### All GRE Math Resources

## Example Questions

### Example Question #1 : Mixed / Improper Fractions

and are positive integers.

is a multiple of .

Quantity A:

Quantity B:

**Possible Answers:**

The relationship cannot be determined.

Quantity A is greater.

The two quantities are equal.

Quantity B is greater.

**Correct answer:**

The relationship cannot be determined.

Recall that the exponent of the denominator is sutracted from the exponent of the numerator.

Therefore Quantity A is equivalent to x^{5–y}, and because we would then be comparing an arithmetic operation to a geometric operation, it does not matter whether y is a multiple of 5. The two quantities cannot be compared.

### Example Question #1 : How To Find Out A Mixed Fraction From An Improper Fraction

Which of the following is the mixed fraction equivalent to ?

**Possible Answers:**

**Correct answer:**

To begin, notice that using your calculator, you can find:

Now, the closest even multiple of that is less than is . Therefore, you know that your number is:

This is the same as:

, or simply, . This is your mixed fraction.

### Example Question #2 : How To Find Out A Mixed Fraction From An Improper Fraction

Which of the following is equivalent to ?

**Possible Answers:**

**Correct answer:**

Although there are many ways to convert improper fractions into mixed fractions, the easiest way is to use your calculator to your advantage. Begin by dividing by . This gives you . Therefore, you can eliminate all the options that have do not have for their first portion. Next, multiply by the denominator (), and get . This means that you have and , or . Thus, your answer is .

### Example Question #4 : How To Find Out A Mixed Fraction From An Improper Fraction

Quantity A:

Quantity B:

Which of the following is true?

**Possible Answers:**

The two quantities are equal

Quantity A is larger.

The relationship of the two quantities cannot be determined based on the information provided.

Quantity B is larger.

**Correct answer:**

The two quantities are equal

Though there are several ways you could solve this, let's convert the improper fraction into a mixed one so we can compare them. Start by dividing by . This gives you

Now, since we know that the two numbers have the same whole-number value, we need to compare their decimal portions. Compare to . The latter is indeed Therefore, the two values are equal.