have to convert the fraction into a decimal, which you can do by dividing three by seven:

The decimal appears to be non-repeating, non-terminating, but that's irrelevant, as the problem cautioned you to round to the nearest tenth of a percent. You can convert to a percent, the first two digits of the decimal will be the percentage, and the third will be the tenth of a percent place, and the fourth will determine whether you round up or down:

%

### Example Question #3 : Fractions And Percentage

Choose the answer which best converts the following fraction into a percentage, rounded to the nearest tenth of a percent, if necessary:

**Possible Answers:**

%

Not possible to convert.

%

%

%

**Correct answer:**

%

To convert, first divide four by three:

repeating

Now, to convert the decimal into a percentage, the ones digit becomes the hundredes digit of the percentage, and the others follow suit. As the decimal above is repeating, and repeats at three, when you round to the nearest tenth a percent, you will have a three as your final digit:

%

### Example Question #4 : Fractions And Percentage

Lauren has finished of her homework.

Express her percent of homework finished as a fraction in simplest form.

**Possible Answers:**

**Correct answer:**

First write the percent as a decimal. To convert the decimal into a fraction, multiply the decimal by , then place that number over :

.

Then place over : .

Therefore,

.

Then, reduce the fraction to its lowest terms by dividing through by the greatest common factor of and , which is :

.

So, Lauren has finished of her homework.

### Example Question #5 : Fractions And Percentage

Convert to a fraction.

**Possible Answers:**

**Correct answer:**

To convert percentages to fractions, take the value and divide by .

Let's get rid of the decimal by multiplying top and bottom by or moving the decimal places to the right and adding zeroes to the bottom.

Then reduce by dividing the bottom by to get .

### Example Question #6 : Fractions And Percentage

Convert to a fraction.

**Possible Answers:**

**Correct answer:**

To convert percentages to fractions, take the value and divide it by .

Then simplify as follows.

### Example Question #7 : Fractions And Percentage

Convert to a fraction.

**Possible Answers:**

**Correct answer:**

First convert the complex fraction into an improper fraction.

Multiply the number in front of the fraction with the denominator and then add that to the numerator.

Then to convert percentages to fractions, take the value and divide by .

### Example Question #8 : Fractions And Percentage

Billy scored a on his last math exam. If there were one hundred questions on the test, what is the ratio of his correct answers to total questions? Express the answer as a fraction, and simplify.

**Possible Answers:**

**Correct answer:**

This problem is fairly simple. If we know he scored a , then we know that he got correct answers.

Both the numerator and denominator of the expression are divisible by two, so your final, simplified answer should be:

.

### Example Question #9 : Fractions And Percentage

Choose the answer which best converts the following percentage into a fraction (the answer should be simplified):

**Possible Answers:**

**Correct answer:**

To solve this problem, first convert the percentage into a decimal by dividing the percentage by 100:

Then, you can convert the decimal into a fraction:

Both the numerator and the denomenator are divisible by , so now you may simplify:

### Example Question #1 : Fractions And Percentage

Choose the answer below which best expresses the following percentage as a fraction (the answer should be simplified as much as possible):

%

**Possible Answers:**

**Correct answer:**

To find your answer, first convert the percentage into a decimal:

Then, you can place the digits of the decimal over one, followed by a number of zeroes equal to the number of digits (in this case, 1,000):

Both the numerator and denomenator are divisible by , so you can simplify to: